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Yellow Sale Mathematics 2017

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Lakshmikantham, Vangipuram, Leela, Srinivasa, Martynyuk, Anatoly A.
Stability Analysis of Nonlinear Systems
Springer International Publishing
Seiten xi,329
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319271996
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The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners.

Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.



Scriba, Christoph J., Schreiber, Peter, Schreiber, Jana
5000 Years of Geometry
Mathematics in History and Culture
Springer Basel
Seiten xii,626
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783034808972
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The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering.

Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries.

Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr

y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times.

The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history.

From letters to the authors for the German language edition

I hope it gets a translation, as there is no comparable work.

Prof. J. Grattan-Guinness (Middlesex University London)

`Five Thousand Years of Geometry` - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically!

Prof. J.W. Dauben (City University of New York)

An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. …

The graphic design is also excellent.

Prof. Z. Nádenik (Czech Technical University in Prague)


Simmonds, James G.
A Brief on Tensor Analysis
Springer New York
Seiten xiv,114
Erscheinungsjahr 1994
Einband: Hardcover
ISBN 9780387940885
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In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.


Simmonds, James G.
A Brief on Tensor Analysis
Springer New York
Seiten xiv,114
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9781461264248
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In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.


Kemper, Gregor
A Course in Commutative Algebra
Springer Berlin Heidelberg
Seiten xii,248
Erscheinungsjahr 2011
Einband: Hardcover
ISBN 9783642035449
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This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
The author is professor of algorithmic algebra at the Technische Universität München, in Munich. He regularly teaches courses in commutative algebra, invariant theory, and computer algebra. In 2007 he received an award from the state of Bavaria for excellence in teaching.

Kemper, Gregor
A Course in Commutative Algebra
Springer Berlin Heidelberg
Seiten xii,248
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9783642266324
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This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
The author is professor of algorithmic algebra at the Technische Universität München, in Munich. He regularly teaches courses in commutative algebra, invariant theory, and computer algebra. In 2007 he received an award from the state of Bavaria for excellence in teaching.

Bühlmann, Hans, Gisler, Alois
A Course in Credibility Theory and its Applications
Springer Berlin Heidelberg
Seiten xviii,338
Erscheinungsjahr 2005
Einband: Softcover
ISBN 9783540257530
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This book is ideal for practicing experts in particular actuaries in the field of property-casualty insurance, life insurance, reinsurance and insurance supervision, as well as teachers and students. It provides an exploration of Credibility Theory, covering most aspects of this topic from the simplest case to the most detailed dynamic model. The book closely examines the tasks an actuary encounters daily: estimation of loss ratios, claim frequencies and claim sizes.

Hans Bühlmann

Hans Bühlmann is professor emeritus of ETH Zürich, where he taught mathematics for more than thirty years. He has held visiting appointments at UC Berkeley, University of Michigan, UL Bruxelles, University of Tokyo, University of Manitoba, Università La Sapienza in Rome, Scuola Normale Superiore Pisa. His interest in actuarial science dates back to his first employment after his doctorate, when he worked in the insurance industry. His book `Mathematical Methods in Risk Theory` (Springer Grundlehren) is a classic in the actuarial literature.
www.math.ethz.ch/~hbuhl

 


Alois Gisler

Alois Gisler is chief actuary at Winterthur Insurance Company and professor at ETH Zürich, where he teaches non-life insurance mathematics and credibility. He wrote his doctoral thesis with Hans Bühlmann at ETH, and since then has worked for more than twenty years in the insurance industry. While a full time practising actuary, he has always kept in close contact with actuarial science: he was co-editor of the ASTIN-Bulletin for 10 years and has published many articles, mainly in credibility theory.

www.math.ethz.ch/~gisler


Koblitz, Neal
A Course in Number Theory and Cryptography
Springer New York
Seiten x,235
Erscheinungsjahr 1994
Einband: Hardcover
ISBN 9780387942933
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This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Koblitz, Neal
A Course in Number Theory and Cryptography
Springer New York
Seiten x,235
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9781461264422
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This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Tkachuk, Vladimir V.
A Cp-Theory Problem Book
Special Features of Function Spaces
Springer International Publishing
Seiten xiv,583
Erscheinungsjahr 2014
Einband: Hardcover
ISBN 9783319047461
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This work is a continuation of the first volume published by Springer in 2011, entitled `A Cp-Theory Problem Book: Topological and Function Spaces.` The first volume provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. This present volume covers a wide variety of topics in Cp-theory and general topology at the professional level bringing the reader to the frontiers of modern research. The volume contains 500 problems and exercises with complete solutions. It can also be used as an introduction to advanced set theory and descriptive set theory. The book presents diverse topics of the theory of function spaces with the topology of pointwise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from these areas of research. Moreover, this book gives a reasonably complete coverage of Cp-theory through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research.
Vladimir V. Tkachuk is a professor in the Department of Mathematics of Autonomous Metropolitan University in Mexico City. He holds a PhD from Moscow State University and is the author of `A Cp-Theory Problem Book: Topological and Function Spaces` (Springer, 2011).

Tkachuk, Vladimir V.
A Cp-Theory Problem Book
Special Features of Function Spaces
Springer International Publishing
Seiten xiv,583
Erscheinungsjahr 2014
Einband: Softcover
ISBN 9783319377940
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This work is a continuation of the first volume published by Springer in 2011, entitled `A Cp-Theory Problem Book: Topological and Function Spaces.` The first volume provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. This present volume covers a wide variety of topics in Cp-theory and general topology at the professional level bringing the reader to the frontiers of modern research. The volume contains 500 problems and exercises with complete solutions. It can also be used as an introduction to advanced set theory and descriptive set theory. The book presents diverse topics of the theory of function spaces with the topology of pointwise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from these areas of research. Moreover, this book gives a reasonably complete coverage of Cp-theory through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research.
Vladimir V. Tkachuk is a professor in the Department of Mathematics of Autonomous Metropolitan University in Mexico City. He holds a PhD from Moscow State University and is the author of `A Cp-Theory Problem Book: Topological and Function Spaces` (Springer, 2011).

Logan, J. David
A First Course in Differential Equations
Springer International Publishing
Seiten xiii,369
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319178516
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The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students in physics, engineering, the biosciences, economics and mathematics. Instructors are likely to find that the first four or five chapters are suitable for a first course in the subject.

This edition contains a healthy increase over earlier editions in the number of worked examples and exercises, particularly those routine in nature. Two appendices include a review with practice problems, and a MATLAB® supplement that gives basic codes and commands for solving differential equations. MATLAB® is not required; students are encouraged to utilize available software to plot many of their solutions. Solutions to even-numbered problems are available on springer.com.

From the reviews of the second edition:

“The coverage of linear systems in the plane is nicely detailed and illustrated. …Simple numerical methods are illustrated and the use of Maple and MATLAB is encouraged. …select Dave Logan’s new and improved text for my course.”

—Robert E. O’Malley, Jr., SIAM Review, Vol. 53 (2), 2011

“Aims to provide material for a one-semester course that emphasizes the basic ideas, solution methods, and an introduction to modeling. …The book that results offers a concise introduction to the subject for students of mathematics, science and engineering who have completed the introductory calculus sequence. …This book is worth a careful look as a candidate text for the next differential equations course you teach.”

—William J. Satzer, MAA Reviews, January, 2011

J. David Logan is Willa Cather Professor of Mathematics at the University of Nebraska Lincoln. He received his PhD from The Ohio State University and has served on the faculties at the University of Arizona, Kansas State University, and Rensselaer Polytechnic Institute. For many years he served as a visiting scientist at Los Alamos and Lawrence Livermore National Laboratories. He has published widely in differential equations, mathematical physics, fluid and gas dynamics, hydrogeology, and mathematical biology. Dr. Logan has authored 7 books, among them Applied Partial Differential Equations, now in its 3rd edition, published by Springer.


Logan, J. David
A First Course in Differential Equations
Springer International Publishing
Seiten xiii,369
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319330754
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The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students in physics, engineering, the biosciences, economics and mathematics. Instructors are likely to find that the first four or five chapters are suitable for a first course in the subject.

This edition contains a healthy increase over earlier editions in the number of worked examples and exercises, particularly those routine in nature. Two appendices include a review with practice problems, and a MATLAB® supplement that gives basic codes and commands for solving differential equations. MATLAB® is not required; students are encouraged to utilize available software to plot many of their solutions. Solutions to even-numbered problems are available on springer.com.

From the reviews of the second edition:

“The coverage of linear systems in the plane is nicely detailed and illustrated. …Simple numerical methods are illustrated and the use of Maple and MATLAB is encouraged. …select Dave Logan’s new and improved text for my course.”

—Robert E. O’Malley, Jr., SIAM Review, Vol. 53 (2), 2011

“Aims to provide material for a one-semester course that emphasizes the basic ideas, solution methods, and an introduction to modeling. …The book that results offers a concise introduction to the subject for students of mathematics, science and engineering who have completed the introductory calculus sequence. …This book is worth a careful look as a candidate text for the next differential equations course you teach.”

—William J. Satzer, MAA Reviews, January, 2011

J. David Logan is Willa Cather Professor of Mathematics at the University of Nebraska Lincoln. He received his PhD from The Ohio State University and has served on the faculties at the University of Arizona, Kansas State University, and Rensselaer Polytechnic Institute. For many years he served as a visiting scientist at Los Alamos and Lawrence Livermore National Laboratories. He has published widely in differential equations, mathematical physics, fluid and gas dynamics, hydrogeology, and mathematical biology. Dr. Logan has authored 7 books, among them Applied Partial Differential Equations, now in its 3rd edition, published by Springer.


Krantz, Steven G., Parks, Harold R.
A Mathematical Odyssey
Journey from the Real to the Complex
Springer US
Seiten xvi,382
Erscheinungsjahr 2014
Einband: Softcover
ISBN 9781489978448
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Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone.

This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe.

Mathematics is one of mankind`s oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.

Steven G. Krantz and Harold R. Parks have co-authored several classic texts including “A Primer of Real Analytic Functions, 2nd ed.” © 2002 Birkhäuser, “The Implicit Function Theorem”, © 2003 Birkhäuser, “Geometric Integration Theory”, © 2008 Birkhäuser, “The Geometry of Domains in Space”, © 1999 Birkhäuser.  Steven Krantz’s current affiliation is Washington University in St. Louis, MO, and Harold Park’s is currently Professor Emeritus at Oregon State University, Corvalis, OR.

 

Krantz, Steven G., Parks, Harold R.
A Mathematical Odyssey
Journey from the Real to the Complex
Springer US
Seiten xvi,382
Erscheinungsjahr 2014
Einband: Hardcover
ISBN 9781461489382
Yellow Sale Preis
26.74
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Lieferstatus  
 

Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone.

This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe.

Mathematics is one of mankind`s oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.

Steven G. Krantz and Harold R. Parks have co-authored several classic texts including “A Primer of Real Analytic Functions, 2nd ed.” © 2002 Birkhäuser, “The Implicit Function Theorem”, © 2003 Birkhäuser, “Geometric Integration Theory”, © 2008 Birkhäuser, “The Geometry of Domains in Space”, © 1999 Birkhäuser.  Steven Krantz’s current affiliation is Washington University in St. Louis, MO, and Harold Park’s is currently Professor Emeritus at Oregon State University, Corvalis, OR.

 

Ikeda, Susumu, Kotani, Motoko
A New Direction in Mathematics for Materials Science
Springer Japan
Seiten x,86
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9784431558620
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This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interdisciplinary movement in the 1950s and 1960s. Materials science was formed by the integration of metallurgy, polymer science, ceramics, solid state physics, and related disciplines. We believe that such historical background helps readers to understand the importance of interdisciplinary interaction such as mathematics–materials science collaboration. 

The middle part of the book describes mathematical ideas and methods that can be applied to materials problems and introduces some examples of specific studies—for example, computational homology applied to structural analysis of glassy materials, stochastic models for the formation process of materials, new geometric measures for finite carbon nanotube molecules, mathematical technique predicting a molecular magnet, and network analysis of nanoporous materials. The details of these works will be shown in the subsequent volumes of this SpringerBriefs in the Mathematics of Materials series by the individual authors. 

The posterior section of the book presents how breakthroughs based on mathematics–materials science collaborations can emerge. The authors` argument is supported by the experiences at the Advanced Institute for Materials Research (AIMR), where many researchers from various fields gathered and tackled interdisciplinary research.

Aksoy, Asuman G., Khamsi, Mohamed A.
A Problem Book in Real Analysis
Springer New York
Seiten x,254
Erscheinungsjahr 2010
Einband: Hardcover
ISBN 9781441912954
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Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

Rosenthal, Daniel, Rosenthal, David, Rosenthal, Peter
A Readable Introduction to Real Mathematics
Springer International Publishing
Seiten xii,161
Erscheinungsjahr 2014
Einband: Hardcover
ISBN 9783319056531
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Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat`s little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.
Daniel Rosenthal is a mathematics student at the University of Toronto. David Rosenthal is Associate Professor of Mathematics at St. John`s University in New York City. Peter Rosenthal is Professor Emeritus of Mathematics at the University of Toronto.

Rosenthal, Daniel, Rosenthal, David, Rosenthal, Peter
A Readable Introduction to Real Mathematics
Springer International Publishing
Seiten xii,161
Erscheinungsjahr 2014
Einband: Softcover
ISBN 9783319379500
Yellow Sale Preis
21.39
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Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat`s little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.
Daniel Rosenthal is a mathematics student at the University of Toronto. David Rosenthal is Associate Professor of Mathematics at St. John`s University in New York City. Peter Rosenthal is Professor Emeritus of Mathematics at the University of Toronto.

Bacaër, Nicolas
A Short History of Mathematical Population Dynamics
Springer London
Seiten x,160
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9780857291141
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<p>As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers.</p>

<p>This book traces the history of population dynamics---a theoretical subject closely connected to  genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel`s laws and the question of extinction of family names to  percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine.</p>

<p>The reader of this book will see, from a different perspective, the problems that scientists face when  governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.</p>


Runde, Volker
A Taste of Topology
Springer New York
Seiten x,182
Erscheinungsjahr 2005
Einband: Softcover
ISBN 9780387257907
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This should be a revelation for mathematics undergraduates. Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde’s text treats its material differently to other books on the subject, providing a fresh perspective.


Huggett, Stephen, Jordan, David
A Topological Aperitif
Springer London
Seiten ix,152
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9781848009127
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Topologyhasbeenreferredtoas“rubber-sheetgeometry”.Thenameisapt,for the subject is concerned with properties of an object that would be preserved, no matter how much it is stretched, squashed, or distorted, so long as it is not in any way torn apart or glued together. One’s ?rst reaction might be that such animprecise-soundingsubjectcouldhardlybepartofseriousmathematics,and wouldbeunlikelytohaveapplicationsbeyondtheamusementofsimpleparlour games. This reaction could hardly be further from the truth. Topology is one of the most important and broad-ranging disciplines of modern mathematics. It is a subject of great precision and of breadth of development. It has vastly many applications, some of great importance, ranging from particle physics to cosmology, and from hydrodynamics to algebra and number theory. It is also a subject of great beauty and depth. To appreciate something of this, it is not necessary to delve into the more obscure aspects of mathematical formalism. For topology is, at least initially, a very visual subject. Some of its concepts apply to spaces of large numbers of dimensions, and therefore do not easily submit to reasoning that depends upon direct pictorial representation. But even in such cases, important insights can be obtained from the visual - rusal of a simple geometrical con?guration. Although much modern topology depends upon ?nely tuned abstract algebraic machinery of great mathematical sophistication, the underlying ideas are often very simple and can be appre- ated by the examination of properties of elementary-looking drawings.

Luke, Douglas
A User’s Guide to Network Analysis in R
Springer International Publishing
Seiten xii,238
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319238821
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Presenting a comprehensive resource for the mastery of network analysis in R, the goal of Network Analysis with R is to introduce modern network analysis techniques in R to social, physical, and health scientists. The mathematical foundations of network analysis are emphasized in an accessible way and readers are guided through the basic steps of network studies: network conceptualization, data collection and management, network description, visualization, and building and testing statistical models of networks. As with all of the books in the Use R! series, each chapter contains extensive R code and detailed visualizations of datasets. Appendices will describe the R network packages and the datasets used in the book. An R package developed specifically for the book, available to readers on GitHub, contains relevant code and real-world network datasets as well.
Douglas Luke is Professor and Director of the Center for Public Health Systems Science at the George Warren Brown School of Social Work at Washington University in St. Louis. He is a leading researcher in the fields of health policy, and his work focuses on the evaluation, dissemination, and implementation of evidence-based public health policies. Dr. Luke has worked extensively with systems science methodologies, especially the analysis of social networks with regards to the implementation of public health policies. He is a member of the Institute for Public Health, a founding member of the Washington University Network of Dissemination and Implementation Researchers (WUNDIR), and serves on the Interagency Committee on Smoking and Health at the U.S. Department of Health and Human Services.

Fuchs, László
Abelian Groups
Springer International Publishing
Seiten xxi,747
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319194219
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Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs.

The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of un decidability problems. The treatment of the latter trend includes Shelah’s seminal work on the un decidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology and homological algebra.

An abundance of exercises are included to test the reader’s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject’s further development.

László Fuchs is the Evelyn and John G. Phillips Distinguished Professor Emeritus in Mathematics at Tulane University. He was awarded the Kossuth Prize in 1953 and is a foreign member of the Hungarian Academy of Sciences.

Finston, David R., Morandi, Patrick J.
Abstract Algebra
Structure and Application
Springer International Publishing
Seiten ix,187
Erscheinungsjahr 2014
Einband: Mixed Media
ISBN 9783319044972
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This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences.

Applications include:

  • Identification numbers and modular arithmetic
  • (linear) error-correcting codes, including cyclic codes
  • ruler and compass constructions
  • cryptography
  • symmetry of patterns in the real plane

Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.


Curtis, Morton L., Place, Paul
Abstract Linear Algebra
Springer New York
Seiten x,168
Erscheinungsjahr 1990
Einband: Softcover
ISBN 9780387972633
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Intended for a first course on the subject, this text begins from scratch and develops the standard topics of Linear Algebra. Its progresses simply towards its ultimate goal, the Theorem of Hurwitz, which argues that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. The book stresses the complete logical development of the subject.


Brezinski, Claude
Acceleration de la convergence en analyse numerique
Springer Berlin Heidelberg
Seiten iv,313
Erscheinungsjahr 1977
Einband: Softcover
ISBN 9783540082415
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Bender, Carl M., Orszag, Steven A.
Advanced Mathematical Methods for Scientists and Engineers I
Asymptotic Methods and Perturbation Theory
Springer New York
Seiten xiv,593
Erscheinungsjahr 1999
Einband: Hardcover
ISBN 9780387989310
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A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

Bender, Carl M., Orszag, Steven A.
Advanced Mathematical Methods for Scientists and Engineers I
Asymptotic Methods and Perturbation Theory
Springer New York
Seiten xiv,593
Erscheinungsjahr 1999
Einband: Softcover
ISBN 9781441931870
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A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

Knapp, Anthony W.
Advanced Real Analysis
Birkhäuser Boston
Seiten xxiv,466
Erscheinungsjahr 2005
Einband: Hardcover
ISBN 9780817643829
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* Presents a comprehensive treatment with a global view of the subject

* Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician


Silverman, Joseph H.
Advanced Topics in the Arithmetic of Elliptic Curves
Springer New York
Seiten xiii,528
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9780387943282
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In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that `the theory of elliptic curves is rich, varied, and amazingly vast,` and as a consequence, `many important topics had to be omitted.` I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate`s algorithm, and Ogg`s conductor-discriminant formula. V. Tate`s theory of q-curves over p-adic fields. VI. Neron`s theory of canonical local height functions.

Stichtenoth, Henning
Algebraic Function Fields and Codes
Springer Berlin Heidelberg
Seiten xiv,360
Erscheinungsjahr 2009
Einband: Hardcover
ISBN 9783540768777
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This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil`s theorem as well as Goppa` s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.


Stichtenoth, Henning
Algebraic Function Fields and Codes
Springer Berlin Heidelberg
Seiten xiv,360
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9783642095566
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This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil`s theorem as well as Goppa` s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.


Bosch, Siegfried
Algebraic Geometry and Commutative Algebra
Springer London
Seiten x,504
Erscheinungsjahr 2013
Einband: Softcover
ISBN 9781447148289
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Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor.

The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level.

Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.


Mumford, David
Algebraic Geometry I
Complex Projective Varieties
Springer Berlin Heidelberg
Seiten x,186
Erscheinungsjahr 1995
Einband: Softcover
ISBN 9783540586579
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From the reviews: `Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford`s `Volume I` is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!` Zentralblatt

Biography of  David Mumford

David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics.

Mumford worked in the fields of Algebraic Gemetry in the 60`s and 70`s, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.


Godsil, Chris, Royle, Gordon F.
Algebraic Graph Theory
Springer New York
Seiten xix,443
Erscheinungsjahr 2001
Einband: Hardcover
ISBN 9780387952413
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Godsil, Chris, Royle, Gordon F.
Algebraic Graph Theory
Springer New York
Seiten xix,443
Erscheinungsjahr 2001
Einband: Softcover
ISBN 9780387952208
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Srinivas, Vasudevan
Algebraic K-Theory
Birkhäuser Boston
Seiten xvii,341
Erscheinungsjahr 1996
Einband: Softcover
ISBN 9780817647360
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Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.


Jarvis, Frazer
Algebraic Number Theory
Springer International Publishing
Seiten xiii,292
Erscheinungsjahr 2014
Einband: Softcover
ISBN 9783319075440
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The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic.

Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform.

The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

Frazer Jarvis obtained his PhD from the University of Cambridge under the supervision of Richard Taylor in 1995. After postdoctoral periods in Strasbourg, Durham and Oxford, he has been a lecturer at Sheffield since 1998. His research has focused on modular forms and Galois representations over totally real fields, and he is currently interested in GSp(4).

Fulton, William
Algebraic Topology
A First Course
Springer New York
Seiten xviii,430
Erscheinungsjahr 1995
Einband: Softcover
ISBN 9780387943275
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To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re­ lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ­ ential topology, etc.), we concentrate our attention on concrete prob­ lems in low dimensions, introducing only as much algebraic machin­ ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol­ ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel­ opment of the subject. What would we like a student to know after a first course in to­ pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under­ standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind­ ing numbers and degrees of mappings, fixed-point theorems; appli­ cations such as the Jordan curve theorem, invariance of domain; in­ dices of vector fields and Euler characteristics; fundamental groups

Switzer, Robert M.
Algebraic Topology — Homotopy and Homology
Springer Berlin Heidelberg
Seiten xiii,526
Erscheinungsjahr 2002
Einband: Softcover
ISBN 9783540427506
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From the reviews: `The author has attempted an ambitious and most commendable project. […] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature.` Mathematical Reviews

Biography of Robert M. Switzer

Robert M. Switzer was born in Tennessee (USA) in 1940.

After majoring in mathematics at Harvard College, he completed his PhD at Stanford University in 1965. He spent 5 years as lecturer at the University of Manchester, England, and then moved to Goettingen, Germany, where he has been Professor of Mathematics since 1973. In the early 1980s his research concentrated on obstruction theory in connection with holomorphic bundles on projective spaces.

In 1984 he switched his attention to Computer Science and has been teaching and working in that field ever since.


Bourbaki, N.
Algèbre
Chapitre 4 à 7
Springer Berlin Heidelberg
Seiten viii,422
Erscheinungsjahr 2007
Einband: Softcover
ISBN 9783540343981
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Ce deuxième volume du Livre d’Algèbre, deuxième Livre des Éléments de mathématique, traite notamment des extensions de corps et de la théorie de Galois. Il comprend les chapitres : 4. Polynômes et fractions rationnelles ; 5. Corps commutatifs ; 6. Groupes et corps ordonnés ; 7. Modules sur les anneaux principaux.


Bourbaki, N.
Algèbre
Chapitres 1 à 3
Springer Berlin Heidelberg
Seiten xiii,636
Erscheinungsjahr 2007
Einband: Softcover
ISBN 9783540338499
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Les Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.

Ce premier volume du Livre d’Algèbre, deuxième Livre des Éléments de mathématique, comprend les chapitres : Structures algébriques.- Algèbre linéaire.- Algèbres tensorielles, algèbres, extérieures, algèbres symétriques


Bourbaki, N.
Algèbre
Chapitre 8
Springer Berlin Heidelberg
Seiten x,489
Erscheinungsjahr 2012
Einband: Softcover
ISBN 9783540353157
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Ce huitième chapitre du Livre d`Algèbre, deuxième Livre des Éléments de mathématique, est consacré à l`étude de certaines classes d`anneaux et des modules sur ces anneaux.

Il couvre les notions de module et d`anneau noethérien et artinien, ainsi que celle de radical. Ce chapitre décrit également la structure des anneaux semi-simples. Nous y donnons aussi la définition de divers groupes de Grothendieck qui jouent un rôle universel pour les invariants de modules et plusieurs descriptions du groupe de Brauer qui intervient dans la classification des anneaux simples.

Une note historique en fin de volume, reprise de l`édition précédente, retrace l`émergence d`une grande partie des notions développées.

Ce volume est une deuxième édition entièrement refondue de l`édition de 1958.


Gabriel, Pierre, Serre, Jean-Pierre
Algèbre Locale, Multiplicités
Cours au Collège de France, 1957 - 1958
Springer Berlin Heidelberg
Seiten x,160
Erscheinungsjahr 1975
Einband: Softcover
ISBN 9783540070283
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Chapitre I. 1DIAUX PIlEMIEIS IT LOCALISATION I I. Wotationa et definitions I 2. Lemme de Bakay. . . . 2 3. Localisation • • • 4. Anneaux et 80dules noethiriens 2 5. Spectre•••••• 3 4 6. Le cas noetherien. 4 7. Ideaux pre. iers associe. Chapitre 11. OUTILS IT SOUTES A) Filtr·ations et graduations. 8 I. Anneaux et modules filtres • 8 2. Topologie definie par UDe filtration 9 10 3. Coapletion des modules filtres • • • II 4. Anneaux et modules graduis • • • • • 5. au tout redevient noethirien; filtrations ~-adiques. 15 20 6. Modules differentiels filtres•••••••••••• B) Polynoaes de Hilbert-SamueL ••••••••••• 26 I. Rappel sur les polynOmes Ii valeurs entieres•••• 26 27 2. Fonctions additives sur les categories de modules. 29 3. Le polynOme caractiristique de Hilbert 32 4. Les invariants de Hilbert-Samuel Chapitre 111. T1I£ORlE DE LA DDlE!ISION A) Dimension des extensions. entieres. 38 I. Definitions. • • • • • • • • • • • • 38 2. Le premier theore- de Cohen-Seidenberg. 39 3. Le second theoreme de Cohen-Seidenberg • 4I B) Dimension dans les anneaux noetheriens. 43 I. Dimension d`un module. • • • 43 2. Le cas semi-local noetherien 44 3. Syste. es de parametres 47 C) Anneaux normaux 48 I. caracterisation des anneaux normaux. 48 2. Proprietes des anneaux noraaux 51 3. Fermeture integrale. 53 D) Anneaux de polynomes. • • • • • 54 I.

Nierhaus, Gerhard
Algorithmic Composition
Paradigms of Automated Music Generation
Springer Vienna
Seiten x,287
Erscheinungsjahr 2009
Einband: Hardcover
ISBN 9783211755396
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28.88
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Algorithmic composition – composing by means of formalizable methods – has a century old tradition not only in occidental music history. This is the first book to provide a detailed overview of prominent procedures of algorithmic composition in a pragmatic way rather than by treating formalizable aspects in single works. In addition to an historic overview, each chapter presents a specific class of algorithm in a compositional context by providing a general introduction to its development and theoretical basis and describes different musical applications. Each chapter outlines the strengths, weaknesses and possible aesthetical implications resulting from the application of the treated approaches. Topics covered are: markov models, generative grammars, transition networks, chaos and self-similarity, genetic algorithms, cellular automata, neural networks and artificial intelligence are covered. The comprehensive bibliography makes this work ideal for the musician and the researcher alike.


Nierhaus, Gerhard
Algorithmic Composition
Paradigms of Automated Music Generation
Springer Vienna
Seiten x,287
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9783211999158
Yellow Sale Preis
28.88
(inkl. 7% Mwst)
Lieferstatus  
 

Algorithmic composition – composing by means of formalizable methods – has a century old tradition not only in occidental music history. This is the first book to provide a detailed overview of prominent procedures of algorithmic composition in a pragmatic way rather than by treating formalizable aspects in single works. In addition to an historic overview, each chapter presents a specific class of algorithm in a compositional context by providing a general introduction to its development and theoretical basis and describes different musical applications. Each chapter outlines the strengths, weaknesses and possible aesthetical implications resulting from the application of the treated approaches. Topics covered are: markov models, generative grammars, transition networks, chaos and self-similarity, genetic algorithms, cellular automata, neural networks and artificial intelligence are covered. The comprehensive bibliography makes this work ideal for the musician and the researcher alike.


Shen, Alexander
Algorithms and Programming
Problems and Solutions
Springer New York
Seiten xii,272
Erscheinungsjahr 2010
Einband: Hardcover
ISBN 9781441917478
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This text is structured in a problem-solution format that requires the student to think through the programming process. New to the second edition are additional chapters on suffix trees, games and strategies, and Huffman coding as well as an Appendix illustrating the ease of conversion from Pascal to C.


Alpay, Daniel
An Advanced Complex Analysis Problem Book
Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions
Springer International Publishing
Seiten ix,521
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319160580
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This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

Prof. Daniel Alpay is a faculty member of the department of mathematics at Ben Gurion University, Beer Sheva, Israel. He is the incumbent of the Earl Katz Family chair in algebraic system theory. He has a double formation of electrical engineer (Telecom Paris, graduated 1978) and mathematician (PhD, Weizmann Institute, 1986). His research includes operator theory, stochastic analysis, and the theory of linear systems. Daniel Alpay is one of the initiators and responsible of the dual track electrical-engineering mathematics at Ben-Gurion University.

He is the author of `A Complex Analysis Problem Book` (Birkhäuser, 2011). Together with co-authors, he has written four books and more than 220 research papers, and edited twelve books of research papers.


Roman, Steven
An Introduction to Catalan Numbers
Springer International Publishing
Seiten xii,121
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319221434
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This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers.

“Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.”

 - From the foreword by Richard Stanley

Steven Roman is Professor Emeritus of Mathematics at California State University Fullerton.  He is the author of numerous other mathematics textbooks, including Field Theory (2006), Advanced Linear Algebra(2008), Fundamentals of Group Theory (2012), Introduction to the Mathematics of Finance (2012), and An Introduction to Catalan Numbers (2015).                        

Agarwal, Ravi P., Perera, Kanishka, Pinelas, Sandra
An Introduction to Complex Analysis
Springer US
Seiten xiv,331
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9781489997166
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This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

Agarwal, Ravi P., Perera, Kanishka, Pinelas, Sandra
An Introduction to Complex Analysis
Springer US
Seiten xiv,331
Erscheinungsjahr 2011
Einband: Hardcover
ISBN 9781461401940
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This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

Capasso, Vincenzo, Bakstein, David
An Introduction to Continuous-Time Stochastic Processes
Theory, Models, and Applications to Finance, Biology, and Medicine
Springer New York
Seiten xvi,482
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9781493927562
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This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: Markov processes Stochastic differential equations Arbitrage-free markets and financial derivatives Insurance risk Population dynamics, and epidemics Agent-based models New to the Third Edition: Infinitely divisible distributions Random measures Levy processes Fractional Brownian motion Ergodic theory Karhunen-Loeve expansion Additional applications Additional  exercises Smoluchowski  approximation of  Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Edition will be of interest to a broad audience of students, pure and applied mathematicians, and researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduate courses, as well as European Masters courses (according to the two-year-long second cycle of the “Bologna Scheme”), the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. From reviews of previous editions: `The book is ... an account of fundamental concepts as they appear in relevant modern applications and literature. ... The book addresses three main groups: first, mathematicians working in a different field; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications.` -Zentralblatt MATH
Vincenzo Capasso is a Professor of Probability and Mathematical Statistics at the University of Milan.  His research interests include spatially structured stochastic processes, stochastic geometry, reaction-diffusion systems, and statistics of structured stochastic processes. David Bakstein is a professor at the University of Milan, in ADAMSS (Interdisciplinary Center for Advanced Applied Mathematical and Statistical Sciences).

Capasso, Vincenzo, Bakstein, David
An Introduction to Continuous-Time Stochastic Processes
Theory, Models, and Applications to Finance, Biology, and Medicine
Springer New York
Seiten xvi,482
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9781493938360
Yellow Sale Preis
58.84
(inkl. 7% Mwst)
Lieferstatus  
 
This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: Markov processes Stochastic differential equations Arbitrage-free markets and financial derivatives Insurance risk Population dynamics, and epidemics Agent-based models New to the Third Edition: Infinitely divisible distributions Random measures Levy processes Fractional Brownian motion Ergodic theory Karhunen-Loeve expansion Additional applications Additional  exercises Smoluchowski  approximation of  Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Edition will be of interest to a broad audience of students, pure and applied mathematicians, and researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduate courses, as well as European Masters courses (according to the two-year-long second cycle of the “Bologna Scheme”), the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. From reviews of previous editions: `The book is ... an account of fundamental concepts as they appear in relevant modern applications and literature. ... The book addresses three main groups: first, mathematicians working in a different field; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications.` -Zentralblatt MATH
Vincenzo Capasso is a Professor of Probability and Mathematical Statistics at the University of Milan.  His research interests include spatially structured stochastic processes, stochastic geometry, reaction-diffusion systems, and statistics of structured stochastic processes. David Bakstein is a professor at the University of Milan, in ADAMSS (Interdisciplinary Center for Advanced Applied Mathematical and Statistical Sciences).

Lafontaine, Jacques
An Introduction to Differential Manifolds
Springer International Publishing
Seiten xix,395
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319207346
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This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces.

Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them.

The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory.

The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years.

Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.

Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.

Layek, G.C.
An Introduction to Dynamical Systems and Chaos
Springer India
Seiten xviii,622
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9788132225553
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The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book.
 
Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.
G. C. LAYEK is professor at the Department of Mathematics, The University of Burdwan, India. He obtained his PhD degree from Indian Institute of Technology Kharagpur and did his postdoctoral studies at Indian Statistical Institute, Kolkata. His areas of research are theoretical fluid dynamics of viscous fluid, fluid turbulence and chaotic systems. Professor Layek has published several research papers in international journals of repute and has visited several international universities including Saint Petersburg State University, Kazan State Technological University, Russia, for collaborative research work and teaching.

Dyke, Phil
An Introduction to Laplace Transforms and Fourier Series
Springer London
Seiten xv,318
Erscheinungsjahr 2014
Einband: Softcover
ISBN 9781447163947
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Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms.

In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets.

Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems.

Phil Dyke has over 40 years experience teaching at UK Universities, and for the past 6 years has based a course on the subject of this book. He has also used Laplace transforms and Fourier methods in his research. He has been a professor of applied mathematics at Plymouth University for over 20 years.

Tu, Loring W.
An Introduction to Manifolds
Springer New York
Seiten xviii,410
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9781441973993
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Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, `Introduction to Manifolds` is also an excellent foundation for Springer`s GTM 82, `Differential Forms in Algebraic Topology`.
Loring W. Tu was born in Taipei, Taiwan, and grew up in Taiwan,Canada, and the United States. He attended McGill University and Princeton University as an undergraduate, and obtained his Ph.D. from Harvard University under the supervision of Phillip A. Griffiths. He has taught at the University of Michigan, Ann Arbor, and at Johns Hopkins University, and is currently Professor of Mathematics at Tufts University in Massachusetts. An algebraic geometer by training, he has done research at the interface of algebraic geometry,topology, and differential geometry, including Hodge theory, degeneracy loci, moduli spaces of vector bundles, and equivariant cohomology. He is the coauthor with Raoul Bott of `Differential Forms in Algebraic Topology.`

Martcheva, Maia
An Introduction to Mathematical Epidemiology
Springer US
Seiten xiv,453
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9781489976116
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The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models.

Maia Martcheva is a Professor in the Department of Mathematics at the University of Florida, USA.  Her areas of interest and research include: epidemic models of multi-strain interactions, spatial epidemic modeling, immunological modeling, and immune-epidemiological modeling.

Renardy, Michael, Rogers, Robert C.
An Introduction to Partial Differential Equations
Springer New York
Seiten xiv,434
Erscheinungsjahr 2004
Einband: Hardcover
ISBN 9780387004440
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Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.


Renardy, Michael, Rogers, Robert C.
An Introduction to Partial Differential Equations
Springer New York
Seiten xiv,434
Erscheinungsjahr 2004
Einband: Softcover
ISBN 9781441918208
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Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.


Jeevanjee, Nadir
An Introduction to Tensors and Group Theory for Physicists
Springer International Publishing
Seiten xvi,305
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319330891
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The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students.

Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory.  Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques.

Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these.  Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups.

Reviews of the First Edition

“[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them… From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view…[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems… Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student.  [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.”

—Physics Today

`Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning.  The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.”

—MAA Reviews

Nadir Jeevanjee is a graduate student research assistant at the Lawrence Berkeley National Laboratory in Berkeley, CA.


Jeevanjee, Nadir
An Introduction to Tensors and Group Theory for Physicists
Springer International Publishing
Seiten xvi,305
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319147932
Yellow Sale Preis
26.74
(inkl. 7% Mwst)
Lieferstatus  
 

The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students.

Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory.  Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques.

Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these.  Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups.

Reviews of the First Edition

“[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them… From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view…[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems… Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student.  [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.”

—Physics Today

`Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning.  The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.”

—MAA Reviews

Nadir Jeevanjee is a graduate student research assistant at the Lawrence Berkeley National Laboratory in Berkeley, CA.


Daley, D.J., Vere-Jones, David
An Introduction to the Theory of Point Processes
Volume II: General Theory and Structure
Springer New York
Seiten xvii,573
Erscheinungsjahr 2008
Einband: Hardcover
ISBN 9780387213378
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This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.


Daley, D.J., Vere-Jones, David
An Introduction to the Theory of Point Processes
Volume II: General Theory and Structure
Springer New York
Seiten xvii,573
Erscheinungsjahr 2008
Einband: Softcover
ISBN 9781489985385
Yellow Sale Preis
93.08
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Lieferstatus  
 

This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.


Bajnok, Béla
An Invitation to Abstract Mathematics
Springer New York
Seiten xiv,406
Erscheinungsjahr 2013
Einband: Softcover
ISBN 9781489995605
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This undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind.  The heart and soul of this book is problem solving, where each problem is carefully chosen to clarify a concept, demonstrate a technique, or to enthuse.  The exercises require relatively extensive arguments, creative approaches, or both, thus providing motivation for the reader.  With a unified approach to a diverse collection of topics, this text points out connections, similarities, and differences among subjects whenever possible.  This book shows students that mathematics is a vibrant and dynamic human enterprise by including historical perspectives and notes on the giants of mathematics, by mentioning current activity in the mathematical community, and by discussing many famous and less well-known questions that remain open for future mathematicians.

Ideally, this text should be used for a two semester course, where the first course has no prerequisites and the second is a more challenging course for math majors; yet, the flexible structure of the book allows it to be used in a variety of settings, including as a source of various independent-study and research projects.

Béla Bajnok is a native of Hungary, and he remains greatly influenced by the excellent education he received there. He currently holds the endowed position of Alumni Chair Professor at Gettysburg College. He is also the recipient of the Mathematical Association of America`s 2012 James P. Crawford EPADEL Teaching Award.

Smith, Karen E., Kahanpää, Lauri, Kekäläinen, Pekka, Traves, William
An Invitation to Algebraic Geometry
Springer New York
Seiten xvi,164
Erscheinungsjahr 2000
Einband: Hardcover
ISBN 9780387989808
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This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Smith, Karen E., Kahanpää, Lauri, Kekäläinen, Pekka, Traves, William
An Invitation to Algebraic Geometry
Springer New York
Seiten xvi,164
Erscheinungsjahr 2000
Einband: Softcover
ISBN 9781441931955
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This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Bergman, George M.
An Invitation to General Algebra and Universal Constructions
Springer International Publishing
Seiten x,572
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319114774
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Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader`s grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

George M. Bergman is Professor Emeritus of Mathematics at the University of California, Berkeley. He has published over 100 research articles in logic, ring theory, universal algebra, and category theory.


Poenaru, V.
Analyse differentielle
Springer Berlin Heidelberg
Erscheinungsjahr 1974
Einband: Softcover
ISBN 9783540066651
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Spain, P., Godement, Roger
Analysis I
Convergence, Elementary functions
Springer Berlin Heidelberg
Seiten xxi,430
Erscheinungsjahr 2004
Einband: Softcover
ISBN 9783540059233
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Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.

Spain, P., Godement, Roger
Analysis II
Differential and Integral Calculus, Fourier Series, Holomorphic Functions
Springer Berlin Heidelberg
Seiten vii,448
Erscheinungsjahr 2005
Einband: Softcover
ISBN 9783540209218
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26.74
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Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.

Godement, Roger, Ray, Urmie
Analysis III
Analytic and Differential Functions, Manifolds and Riemann Surfaces
Springer International Publishing
Seiten vii,321
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319160528
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Volume III sets out classical Cauchy theory. It is much more geared towards its innumerable applications than towards a more or less complete theory of analytic functions. Cauchy-type curvilinear integrals are then shown to generalize to any number of real variables (differential forms, Stokes-type formulas). The fundamentals of the theory of manifolds are then presented, mainly to provide the reader with a `canonical`` language and with some important theorems (change of variables in integration, differential equations). A final chapter shows how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject that is rarely addressed in the general literature though it only requires elementary techniques.

Besides the Lebesgue integral, Volume IV will set out a piece of specialized mathematics towards which the entire content of the previous volumes will converge: Jacobi, Riemann, Dedekind series and infinite products, elliptic functions, classical theory of modular functions and its modern version using the structure of the Lie algebra of SL(2,R).

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.

Godement, Roger, Ray, Urmie
Analysis IV
Integration and Spectral Theory, Harmonic Analysis, the Garden of Modular Delights
Springer International Publishing
Seiten xi,527
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319169064
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Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern` and `classical`, is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.
Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.

Pomerance, Carl, Rassias, Michael Th.
Analytic Number Theory
In Honor of Helmut Maier’s 60th Birthday
Springer International Publishing
Seiten viii,379
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319222394
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This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and  trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource.

Contributors to this volume:

Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivi?, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwi??, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.


Olver, Peter J.
Applications of Lie Groups to Differential Equations
Springer New York
Seiten xxviii,513
Erscheinungsjahr 1993
Einband: Softcover
ISBN 9780387950006
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A solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented such that graduates and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasising explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter.

Niederreiter, Harald, Winterhof, Arne
Applied Number Theory
Springer International Publishing
Seiten x,442
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319223209
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This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas.

Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc.

Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory.

Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.

Harald Niederreiter: Full member, Austrian Academy of Sciences; Full member and former member of the presidium, German Academy of Natural Sciences Leopoldina; Cardinal Innitzer Prize for Natural Sciences in Austria; Invited speaker at ICM 1998 (Berlin) and ICIAM 2003 (Sydney): Singapore National Science Award 2003; Fellow of the American Mathematical Society

Arne Winterhof: Edmund and Rosa Hlawka Prize 2004; Advancement Award of the Austrian Mathematical Society 2010


Øksendal, Bernt, Sulem, Agnès
Applied Stochastic Control of Jump Diffusions
Springer Berlin Heidelberg
Seiten xiv,262
Erscheinungsjahr 2007
Einband: Softcover
ISBN 9783540698258
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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.


Williams, Kim, Ostwald, Michael J.
Architecture and Mathematics from Antiquity to the Future
Volume II: The 1500s to the Future
Springer International Publishing
Seiten xix,690
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319343112
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Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals.

Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume’s content includes works in the United States of America and Australia, in addition to those in Europe and Asia.


Williams, Kim, Ostwald, Michael J.
Architecture and Mathematics from Antiquity to the Future
Volume I: Antiquity to the 1500s
Springer International Publishing
Seiten xix,735
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319374864
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Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals.

Volume I covers architecture from antiquity through Egyptian, Mayan, Greek, Roman, Medieval, Inkan, Gothic and early Renaissance eras and styles. The themes that are covered range from symbolism and proportion to measurement and structural stability. From Europe to Africa, Asia and South America, the chapters span different countries, cultures and practices.

Williams, Kim, Ostwald, Michael J.
Architecture and Mathematics from Antiquity to the Future
Volume I: Antiquity to the 1500s
Springer International Publishing
Seiten xix,735
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319001364
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Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals.

Volume I covers architecture from antiquity through Egyptian, Mayan, Greek, Roman, Medieval, Inkan, Gothic and early Renaissance eras and styles. The themes that are covered range from symbolism and proportion to measurement and structural stability. From Europe to Africa, Asia and South America, the chapters span different countries, cultures and practices.

Williams, Kim, Ostwald, Michael J.
Architecture and Mathematics from Antiquity to the Future
Volume II: The 1500s to the Future
Springer International Publishing
Seiten xix,690
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319001425
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64.19
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Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals.

Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume’s content includes works in the United States of America and Australia, in addition to those in Europe and Asia.


Bodine, Sigrun, Lutz, Donald A.
Asymptotic Integration of Differential and Difference Equations
Springer International Publishing
Seiten xi,402
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319182476
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This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations.

After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales.

Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites. 


Hiriart-Urruty, Jean-Baptiste
Bases, outils et principes pour l`analyse variationnelle
Springer Berlin Heidelberg
Seiten xiii,171
Erscheinungsjahr 2013
Einband: Softcover
ISBN 9783642307348
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L’étude mathématique des problèmes d’optimisation, ou de ceux dits variationnels de manière générale (c’est-à-dire, « toute situation où il y a quelque chose à minimiser sous des contraintes »), requiert en préalable qu’on en maîtrise les bases, les outils fondamentaux et quelques principes. Le présent ouvrage est un cours répondant en partie à cette demande, il est principalement destiné à des étudiants de Master en formation, et restreint à l’essentiel. Sont abordés successivement : La semicontinuité inférieure, les topologies faibles, les résultats fondamentaux d’existence en optimisation ; Les conditions d’optimalité approchée ; Des développements sur la projection sur un convexe fermé, notamment sur un cône convexe fermé ; L’analyse convexe dans son rôle opératoire ; Quelques schémas de dualisation dans des problèmes d’optimisation non convexe structurés ; Une introduction aux sous-différentiels généralisés de fonctions non différentiables.

Weil, Andre
Basic Number Theory
Springer Berlin Heidelberg
Seiten xviii,316
Erscheinungsjahr 1995
Einband: Softcover
ISBN 9783540586555
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From the reviews: `L.R. Shafarevich showed me the first edition […] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form.` Zentralblatt MATH

Biography of André Weil

André Weil was born on May 6, 1906 in Paris. After studying mathematics at the École Normale Supérieure and receiving a doctoral degree from the University of Paris in 1928, he held professorial positions in India, France, the United States and Brazil before being appointed to the Institute for Advanced Study, Princeton in 1958, where he remained until he died on August 6, 1998.

André Weil`s work laid the foundation for abstract algebraic geometry and the modern theory of abelian varieties. A great deal of his work was directed towards establishing the links between number theory and algebraic geometry and devising modern methods in analytic number theory. Weil was one of the founders, around 1934, of the group that published, under the collective name of  N. Bourbaki, the highly influential multi-volume treatise Eléments de mathématique.


Knapp, Anthony W.
Basic Real Analysis
Birkhäuser Boston
Seiten xxiv,656
Erscheinungsjahr 2005
Einband: Hardcover
ISBN 9780817632502
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Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established

A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics

Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.


Albert, Jim
Bayesian Computation with R
Springer New York
Seiten xii,300
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9780387922973
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There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of books,andtheextensivenumberofapplicationsofBayesianarticlesinapplied disciplines such as science and engineering. One reason for the dramatic growth in Bayesian modeling is the availab- ity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern c- puters, it is now possible to use the Bayesian paradigm to ?t very complex models that cannot be ?t by alternative frequentist methods. To ?t Bayesian models, one needs a statistical computing environment. This environment should be such that one can: write short scripts to de?ne a Bayesian model use or write functions to summarize a posterior distribution use functions to simulate from the posterior distribution construct graphs to illustrate the posterior inference An environment that meets these requirements is the R system. R provides a wide range of functions for data manipulation, calculation, and graphical d- plays. Moreover, it includes a well-developed, simple programming language that users can extend by adding new functions. Many such extensions of the language in the form of packages are easily downloadable from the Comp- hensive R Archive Network (CRAN).

de Souza, Paulo Ney, Silva, Jorge-Nuno
Berkeley Problems in Mathematics
Springer New York
Seiten xiv,593
Erscheinungsjahr 2004
Einband: Softcover
ISBN 9780387008929
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This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.


de Souza, Paulo Ney, Silva, Jorge-Nuno
Berkeley Problems in Mathematics
Springer New York
Seiten xiv,593
Erscheinungsjahr 2004
Einband: Hardcover
ISBN 9780387204291
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80.24
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This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.


Laugwitz, Detlef, Shenitzer, Abe
Bernhard Riemann 1826–1866
Turning Points in the Conception of Mathematics
Birkhäuser Boston
Seiten xvii,357
Erscheinungsjahr 1999
Einband: Softcover
ISBN 9780817647766
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The name of Bernard Riemann is well known to mathematicians and physicists around the world. His name is indelibly stamped on the literature of mathematics and physics. This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.


Luna-Elizarrarás, M. Elena, Shapiro, Michael, Struppa, Daniele C., Vajiac, Adrian
Bicomplex Holomorphic Functions
The Algebra, Geometry and Analysis of Bicomplex Numbers
Springer International Publishing
Seiten viii,231
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319248660
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The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers.

Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in real-dimension four, while almost simultaneously James Cockle introduced a commutative four-dimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something that for a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable.

While the algebra of bicomplex numbers is a four-dimensional real algebra, it is useful to think of it as a “complexification” of the field of complex

numbers; from this perspective, the bicomplex algebra possesses the properties of a one-dimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike.

The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one- or multidimensional complex analysis.


Kassel, Christian, Dodane, O., Turaev, Vladimir
Braid Groups
Springer New York
Seiten x,338
Erscheinungsjahr 2008
Einband: Hardcover
ISBN 9780387338415
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In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices.

Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.

Dr. Christian Kassel is the director of CNRS (Centre National de la Recherche Scientifique in France), was the director of l`Institut de Recherche Mathematique Avancee from 2000 to 2004, and is an editor for the Journal of Pure and Applied Algebra. Kassel has numerous publications, including the book Quantum Groups in the Springer Gradate Texts in Mathematics series.

Dr. Vladimir Turaev was also a professor at the CNRS and is currently at Indiana University in the Department of Mathematics.


Kassel, Christian, Dodane, O., Turaev, Vladimir
Braid Groups
Springer New York
Seiten x,338
Erscheinungsjahr 2008
Einband: Softcover
ISBN 9781441922205
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26.74
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In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices.

Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.

Dr. Christian Kassel is the director of CNRS (Centre National de la Recherche Scientifique in France), was the director of l`Institut de Recherche Mathematique Avancee from 2000 to 2004, and is an editor for the Journal of Pure and Applied Algebra. Kassel has numerous publications, including the book Quantum Groups in the Springer Gradate Texts in Mathematics series.

Dr. Vladimir Turaev was also a professor at the CNRS and is currently at Indiana University in the Department of Mathematics.


Shi, Zhan
Branching Random Walks
École d`Été de Probabilités de Saint-Flour XLII – 2012
Springer International Publishing
Seiten x,133
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319253718
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18.18
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Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time.

Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.


Karatzas, Ioannis, Shreve, Steven
Brownian Motion and Stochastic Calculus
Springer New York
Seiten xxiii,470
Erscheinungsjahr 1998
Einband: Softcover
ISBN 9780387976556
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A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.

Abramenko, Peter, Brown, Kenneth S.
Buildings
Theory and Applications
Springer New York
Seiten xxii,754
Erscheinungsjahr 2008
Einband: Hardcover
ISBN 9780387788340
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This book treats Jacques Tit`s beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beginners can use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher.

This book is suitable as a textbook, with many exercises, and it may also be used for self-study.

Kenneth S. Brown has been a professor at Cornell since 1971. He received his Ph.D. in 1971 from MIT. He has published many works, including Buildings with Springer-Verlag in 1989, reprinted in 1998.

Peter Abramenko received his Ph.D. in 1987 from the University of Frankfurt, Germany. He held various academic positions afterwards, including a Heisenberg fellowship from 1998 until 2001. Since 2001, he is Associate Professor at the University of Virginia in Charlottesville. He has previously published Twin Buildings and Applications to S-Arithmetic Groups for the Lecture Notes in Mathematics series for Springer (1996).


Abramenko, Peter, Brown, Kenneth S.
Buildings
Theory and Applications
Springer New York
Seiten xxii,754
Erscheinungsjahr 2008
Einband: Softcover
ISBN 9781441927019
Yellow Sale Preis
26.74
(inkl. 7% Mwst)
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This book treats Jacques Tit`s beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beginners can use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher.

This book is suitable as a textbook, with many exercises, and it may also be used for self-study.

Kenneth S. Brown has been a professor at Cornell since 1971. He received his Ph.D. in 1971 from MIT. He has published many works, including Buildings with Springer-Verlag in 1989, reprinted in 1998.

Peter Abramenko received his Ph.D. in 1987 from the University of Frankfurt, Germany. He held various academic positions afterwards, including a Heisenberg fellowship from 1998 until 2001. Since 2001, he is Associate Professor at the University of Virginia in Charlottesville. He has previously published Twin Buildings and Applications to S-Arithmetic Groups for the Lecture Notes in Mathematics series for Springer (1996).


Laza, Radu, Schütt, Matthias, Yui, Noriko
Calabi-Yau Varieties: Arithmetic, Geometry and Physics
Lecture Notes on Concentrated Graduate Courses
Springer New York
Seiten x,547
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9781493928293
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This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area.

The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.”  The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.


Coleman, Rodney
Calculus on Normed Vector Spaces
Springer New York
Seiten xi,249
Erscheinungsjahr 2012
Einband: Softcover
ISBN 9781461438939
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This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary.

In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts.  The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.

Rodney Coleman lives close to Grenoble in France, where he is engaged in teaching and research. His interests include literature, bicycle riding and hiking in the mountains.

Hochstättler, Winfried, Schliep, Alexander
CATBox
An Interactive Course in Combinatorial Optimization
Springer Berlin Heidelberg
Seiten xii,190
Erscheinungsjahr 2010
Einband: Softcover
ISBN 9783540148876
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Graph algorithms are easy to visualize and indeed there already exists a variety of packages to animate the dynamics when solving problems from graph theory. Still it can be difficult to understand the ideas behind the algorithm from the dynamic display alone.

CATBox consists of a software system for animating graph algorithms and a course book which we developed simultaneously. The software system presents both the algorithm and the graph and puts the user always in control of the actual code that is executed. In the course book, intended for readers at advanced undergraduate or graduate level, computer exercises and examples replace the usual static pictures of algorithm dynamics.

For this volume we have chosen solely algorithms for classical problems from combinatorial optimization, such as minimum spanning trees, shortest paths, maximum flows, minimum cost flows, weighted and unweighted matchings both for bipartite and non-bipartite graphs.

Find more information at http://schliep.org/CATBox/.

Winfried Hochstättler is a professor of `Discrete Mathematics and Optimization` at FernUniversität in Hagen. The material of this book has been used for teaching in several courses.

Alexander Schliep is a professor in the department of computer science and the BioMaPS institute for quantitative biology at Rutgers University.  Gato, derived tools, and parts of CATBox have been used in graduate training at the Max Planck Institut for Molecular Genetics in Berlin.


Hesthaven, Jan S, Rozza, Gianluigi, Stamm, Benjamin
Certified Reduced Basis Methods for Parametrized Partial Differential Equations
Springer International Publishing
Seiten xiii,131
Erscheinungsjahr 2016
Einband: Softcover
ISBN 9783319224695
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This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.


Dies, J.-E.
Chaines de Markov sur les Permutations
Springer Berlin Heidelberg
Seiten ix,226
Erscheinungsjahr 1983
Einband: Softcover
ISBN 9783540126690
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Deergha Rao, K.
Channel Coding Techniques for Wireless Communications
Springer India
Seiten xxi,394
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9788132235378
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The book discusses modern channel coding techniques for wireless communications such as turbo codes, low parity check codes (LDPC), space-time coding, Reed Solomon (RS) codes and convolutional codes. Many illustrative examples are included in each chapter for easy understanding of the coding techniques. The text is integrated with MATLAB-based programs to enhance the understanding of the subject’s  underlying theories. It includes current topics of increasing importance such as turbo codes, LDPC codes, LT codes, Raptor codes and space-time coding in detail, in addition to the traditional codes such as cyclic codes, BCH and RS codes and convolutional codes. MIMO communications is a multiple antenna technology, which is an effective method for high-speed or high-reliability wireless communications. PC-based MATLAB m-files for the illustrative examples are included and also provided on the accompanying CD, which will help students and researchers involved in advanced and current concepts in coding theory. Channel coding, the core of digital communication and data storage, has undergone a major revolution as a result of the rapid growth of mobile and wireless communications.

The book is divided into 11 chapters. Assuming no prior knowledge in the field of channel coding, the opening chapters (1 - 2) begin with basic theory and discuss how to improve the performance of wireless communication channels using channel coding. Chapters 3 and 4 introduce Galois fields and present detailed coverage of BCH codes and Reed-Solomon codes. Chapters 5–7 introduce the family of convolutional codes, hard and soft-decision Viterbi algorithms, turbo codes, BCJR algorithm for turbo decoding and studies trellis coded modulation (TCM), turbo trellis coded modulation (TTCM), bit-interleaved coded modulation (BICM) as well as iterative BICM (BICM-ID) and compares them under various channel conditions. Chapters 8 and 9 focus on low-density parity-check (LDPC) codes, LT codes and Raptor codes. Chapters 10 and 11 discuss MIMO systems and space-time (ST) coding.

K. DEERGHA RAO is director and professor in the Navigational Electronics Research and Training Unit (NERTU), University College of Engineering, Osmania University, Hyderabad, India. Earlier, he was a postdoctoral fellow and part-time professor at the Department of Electronics and Communication Engineering, Concordia University, Montreal, Canada. He has executed several research projects for premium Indian organizations such as Defence Research and Development Organization (DRDO), Hindustan Aeronautical Limited (HAL) and Bharat Electronics Limited (BEL). His teaching areas are digital signal processing, digital image processing, coding theory for wireless channels and MIMO wireless communications, whereas his research interests include GPS signal processing, wireless channel coding, blind equalization, robust multiuser detection, OFDM UWB signal processing, MIMO SFBC OFDM, image processing, cryptosystems and VLSI signal  processing. Professor Rao has presented papers at IEEE international conferences several times in the U.S.A., Switzerland and Russia. He has more than 100 publications to his credit, including more than 60 publications in IEEE journals and conference proceedings. He is a senior member of IEEE and has served as chairman of communications and signal processing societies joint chapter of IEEE Hyderabad section. He is currently a member of the IEEE SPS chapters committee. He was awarded  2013 IETE K.S. Krishnan Memorial Award for the best system oriented paper. He has served as Communications Track Chair for IEEE INDICON 2011 held at Hyderabad. He is an editorial board member of the International Journal of Sustainable Aviation (Inderscience Publishers, U.K.). He has coauthored a book, Digital Signal Processing (Jaico Publishing House, India).


Deergha Rao, K.
Channel Coding Techniques for Wireless Communications
Springer India
Seiten xxi,394
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9788132222910
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58.84
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The book discusses modern channel coding techniques for wireless communications such as turbo codes, low parity check codes (LDPC), space-time coding, Reed Solomon (RS) codes and convolutional codes. Many illustrative examples are included in each chapter for easy understanding of the coding techniques. The text is integrated with MATLAB-based programs to enhance the understanding of the subject’s  underlying theories. It includes current topics of increasing importance such as turbo codes, LDPC codes, LT codes, Raptor codes and space-time coding in detail, in addition to the traditional codes such as cyclic codes, BCH and RS codes and convolutional codes. MIMO communications is a multiple antenna technology, which is an effective method for high-speed or high-reliability wireless communications. PC-based MATLAB m-files for the illustrative examples are included and also provided on the accompanying CD, which will help students and researchers involved in advanced and current concepts in coding theory. Channel coding, the core of digital communication and data storage, has undergone a major revolution as a result of the rapid growth of mobile and wireless communications.

The book is divided into 11 chapters. Assuming no prior knowledge in the field of channel coding, the opening chapters (1 - 2) begin with basic theory and discuss how to improve the performance of wireless communication channels using channel coding. Chapters 3 and 4 introduce Galois fields and present detailed coverage of BCH codes and Reed-Solomon codes. Chapters 5–7 introduce the family of convolutional codes, hard and soft-decision Viterbi algorithms, turbo codes, BCJR algorithm for turbo decoding and studies trellis coded modulation (TCM), turbo trellis coded modulation (TTCM), bit-interleaved coded modulation (BICM) as well as iterative BICM (BICM-ID) and compares them under various channel conditions. Chapters 8 and 9 focus on low-density parity-check (LDPC) codes, LT codes and Raptor codes. Chapters 10 and 11 discuss MIMO systems and space-time (ST) coding.

K. DEERGHA RAO is director and professor in the Navigational Electronics Research and Training Unit (NERTU), University College of Engineering, Osmania University, Hyderabad, India. Earlier, he was a postdoctoral fellow and part-time professor at the Department of Electronics and Communication Engineering, Concordia University, Montreal, Canada. He has executed several research projects for premium Indian organizations such as Defence Research and Development Organization (DRDO), Hindustan Aeronautical Limited (HAL) and Bharat Electronics Limited (BEL). His teaching areas are digital signal processing, digital image processing, coding theory for wireless channels and MIMO wireless communications, whereas his research interests include GPS signal processing, wireless channel coding, blind equalization, robust multiuser detection, OFDM UWB signal processing, MIMO SFBC OFDM, image processing, cryptosystems and VLSI signal  processing. Professor Rao has presented papers at IEEE international conferences several times in the U.S.A., Switzerland and Russia. He has more than 100 publications to his credit, including more than 60 publications in IEEE journals and conference proceedings. He is a senior member of IEEE and has served as chairman of communications and signal processing societies joint chapter of IEEE Hyderabad section. He is currently a member of the IEEE SPS chapters committee. He was awarded  2013 IETE K.S. Krishnan Memorial Award for the best system oriented paper. He has served as Communications Track Chair for IEEE INDICON 2011 held at Hyderabad. He is an editorial board member of the International Journal of Sustainable Aviation (Inderscience Publishers, U.K.). He has coauthored a book, Digital Signal Processing (Jaico Publishing House, India).


Alligood, Kathleen T., Sauer, Tim D., Yorke, James A.
Chaos
An Introduction to Dynamical Systems
Springer New York
Seiten xvii,603
Erscheinungsjahr 1996
Einband: Softcover
ISBN 9780387946771
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Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. The only prerequisites are calculus, differential equations, and linear algebra. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise.

Kechris, Alexander
Classical Descriptive Set Theory
Springer New York
Seiten xviii,404
Erscheinungsjahr 1995
Einband: Hardcover
ISBN 9780387943749
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Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.


Kechris, Alexander
Classical Descriptive Set Theory
Springer New York
Seiten xviii,404
Erscheinungsjahr 1995
Einband: Softcover
ISBN 9781461286929
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Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.


Awrejcewicz, Jan
Classical Mechanics
Dynamics
Springer New York
Seiten xiv,466
Erscheinungsjahr 2012
Einband: Hardcover
ISBN 9781461437390
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93.08
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This is the second volume of three books devoted to Mechanics. In this book, dynamical and advanced mechanics problems are stated, illustrated, and discussed, including a few novel concepts in comparison to standard text books and monographs. Apart from being addressed to a wide spectrum of graduate students, postgraduate students, researchers, and teachers from the fields of mechanical and civil engineering, this volume is also intended to be used as a self-contained material for applied mathematicians and physical scientists and researchers.
Jan Awrejcewicz is the 2011 winner of the Humboldt Prize. This award is granted from the Alexander von Humboldt Foundation in Germany and is based on a reasearcher`s entire achievements to date, whose fundamental discoveries, new theories or insights have had significant impact on their own discipline and who are expected to continue producing cutting-edge achievements in the future. Prof. Awrejcewicz is also the main author of “Nonsmooth Dynamics of Contacting Thermoelastic Bodies”, © 2009, Springer (AMMA v. 16), 978-0-387-09562-0. He is also the sole editor of “Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems”, © 2009 Springer, 978-1-4020-8777-6.

Awrejcewicz, Jan
Classical Mechanics
Kinematics and Statics
Springer New York
Seiten xiii,440
Erscheinungsjahr 2012
Einband: Hardcover
ISBN 9781461437901
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This is the first volume of three, devoted to Mechanics. This book contains classical mechanics problems including kinematics and statics. It is recommended as a supplementary textbook for undergraduate and graduate students from mechanical and civil engineering, as well as for physical scientists and engineers. It contains a basic introduction to classical mechanics, including fundamental principles, statics, and the geometry of masses, as well as thorough discussion on kinematics.
Jan Awrejcewicz is the 2011 winner of the Humboldt Prize. This award is granted from the Alexander von Humboldt Foundation in Germany. The award is based on a reasearcher`s entire achievements to date, whose fundamental discoveries, new theories or insights have had significant impact on their own discipline and who are expected to continue producing cutting-edge achievements in the future. Prof. Awrejcewicz is also the main author of “Nonsmooth Dynamics of Contacting Thermoelastic Bodies”, © 2009, Springer (AMMA v. 16), 978-0-387-09562-0. He is also the sole editor of “Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems”, © 2009 Springer, 978-1-4020-8777-6.

Awrejcewicz, Jan, Koruba, Zbigniew
Classical Mechanics
Applied Mechanics and Mechatronics
Springer New York
Seiten xxi,250
Erscheinungsjahr 2012
Einband: Hardcover
ISBN 9781461439776
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This is the last book of three devoted to Mechanics, and uses the theoretical background presented in Classical Mechanics: Kinematics and Statics and Classical Mechanics: Dynamics. It focuses on exhibiting a unique approach, rooted in the classical mechanics, to study mechanical and electromagnetic processes occurring in Mechatronics. Contrary to the majority of the books devoted to Applied Mechanics, this volume places a particular emphasis on theory, modeling, analysis, and control of gyroscopic devices, including the military applications. This volume provides practicing mechanical/mechatronic engineers and designers, researchers, graduate and postgraduate students with a knowledge of mechanics focused directly on advanced applications.
Jan Awrejcewicz is the 2011 winner of the Humboldt Prize. This award is granted from the Alexander von Humboldt Foundation in Germany. The award is based on a reasearcher`s entire achievements to date, whose fundamental discoveries, new theories or insights have had significant impact on their own discipline and who are expected to continue producing cutting-edge achievements in the future. Prof. Awrejcewicz is also the main author of “Nonsmooth Dynamics of Contacting Thermoelastic Bodies”, © 2009, Springer (AMMA v. 16), 978-0-387-09562-0. He is also the sole editor of “Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems”, © 2009 Springer, 978-1-4020-8777-6.

Awrejcewicz, Jan
Classical Mechanics
Dynamics
Springer New York
Seiten xiv,466
Erscheinungsjahr 2012
Einband: Softcover
ISBN 9781489987716
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93.08
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This is the second volume of three books devoted to Mechanics. In this book, dynamical and advanced mechanics problems are stated, illustrated, and discussed, including a few novel concepts in comparison to standard text books and monographs. Apart from being addressed to a wide spectrum of graduate students, postgraduate students, researchers, and teachers from the fields of mechanical and civil engineering, this volume is also intended to be used as a self-contained material for applied mathematicians and physical scientists and researchers.
Jan Awrejcewicz is the 2011 winner of the Humboldt Prize. This award is granted from the Alexander von Humboldt Foundation in Germany and is based on a reasearcher`s entire achievements to date, whose fundamental discoveries, new theories or insights have had significant impact on their own discipline and who are expected to continue producing cutting-edge achievements in the future. Prof. Awrejcewicz is also the main author of “Nonsmooth Dynamics of Contacting Thermoelastic Bodies”, © 2009, Springer (AMMA v. 16), 978-0-387-09562-0. He is also the sole editor of “Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems”, © 2009 Springer, 978-1-4020-8777-6.

Stillwell, John
Classical Topology and Combinatorial Group Theory
Springer New York
Seiten xii,336
Erscheinungsjahr 1993
Einband: Hardcover
ISBN 9780387979700
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In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler`s polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment `undergraduate topology` proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l`isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec­ tions to other parts of mathematics which make topology an important as well as a beautiful subject.

Stillwell, John
Classical Topology and Combinatorial Group Theory
Springer New York
Seiten xii,336
Erscheinungsjahr 1993
Einband: Softcover
ISBN 9781461287490
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In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler`s polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment `undergraduate topology` proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l`isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec­ tions to other parts of mathematics which make topology an important as well as a beautiful subject.

Serre, Jean-Pierre
Cohomologie Galoisienne
Springer Berlin Heidelberg
Seiten ix,181
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9783540580027
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This new edition includes a survey (mostly without proofs) of the main results obtained in the 30 years following original publication. It also incorporates newer material, including two `résumés de cours` at the Collège de France (1990 - 1991 and 1991 - 1992), and an updated bibliography.


Iwasawa, Kenkichi, Satake, Ichiro, Fujisaki, Genjiro, Kazuya, Kato, Kurihara, Masato, Nakajima, Shoichi, Coates, John
Collected Papers
Springer Japan
Seiten xxv,872
Erscheinungsjahr 2001
Einband: Softcover
ISBN 9784431550556
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Iwasawa is one of the most original and influential mathematicians in the 20th century. This Collected Papers of K. Iwasawa contains all 66 published papers, including 11 papers in Japanese, for which English abstracts (by the editors) are attached. Also included is a masterly summery of Iwasawa theory by J. Coates (Cambridge).


Lyndon, Roger C., Schupp, Paul E.
Combinatorial Group Theory
Springer Berlin Heidelberg
Seiten xiv,339
Erscheinungsjahr 2001
Einband: Softcover
ISBN 9783540411581
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From the reviews: `This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference.` Mathematical Reviews

Biography of Roger C. Lyndon

Roger Lyndon, born on Dec. 18, 1917 in Calais (Maine, USA), entered Harvard University in 1935 with the aim of studying literature and becoming a writer. However, when he discovered that, for him, mathematics required less effort than literature, he switched and graduated from Harvard in 1939.

After completing his Master`s Degree in 1941, he taught at Georgia Tech, then returned to Harvard in 1942 and there taught navigation to pilots while, supervised by S. MacLane, he studied for his Ph.D., awarded in 1946 for a thesis entitled The Cohomology Theory of Group Extensions.

Influenced by Tarski, Lyndon was later to work on model theory. Accepting a position at Princeton, Ralph Fox and Reidemeister`s visit in 1948 were major influencea on him to work in combinatorial group theory. In 1953 Lyndon left Princeton for a chair at the University of Michigan where he then remained except for visiting professorships at Berkeley, London, Montpellier and Amiens.

Lyndon made numerous major contributions to combinatorial group theory. These included the development of `small cancellation theory`, his introduction of `aspherical` presentations of groups and his work on length functions. He died on June 8, 1988.

 

Biography of Paul E. Schupp

Paul Schupp, born on March 12, 1937 in Cleveland, Ohio was a student of  Roger Lyndon`s at the Univ. of Michigan. Where he wrote a thesis on `Dehn`s Algorithm and the Conjugacy Problem`. After a year at the University of Wisconsin he moved to the University of Illinois where he remained. For several years he was also concurrently Visiting Professor at the University Paris VII and a member of the Laboratoire d`Informatique Théorique et Programmation (founded by M. P. Schutzenberger).

Schupp further developed the use of cancellation diagrams in combinatorial group theory, introducing conjugacy diagrams, diagrams on compact surfaces, diagrams over free products with amalgamation and HNN extensions and applications to Artin groups. He then worked with David Muller on connections between group theory and formal language theory and on the theory of finite automata on infinite inputs. His current interest is using geometric methods to investigate the computational complexity of algorithms in combinatorial group theory.


Benedetti, Bruno, Delucchi, Emanuele, Moci, Luca
Combinatorial Methods in Topology and Algebra
Springer International Publishing
Seiten vii,227
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319201542
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Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects.

This book arises from the INdAM conference `CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,`` which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory.

The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.


Korte, Bernhard, Vygen, Jens
Combinatorial Optimization
Theory and Algorithms
Springer Berlin Heidelberg
Seiten xx,660
Erscheinungsjahr 2012
Einband: Hardcover
ISBN 9783642244872
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This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references.

This fifth edition has again been updated, revised, and significantly extended, with more than 60 new exercises and new material on various topics, including Cayley`s formula, blocking flows, faster b-matching separation, multidimensional knapsack, multicommodity max-flow min-cut ratio, and sparsest cut. Thus, this book represents the state of the art of combinatorial optimization.


Korte, Bernhard, Vygen, Jens
Combinatorial Optimization
Theory and Algorithms
Springer Berlin Heidelberg
Seiten xx,660
Erscheinungsjahr 2012
Einband: Softcover
ISBN 9783642427671
Yellow Sale Preis
37.44
(inkl. 7% Mwst)
Lieferstatus  
 

This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references.

This fifth edition has again been updated, revised, and significantly extended, with more than 60 new exercises and new material on various topics, including Cayley`s formula, blocking flows, faster b-matching separation, multidimensional knapsack, multicommodity max-flow min-cut ratio, and sparsest cut. Thus, this book represents the state of the art of combinatorial optimization.


Eisenbud, David
Commutative Algebra
with a View Toward Algebraic Geometry
Springer New York
Seiten xvi,788
Erscheinungsjahr 1995
Einband: Softcover
ISBN 9780387942698
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This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.


Lombardi, Henri, Quitté, Claude
Commutative Algebra: Constructive Methods
Finite Projective Modules
Springer Netherlands
Seiten xlix,996
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9789401799430
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Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative.

The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century.

This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors and theoretical computer scientists.

Henri Lombardi is a researcher in constructive mathematics, real algebra and algorithmic complexity. Since 2003, with Marie-Françoise Roy and Thierry Coquand, he has developed the international group MAP (Mathematics, Algorithms, Proofs). He has published E?piste?mologie mathe?matique, (Ellipse, 2011), and Me?thodes matricielles. Introduction a? la complexite? alge?brique, (Springer, 2003, in collaboration with Jounai?di Abdeljaoued).

Claude Quitté is a researcher in effective commutative algebra, computer algebra and computer science. He has published Algorithmique alge?brique, (Masson, 1991) in collaboration with Patrice Naudin.

Henri Lombardi and Claude Quitté also published together with Maria-Gema Díaz-Toca the book Modules sur les anneaux commutatifs (Calvage & Mounet, 2014).


Sepanski, Mark R.
Compact Lie Groups
Springer New York
Seiten xiii,201
Erscheinungsjahr 2007
Einband: Hardcover
ISBN 9780387302638
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Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Coverage includes the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The book develops the necessary Lie algebra theory with a streamlined approach focusing on linear Lie groups.


Sepanski, Mark R.
Compact Lie Groups
Springer New York
Seiten xiii,201
Erscheinungsjahr 2007
Einband: Softcover
ISBN 9781441921383
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21.39
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Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Coverage includes the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The book develops the necessary Lie algebra theory with a streamlined approach focusing on linear Lie groups.


Gamelin, Theodore W.
Complex Analysis
Springer New York
Seiten xviii,478
Erscheinungsjahr 2001
Einband: Softcover
ISBN 9780387950693
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An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.

Gamelin, Theodore W.
Complex Analysis
Springer New York
Seiten xviii,478
Erscheinungsjahr 2001
Einband: Hardcover
ISBN 9780387950938
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An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.

Freitag, Eberhard, Busam, Rolf
Complex Analysis
Springer Berlin Heidelberg
Seiten x,532
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9783540939825
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All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed

Provides a more in-depth introduction to the subject than other existing books in this area

Over 400 exercises including hints for solutions are included


Freitag, Eberhard
Complex Analysis 2
Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions
Springer Berlin Heidelberg
Seiten xiii,506
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9783642205538
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The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ¯rst volume. There is no comparable treatment in the literature.
Prof. Dr. Eberhard Freitag, Universität Heidelberg, Mathematisches Institut

Huybrechts, Daniel
Complex Geometry
An Introduction
Springer Berlin Heidelberg
Seiten xii,309
Erscheinungsjahr 2005
Einband: Softcover
ISBN 9783540212904
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Easily accessible

Includes recent developments

Assumes very little knowledge of differentiable manifolds and functional analysis

Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Daniel Huybrechts is currently Professor of Mathematics at the University Denis Diderot in Paris.

Brief career details:

Studies of math at Humboldt University Berlin and Max-=Planck-Institute Bonn 1985-1992.

Post-doctorial positions at Inst. for Advanced Study Priceton, Ecole Normale Supérieure Paris, Max-Planck-Inst Bonn, University Essen, IHES Paris.

Professor: Cologne 1998-2002, Paris since 2002.


Kodaira, Kunihiko
Complex Manifolds and Deformation of Complex Structures
Springer Berlin Heidelberg
Seiten xiv,465
Erscheinungsjahr 2005
Einband: Softcover
ISBN 9783540226147
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Kodaira is a Fields Medal Prize Winner.  (In the absence of a Nobel prize in mathematics, they are regarded as the highest professional honour a mathematician can attain.)

Kodaira is an honorary member of the London Mathematical Society.

Affordable softcover edition of 1986 classic

Kunihiko Kodaira was born on March 16, 1915 in Tokyo, Japan. He graduated twice from the University of Tokyo, with a degree in mathematics in 1938 and one in physics in 1941. From 1944 until 1949, Kodaira was an associate professor at the University of Tokyo but by this time his work was well known to mathematicians worldwide and in 1949 he accepted an invitation from H. Weyl to come to the Institute for Advanced Study. During his 12 years in Princeton, he was also Professor at Princeton University from 1952 to 1961. After a year at Harvard, he was then appointed in 1962 to the chair of mathematics at Johns Hopkins University, which he left in 1965 for a chair at Stanford University. Finally, after 2 years at Stanford, he returned to Japan to Tokyo University from 1967. He died in Kofu, Japan, in 1997.

Kodaira’s work covers many topics, including applications of Hilbert space methods to differential equations, harmonic integrals , and importantly the application of sheaves to algebraic geometry. Around 1960 he became involved in the classification of compact complex analytic spaces. One of the themes running through much of his work is the Riemann-Roch theorem and this played an important role in much of his research.

Kodaira received many honours for his outstanding research, in particular the Fields Medal, in 1954.


Daras, Nicholas J., Rassias, Michael Th.
Computation, Cryptography, and Network Security
Springer International Publishing
Seiten ix,756
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319372631
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Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April 2013 at the Hellenic Military Academy, and brings together a broad variety of mathematical methods and theories with several applications. It discusses directions and pursuits of scientists that pertain to engineering sciences. It is also presents the theoretical background required for algorithms and techniques applied to a large variety of concrete problems. A number of open questions as well as new future areas are also highlighted.

This book will appeal to operations research analysts, engineers, community decision makers, academics, the military community, practitioners sharing the current “state-of-the-art,” and analysts from coalition partners. Topics covered include Operations Research, Games and Control Theory, Computational Number Theory and Information Security, Scientific Computing and Applications, Statistical Modeling and Applications, Systems of Monitoring and Spatial Analysis.


Daras, Nicholas J., Rassias, Michael Th.
Computation, Cryptography, and Network Security
Springer International Publishing
Seiten ix,756
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319182742
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82.38
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Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April 2013 at the Hellenic Military Academy, and brings together a broad variety of mathematical methods and theories with several applications. It discusses directions and pursuits of scientists that pertain to engineering sciences. It is also presents the theoretical background required for algorithms and techniques applied to a large variety of concrete problems. A number of open questions as well as new future areas are also highlighted.

This book will appeal to operations research analysts, engineers, community decision makers, academics, the military community, practitioners sharing the current “state-of-the-art,” and analysts from coalition partners. Topics covered include Operations Research, Games and Control Theory, Computational Number Theory and Information Security, Scientific Computing and Applications, Statistical Modeling and Applications, Systems of Monitoring and Spatial Analysis.


Bermúdez de Castro, Alfredo, Valli, Alberto, Haddar, Houssem, Hiptmair, Ralf, Monk, Peter, Rodríguez, Rodolfo
Computational Electromagnetism
Cetraro, Italy 2014
Springer International Publishing
Seiten vii,240
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319193052
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Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro in June 2014, the material covered includes the spatial discretization of Maxwell’s equations in a bounded domain, the numerical approximation of the eddy current model in harmonic regime, the time domain integral equation method (with an emphasis on the electric-field integral equation) and an overview of qualitative methods for inverse electromagnetic scattering problems.

Assuming some knowledge of the variational formulation of PDEs and of finite element/boundary element methods, the book is suitable for PhD students and researchers interested in numerical approximation of partial differential equations and scientific computing.


Derksen, Harm, Kemper, Gregor
Computational Invariant Theory
Springer Berlin Heidelberg
Seiten xxii,366
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783662484203
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This book is about the computational aspects of invariant theory. Of central interest is the question how the  invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision.

The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest.

More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi

r Popov, and an addendum by Norbert A`Campo and Vladimir Popov.   

    

Beck, Matthias, Robins, Sinai
Computing the Continuous Discretely
Integer-Point Enumeration in Polyhedra
Springer New York
Seiten xx,285
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9781493929689
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This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device.

The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more.

With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume?

Reviews of the first edition:

“You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.”

— MAA Reviews

“The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate

rial, exercises, open problems and an extensive bibliography.”

— Zentralblatt MATH

“This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.”

— Mathematical Reviews

“Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying

way. Beck and Robins have written the perfect text for such a course.”

— CHOICE

Matthias Beck is Professor of Mathematics at San Francisco State University. Sinai Robins is Associate Professor of Mathematics at Nanyang Technological University, Singapore.

Bercu, Bernard, Delyon, Bernard, Rio, Emmanuel
Concentration Inequalities for Sums and Martingales
Springer International Publishing
Seiten x,120
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319220987
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The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales.

The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales.

The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities.

The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided.

The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.


Lütkebohmert, Eva
Concentration Risk in Credit Portfolios
Springer Berlin Heidelberg
Seiten xviii,226
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9783540708698
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Modeling and management of credit risk are the main topics within banks and other lending institutions. Historical experience shows that, in particular, concentration of risk in credit portfolios has been one of the major causes of bank distress. Therefore, concentration risk is highly relevant to anyone who wants to go beyond the very basic portfolio credit risk models.

The book gives an introduction to credit risk modeling with the aim to measure concentration risks in credit portfolios. Taking the basic principles of credit risk in general as a starting point, several industry models are studied. These allow banks to compute a probability distribution of credit losses at the portfolio level. Besides these industry models the Internal Ratings Based model, on which Basel II is based, is treated.

On the basis of these models various methods for the quantification of name and sector concentration risk and the treatment of default contagion are discussed. The book reflects current research in these areas from both an academic and a supervisory perspective


Bix, Robert
Conics and Cubics
A Concrete Introduction to Algebraic Curves
Springer New York
Seiten viii,347
Erscheinungsjahr 2006
Einband: Hardcover
ISBN 9780387318028
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Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout’s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.


Bix, Robert
Conics and Cubics
A Concrete Introduction to Algebraic Curves
Springer New York
Seiten viii,347
Erscheinungsjahr 2006
Einband: Softcover
ISBN 9781441921789
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Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout’s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.


Yengui, Ihsen
Constructive Commutative Algebra
Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases
Springer International Publishing
Seiten vii,271
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319194936
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The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring.

Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented.

Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn`s Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.


Revuz, Daniel, Yor, Marc
Continuous Martingales and Brownian Motion
Springer Berlin Heidelberg
Seiten xiii,602
Erscheinungsjahr 1999
Einband: Hardcover
ISBN 9783540643258
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`This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises.` –BULLETIN OF THE L.M.S.


Revuz, Daniel, Yor, Marc
Continuous Martingales and Brownian Motion
Springer Berlin Heidelberg
Seiten xiii,602
Erscheinungsjahr 1999
Einband: Softcover
ISBN 9783642084003
Yellow Sale Preis
53.49
(inkl. 7% Mwst)
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`This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises.` –BULLETIN OF THE L.M.S.


Jarnicki, Marek, Pflug, Peter
Continuous Nowhere Differentiable Functions
The Monsters of Analysis
Springer International Publishing
Seiten xii,299
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319126692
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This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of ideas and tricks used to study the explicit continuous nowhere differentiable functions of Weierstrass, Takagi–van der Waerden, Bolzano, and others. Modern tools of functional analysis, measure theory, and Fourier analysis are applied to examine the generic nature of continuous nowhere differentiable functions, as well as linear structures within the (nonlinear) space of continuous nowhere differentiable functions. To round out the presentation, advanced techniques from several areas of mathematics are brought together to give a state-of-the-art analysis of Riemann’s continuous, and purportedly nowhere differentiable, function.

For the reader’s benefit, claims requiring elaboration, and open problems, are clearly indicated. An appendix conveniently provides background material from analysis and number theory, and comprehensive indices of symbols, problems, and figures enhance the book’s utility as a reference work. Students and researchers of analysis will value this unique book as a self-contained guide to the subject and its methods.

Marek Jarnicki is Professor of Mathematics at Jagiellonian University, Poland. His primary subject of research is complex analysis, particularly holomorphically invariant (contractible) pseudodistances and pseudometrics; domains of holomorphy with respect to special cases of holomorphic functions; continuation of holomorphic functions with restricted growth; and the extension of separately analytic functions.

Peter Pflug is Professor of Mathematics at the University of Oldenburg, Germany. His primary subject of research is the theory of functions of several complex variables and complex analysis.


Carvalho, Alexandre N., Ruf, Bernhard, Moreira dos Santos, Ederson, M. Soares, Sergio H., Cazenave, Thierry
Contributions to Nonlinear Elliptic Equations and Systems
A Tribute to Djairo Guedes de Figueiredo on the Occasion of his 80th Birthday
Springer International Publishing
Seiten xiv,438
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319199016
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This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday. The articles it contains were born out of the ICMC Summer Meeting on Differential Equations – 2014 Chapter, also dedicated to de Figueiredo and held at the Universidade de São Paulo at São Carlos, Brazil from February 3-7, 2014. The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems.

Djairo Guedes de Figueiredo has had a very active scientific career, publishing 29 monographs and over one hundred research articles. His influence on Brazilian mathematics has made him one of the pillars of the subject in that country. He had a major impact on the development of analysis, especially in its application to nonlinear elliptic partial differential equations and systems throughout the entire world. The articles collected here pay tribute to him and his legacy and are intended for graduate students and researchers in mathematics and related areas who are interested in nonlinear elliptic partial differential equations and systems.


Fleming, Wendell H., Soner, Halil Mete
Controlled Markov Processes and Viscosity Solutions
Springer New York
Seiten xvii,429
Erscheinungsjahr 2006
Einband: Hardcover
ISBN 9780387260457
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This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.


Fleming, Wendell H., Soner, Halil Mete
Controlled Markov Processes and Viscosity Solutions
Springer New York
Seiten xvii,429
Erscheinungsjahr 2006
Einband: Softcover
ISBN 9781441920782
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This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.


Peypouquet, Juan
Convex Optimization in Normed Spaces
Theory, Methods and Examples
Springer International Publishing
Seiten xiv,124
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319137094
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This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.
Juan Peypouquet is an Associate Professor at the Mathematics Department of the Universidad Tecnica Federico Santa Maria.  His main research interest is the study of the asymptotic behavior of dynamical systems in a broad sense, along with their applications in variational analysis and optimization.

Remmel, Jeffrey, Mendes, Anthony
Counting with Symmetric Functions
Springer International Publishing
Seiten x,292
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319236179
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This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics.  It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas.

The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions.  Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions.  Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4.  The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions.  Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties.

Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions.  The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.


Martin, George E.
Counting: The Art of Enumerative Combinatorics
Springer New York
Seiten xii,252
Erscheinungsjahr 2001
Einband: Hardcover
ISBN 9780387952253
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This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

From the reviews:

`Much of Martin’s charming and accessible text could be used with bright school students. … The book is rounded off by a section called ‘The back of the book’ which includes solutions and discussion of many exercises. George E. Martin is a remarkable writer who brings combinatorics alive. He has written a splendid introduction that requires very few prerequisites, yet soon delivers the reader into some highly effective methods of counting. The book is highly recommended.` (S. C. Russen, The Mathematical Gazette, Vol. 88 (551), 2004)

`This truly is an undergraduate mathematics text; parts of it could be the text for a high school combinatorics course. The author has made a successful effort to illuminate and teach the elementary parts of combinatorics. He uses examples and problems to teach; there are 245 problems in Chapter 1! … If I were not retired and had been asked to teach an undergraduate course in combinatorics, I would have liked to use this book.` (W. Moser, Mathematical Reviews, Issue 2002 g)

`This book is a nice textbook on enumerative combinatorics to undergraduates. It introduces the most important ideas … . A lot of ‘easy’ applications are given and homework is listed (with hints). The book also touches some elementary graph enumeration problems. The text is clear and easy to follow. It is even suitable to learn it alone, which is also aided by nice exam problems.` (Péter L. Erdös, Zentralblatt MATH, Vol. 968, 2001)

`The teaching of topics in discrete mathematics is becoming increasingly popular and this text contains chapters on a number of pertinent areas for exposure at an elementary level. … The author uses non-worked discovery-type examples to lead into observations about the material. … There are many interesting exercises for the student to attempt. These are spread throughout the various chapters and are effective in developing interest in the topics. The book contains a ‘Back of the Book’ section rather than an Answers section.` (M. J. Williams, The Australian Mathematical Society Gazette, Vol. 29 (1), 2002)


Martin, George E.
Counting: The Art of Enumerative Combinatorics
Springer New York
Seiten xii,252
Erscheinungsjahr 2001
Einband: Softcover
ISBN 9781441929150
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This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

From the reviews:

`Much of Martin’s charming and accessible text could be used with bright school students. … The book is rounded off by a section called ‘The back of the book’ which includes solutions and discussion of many exercises. George E. Martin is a remarkable writer who brings combinatorics alive. He has written a splendid introduction that requires very few prerequisites, yet soon delivers the reader into some highly effective methods of counting. The book is highly recommended.` (S. C. Russen, The Mathematical Gazette, Vol. 88 (551), 2004)

`This truly is an undergraduate mathematics text; parts of it could be the text for a high school combinatorics course. The author has made a successful effort to illuminate and teach the elementary parts of combinatorics. He uses examples and problems to teach; there are 245 problems in Chapter 1! … If I were not retired and had been asked to teach an undergraduate course in combinatorics, I would have liked to use this book.` (W. Moser, Mathematical Reviews, Issue 2002 g)

`This book is a nice textbook on enumerative combinatorics to undergraduates. It introduces the most important ideas … . A lot of ‘easy’ applications are given and homework is listed (with hints). The book also touches some elementary graph enumeration problems. The text is clear and easy to follow. It is even suitable to learn it alone, which is also aided by nice exam problems.` (Péter L. Erdös, Zentralblatt MATH, Vol. 968, 2001)

`The teaching of topics in discrete mathematics is becoming increasingly popular and this text contains chapters on a number of pertinent areas for exposure at an elementary level. … The author uses non-worked discovery-type examples to lead into observations about the material. … There are many interesting exercises for the student to attempt. These are spread throughout the various chapters and are effective in developing interest in the topics. The book contains a ‘Back of the Book’ section rather than an Answers section.` (M. J. Williams, The Australian Mathematical Society Gazette, Vol. 29 (1), 2002)


Chenciner, Alain
Courbes Algébriques Planes
Springer Berlin Heidelberg
Seiten x,160
Erscheinungsjahr 2008
Einband: Softcover
ISBN 9783540337072
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Issu d’un cours de maîtrise de l’Université Paris VII, ce texte est réédité tel qu’il était paru en 1978. A propos du théorème de Bézout sont introduits divers outils nécessaires au développement de la notion de multiplicité d’intersection de deux courbes algébriques dans le plan projectif complexe. Partant des notions élémentaires sur les sous-ensembles algébriques affines et projectifs, on définit les multiplicités d’intersection et interprète leur somme entermes du résultant de deux polynômes. L’étude locale est prétexte à l’introduction des anneaux de série formelles ou convergentes ; elle culmine dans le théorème de Puiseux dont la convergence est ramenée par des éclatements à celle du théorème des fonctions implicites. Diverses figures éclairent le texte: on y `voit` en particulier que l’équation homogène x3+y3+z3 = 0 définit un tore dans le plan projectif complexe.

 

Sous-ensembles algébriques de C.- Ensembles algébriques affines.- Courbes planes affines.- Ensembles algébriques projectifs.- Courbes projectives planes : le théorème de Bezout.- Le résultant.- Point de vue local : anneaux de series formelles.- Anneaux de series convergentes.- Le théorème de Puiseux.- Théorie locale des intersections de courbes.


Mendes France, M., Tricot, Claude
Courbes et dimension fractale
Springer Berlin Heidelberg
Seiten xx,377
Erscheinungsjahr 1999
Einband: Softcover
ISBN 9783540655046
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Ce livre fait une revue de diverses techniques d`analyse des courbes planes, en vue des applications. Après une première partie sur les ensembles de mesure nulle sur la droite, une seconde traite des courbes `rectifiables` (de longueur finie), et une troisième, la plus importante, des courbes fractales. Cet ouvrage est destiné aux chercheurs en sciences expérimentales, et comporte un minimum de formalisme mathématique.


Takeuchi, Kiyoshi, Hotta, Ryoshi, Takeuchi, Kiyoshi, Tanisaki, Toshiyuki
D-Modules, Perverse Sheaves, and Representation Theory
Birkhäuser Boston
Seiten xi,412
Erscheinungsjahr 2008
Einband: Hardcover
ISBN 9780817643638
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D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors` essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics.

To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.


Law, Kody, Stuart, Andrew, Zygalakis, Konstantinos
Data Assimilation
A Mathematical Introduction
Springer International Publishing
Seiten xviii,242
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319203249
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This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online.

The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters.

This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.   

Kody Law is a Mathematician in the Computer Science and Mathematics Division at Oak Ridge National Laboratory.  He received his PhD in Mathematics from the University of Massachusetts in 2010, and subsequently held positions as a postdoc at the University of Warwick and a research scientist at King Abdullah University of Science and Technology.  He has published in the areas of computational applied mathematics, physics, and dynamical systems.  His current research interests are focused on inverse uncertainty quantification: data assimilation, filtering, and Bayesian inverse problems. 




Andrew M. Stuart is a Professor at the Mathematics Institut

e, Warwick University. He received his PhD from Oxford University, and has previously held permanent positions at Bath University and Stanford University.  His primary research interests are in the field of applied and computational mathematics. He has won numerous awards, including the SIAM JD Crawford Prize and the Monroe Martin Prize in Applied Mathematics; he is also a SIAM Fellow. He has authored over one hundred journal article, and three books, including Multiscale Methods: Averaging and Homogenization (Springer, 2008, with G. Pavliotis).

 

 

              

Konstantinos Zygalakis is a Lecturer in Applied Mathematics at the University of Southampton. He received his PhD from the University of Warwick in 2009 and held postdoctoral positions at the Universities of Cambridge, Oxford and the Swiss Federal Institute of Technology, Lausanne  before joining Southampton in 2012. In 2011 he was awarded a Leslie Fox prize (IMA UK). His research interests span from the theoretical and numerical aspects of stochastic processes and homogenization theory  to applications  in mathematical biology.    


Spector, Phil
Data Manipulation with R
Springer New York
Seiten x,154
Erscheinungsjahr 2008
Einband: Softcover
ISBN 9780387747309
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The R language provides a rich environment for working with data, especially data to be used for statistical modeling or graphics. Coupled with the large variety of easily available packages, it allows access to both well-established and experimental statistical techniques. However techniques that might make sense in other languages are often very ine?cient in R, but, due to R’s ?- ibility, it is often possible to implement these techniques in R. Generally, the problem with such techniques is that they do not scale properly; that is, as the problem size grows, the methods slow down at a rate that might be unexpected. The goal of this book is to present a wide variety of data - nipulation techniques implemented in R to take advantage of the way that R works,ratherthandirectlyresemblingmethodsusedinotherlanguages. Since this requires a basic notion of how R stores data, the ?rst chapter of the book is devoted to the fundamentals of data in R. The material in this chapter is a prerequisite for understanding the ideas introduced in later chapters. Since one of the ?rst tasks in any project involving data and R is getting the data into R in a way that it will be usable, Chapter 2 covers reading data from a variety of sources (text ?les, spreadsheets, ?les from other programs, etc. ), as well as saving R objects both in native form and in formats that other programs will be able to work with.

Conlon, Lawrence
Differentiable Manifolds
Birkhäuser Boston
Seiten xiv,418
Erscheinungsjahr 2001
Einband: Softcover
ISBN 9780817647667
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The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists.


Garcia-Prada, Oscar, Wells, Raymond O.
Differential Analysis on Complex Manifolds
Springer New York
Seiten xiv,304
Erscheinungsjahr 2008
Einband: Hardcover
ISBN 9780387738918
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A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths`s period mapping, quadratic transformations, and Kodaira`s vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.


Garcia-Prada, Oscar, Wells, Raymond O.
Differential Analysis on Complex Manifolds
Springer New York
Seiten xiv,304
Erscheinungsjahr 2008
Einband: Softcover
ISBN 9781441925350
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A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths`s period mapping, quadratic transformations, and Kodaira`s vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.


Cabada, Alberto, F. Tojo, F. Adrián
Differential Equations with Involutions
Atlantis Press
Seiten xiv,154
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9789462391208
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This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.

Said-Houari, Belkacem
Differential Equations: Methods and Applications
Springer International Publishing
Seiten x,212
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319257341
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This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory.
To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included.
The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. 

Dr. Belkacem Said-Houari received his Ph.D degree in partial differential equations (hyperbolic problems and nonclassical thermoelasticity) from Annaba University (Algeria) in 2005.

His research interests focus on analysis of hyperbolic PDE (e.g. in thermoelasticity, Timoshenko systems, nonlinear wave equations), integro-differential equations, parabolic and hyperbolic-parabolic PDE.

He is the author or co-author of 45 research papers published in refereed international journals.

He is the winner of the Abdul Hameed Shoman Award for Young Arab Researchers, Mathematics (2012). 


Do Carmo, Manfredo P.
Differential Forms and Applications
Springer Berlin Heidelberg
Seiten x,118
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9783540576181
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An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to `users` of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes` theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern`s proof of the Gauss-Bonnet theorem for compact surfaces.

Sharpe, R.W., Chern, S.S.
Differential Geometry
Cartan`s Generalization of Klein`s Erlangen Program
Springer New York
Seiten xx,426
Erscheinungsjahr 1997
Einband: Hardcover
ISBN 9780387947327
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Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of `espaces généralisés` (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.

Mukherjee, Amiya
Differential Topology
Springer International Publishing
Seiten xiii,349
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319369389
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This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools. The text includes, in particular, the earlier works of Stephen Smale, for which he was awarded the Fields Medal. Explicitly, the topics covered are Thom transversality, Morse theory, theory of handle presentation, h-cobordism theorem and the generalised Poincaré conjecture. The material is the outcome of lectures and seminars on various aspects of differentiable manifolds and differential topology given over the years at the Indian Statistical Institute in Calcutta, and at other universities throughout India.

The book will appeal to graduate students and researchers interested in these topics. An elementary knowledge of linear algebra, general topology, multivariate calculus, analysis and algebraic topology is recommended.


Mukherjee, Amiya
Differential Topology
Springer International Publishing
Seiten xiii,349
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319190440
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This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools. The text includes, in particular, the earlier works of Stephen Smale, for which he was awarded the Fields Medal. Explicitly, the topics covered are Thom transversality, Morse theory, theory of handle presentation, h-cobordism theorem and the generalised Poincaré conjecture. The material is the outcome of lectures and seminars on various aspects of differentiable manifolds and differential topology given over the years at the Indian Statistical Institute in Calcutta, and at other universities throughout India.

The book will appeal to graduate students and researchers interested in these topics. An elementary knowledge of linear algebra, general topology, multivariate calculus, analysis and algebraic topology is recommended.


Hindry, Marc, Silverman, Joseph H.
Diophantine Geometry
An Introduction
Springer New York
Seiten xiii,561
Erscheinungsjahr 2000
Einband: Hardcover
ISBN 9780387989754
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This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.


Hindry, Marc, Silverman, Joseph H.
Diophantine Geometry
An Introduction
Springer New York
Seiten xiii,561
Erscheinungsjahr 2000
Einband: Softcover
ISBN 9780387989815
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This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.


Bouleau, Nicolas, Denis, Laurent
Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
With Emphasis on the Creation-Annihilation Techniques
Springer International Publishing
Seiten xviii,323
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319258188
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A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calculus theory. This book will be of interest to researchers and graduate students in the fields of stochastic analysis and finance, and in the domain of statistical physics. Professors preparing courses on these topics will also find it useful. The prerequisite is a knowledge of probability theory.

Laurent Denis is currently professor at the Université du Maine. He has been head of the department of mathematics at the University of Evry (France). He is a specialist in Malliavin calculus, the theory of stochastic partial differential equations and mathematical finance.

Nicolas Bouleau is emeritus professor at the Ecole des Ponts ParisTech. He is known for his works in potential theory and on Dirichlet forms with which he transformed the approach to error calculus. He has written more than a hundred articles and several books on mathematics and on other subjects related to the philosophy of science. He holds several awards including the Montyon prize from the French Academy of Sciences and is a member of the Scientific Council of the Nicolas Hulot Foundation.


Dolejší, Vít, Feistauer, Miloslav
Discontinuous Galerkin Method
Analysis and Applications to Compressible Flow
Springer International Publishing
Seiten xiv,572
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319192666
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The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.


Dolejší, Vít, Feistauer, Miloslav
Discontinuous Galerkin Method
Analysis and Applications to Compressible Flow
Springer International Publishing
Seiten xiv,572
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319371238
Yellow Sale Preis
64.19
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The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.


Goodrich, Christopher, Peterson, Allan C.
Discrete Fractional Calculus
Springer International Publishing
Seiten xiii,556
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319255606
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This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book.

The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject.  

Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1—2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers.  For courses where students already have background in elementary real analysis, Chapters 1—2 may be covered quickly and readers may then skip to Chapters 6—7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6—7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1—5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.

Allan C. Peterson is professor of mathematics at the University of Nebraska, Lincoln. Peterson, with Walter Kelley, is author of `The Theory of Differential Equations`, (c) 2010, Universitext. Current research interests include dynamic equations on time scales, fractional calculus, difference equations, and differential equations.
Christopher Goodrich is currently a mathematics instructor at the Creighton Preparatory School in Omaha, Nebraska.

Rogawski, Jonathan D., Lubotzky, Alex
Discrete Groups, Expanding Graphs and Invariant Measures
Birkhäuser Basel
Seiten xi,196
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9783034603317
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In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.

Gelfand, Israel M., Kapranov, Mikhail, Zelevinsky, Andrei
Discriminants, Resultants, and Multidimensional Determinants
Birkhäuser Boston
Seiten x,523
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9780817647704
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`This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory.`—Mathematical Reviews


Jones, Gareth A., Jones, Josephine M.
Elementary Number Theory
Springer London
Seiten xiv,302
Erscheinungsjahr 1998
Einband: Softcover
ISBN 9783540761976
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18.18
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An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat`s Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

Cardin, Franco
Elementary Symplectic Topology and Mechanics
Springer International Publishing
Seiten xvii,222
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319110257
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This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré`s last geometric theorem and the Arnol`d conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.

Stillwell, John
Elements of Algebra
Geometry, Numbers, Equations
Springer New York
Seiten xii,184
Erscheinungsjahr 1994
Einband: Hardcover
ISBN 9780387942902
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Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge­ bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.

Stillwell, John
Elements of Algebra
Geometry, Numbers, Equations
Springer New York
Seiten xii,184
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9781441928399
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Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge­ bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.

Mavron, Vassilis C., Phillips, Timothy N.
Elements of Mathematics for Economics and Finance
Springer London
Seiten x,312
Erscheinungsjahr 2007
Einband: Softcover
ISBN 9781846285608
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This book equips undergraduates with the mathematical skills required for degree courses in economics, finance, management, and business studies. The fundamental ideas are described in the simplest mathematical terms, highlighting threads of common mathematical theory in the various topics. Coverage helps readers become confident and competent in the use of mathematical tools and techniques that can be applied to a range of problems.

Vass Mavron is Professor of Mathematics in the Institute of Mathematical and Physical Sciences at the University of Wales Aberystwyth. Tim Phillips is Professor of Mathematics and Professorial Fellow in the School of Mathematics at Cardiff University.


Stillwell, John
Elements of Number Theory
Springer New York
Seiten xii,256
Erscheinungsjahr 2003
Einband: Hardcover
ISBN 9780387955872
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Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.


Stillwell, John
Elements of Number Theory
Springer New York
Seiten xii,256
Erscheinungsjahr 2003
Einband: Softcover
ISBN 9781441930668
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Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.


Gilbarg, David, Trudinger, Neil S.
Elliptic Partial Differential Equations of Second Order
Springer Berlin Heidelberg
Seiten xiii,518
Erscheinungsjahr 2001
Einband: Softcover
ISBN 9783540411604
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From the reviews: `This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student.` --New Zealand Mathematical Society, 1985

Biography of David Gilbarg

David Gilbarg was born in New York in 1918, and was educated there through udergraduate school. He received his Ph.D. degree at Indiana University in 1941. His work in fluid dynamics during the war years motivated much of his later research on flows with free boundaries. He was on the Mathematics faculty at Indiana University from 1946 to 1957 and at Stanford University from 1957 on. His principal interests and contributions have been in mathematical fluid dynamics and the theory of elliptic partial differential equations.

Biography of Neil S. Trudinger

Neil S. Trudinger was born in Ballarat, Australia in 1942. After schooling and undergraduate education in Australia, he completed his PhD at Stanford University, USA in 1966. He has been a Professor of Mathematics at the Australian National University, Canberra since 1973. His research contributions, while largely focussed on non-linear elliptic partial differential equations, have also spread into geometry, functional analysis and computational mathematics. Among honours received are Fellowships of the Australian Academy of Science and of the Royal Society of London.


Goodwine, Bill
Engineering Differential Equations
Theory and Applications
Springer New York
Seiten xix,745
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9781489981677
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This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.

Goodwine, Bill
Engineering Differential Equations
Theory and Applications
Springer New York
Seiten xix,745
Erscheinungsjahr 2011
Einband: Hardcover
ISBN 9781441979186
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This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.

O`Reilly, Oliver M.
Engineering Dynamics
A Primer
Springer New York
Seiten x,240
Erscheinungsjahr 2010
Einband: Softcover
ISBN 9781441963598
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This Primer is intended to provide the theoretical background for the standard undergraduate, mechanical engineering course in dynamics. The book contains several worked examples and summaries and exercises at the end of each chapter to aid readers in their understanding of the material. Teachers who wish to have a source of more detailed theory for the course, as well as graduate students who need a refresher course on undergraduate dynamics when preparing for certain first year graduate school examinations, and students taking the course will find the work very helpful.

Caspard, Nathalie, Leclerc, Bruno, Monjardet, Bernard
Ensembles ordonnés finis : concepts, résultats et usages
Springer Berlin Heidelberg
Seiten xviii,342
Erscheinungsjahr 2007
Einband: Softcover
ISBN 9783540737551
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Les buts principaux de cet ouvrage qui comble un vide sont de :

- donner les concepts et résultats fondamentaux sur les ensembles ordonnés finis,

- présenter leurs usages dans des domaines variés (de la RO ou l’IA à la micro-économie),

- signaler un certain nombre de résultats et de recherches en cours.


Einsiedler, Manfred, Ward, Thomas
Ergodic Theory
with a view towards Number Theory
Springer London
Seiten xvii,481
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9781447125914
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This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl`s polynomial equidistribution theorem, the ergodic proof of Szemeredi`s theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.


Einsiedler, Manfred, Ward, Thomas
Ergodic Theory
with a view towards Number Theory
Springer London
Seiten xvii,481
Erscheinungsjahr 2011
Einband: Hardcover
ISBN 9780857290205
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This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl`s polynomial equidistribution theorem, the ergodic proof of Szemeredi`s theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.


Griffiths, David F., Dold, John W., Silvester, David J.
Essential Partial Differential Equations
Analytical and Computational Aspects
Springer International Publishing
Seiten xi,368
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319225685
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This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods.

Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems.

The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors.

Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engi

neering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.

John Dold is a professor of applied mathematics, having trained in physics, mathematics and (briefly) history. Apart from some purely experimental studies, particularly of fire behaviour, his research primarily makes use of partial differential equations to model practical problems, including water waves and combustion phenomena. He founded the journal Combustion Theory and Modelling and he has organised or helped to organise major conferences on combustion research. In his teaching of mathematical methods and their application to various physical phenomena he has written a number of coursework texts. One of these has been expanded and improved to create the current volume.

David Griffiths trained originally as an applied mathematician and has spent his academic career as a numerical analyst at the University of Dundee specialising in the numerical solution of partial differential equations. He taught the subject at both undergraduate and postgraduate levels for many years and published over 50 scientific articles on finite difference and finite element methods. He has previously published two textbooks on finite difference methods for ordinary and partial differential equations. David was joint organising secretary of the Dundee Biennial Conferences on Numerical Analysis from 1983 to 2005. He was awarded a “Certificate of Recognition” from NASA in both 1991 and 1993 for his work on spurious solutions that can arise from approximations of nonlinear differential equat

ions.

David Silvester is a Professor in the School of Mathematics at The University of Manchester. His research concerns numerical solution of partial differential equations, computational fluid dynamics, uncertainty quantification, and high performance computing. He received his doctorate in mathematics from the University of Manchester Institute of Science and Technology in 1984 and has had visiting positions at Stanford University, the University of Maryland at College Park, and the Université du Littoral, France. He has served on the editorial boards of SIAM Journal on Scientific Computing and the International Journal for Numerical Methods in Fluids.


Kubrusly, Carlos S.
Essentials of Measure Theory
Springer International Publishing
Seiten xiii,279
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319225050
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Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgue integral are presented as an important particular case of general theory. Part II of the text is more advanced and is addressed to a more experienced reader. The material is designed to cover another one-semester graduate course subsequent to a first course, dealing with measure and integration in topological spaces.

The final section of each chapter in Part I presents problems that are integral to each chapter, the majority of which consist of auxiliary results, extensions of the theory, examples, and counterexamples. Problems which are highly theoretical have accompanying hints. The last section of each chapter of Part II consists of Additional Propositions containing auxiliary and complementary results. The entire book contains collections of suggested readings at the end of each chapter in order to highlight alternate approaches, proofs, and routes toward additional results.

With modest prerequisites, this text is intended to meet the needs of a contemporary course in measure theory for mathematics students and is also accessible to a wider student audience, namely those in statistics, economics, engineering, and physics. Part I may be also accessible to advanced undergraduates who fulfill the prerequisites which include an introductory course in analysis, linear algebra (Chapter 5 only), and elementary set theory.

Carlos S. Kubrusly is currently a professor in the electrical engineering department at the Catholic University of Rio de Janeiro. His current area of research is in operator theory and functional analysis. Over the years, the results of his Work have been published in over 40 journals, 6 monographs/textbooks, and 2 contributed volumes. From 1992-1998 Carlos Kubrusly was the editor-in-chief of the Computational and Applied Mathematics journal which was then co-published with Birkhauser Boston.

Specht, Edward John, Jones, Harold Trainer, Calkins, Keith G., Rhoads, Donald H.
Euclidean Geometry and its Subgeometries
Springer International Publishing
Seiten xix,527
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319237749
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In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties.
There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online covering construction of complex numbers, arc length, the circular functions, angle measure, and the polygonal form of the Jordan Curve theorem.
Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well. It can be regarded as a completion, updating, and expansion of Hilbert`s work, filling a gap in the existing literature.

Petersen, T. Kyle
Eulerian Numbers
Springer New York
Seiten xviii,456
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9781493930906
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This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group.

The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions.

The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology.

This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.?

T. Kyle Petersen is an Associate Professor of Mathematics at DePaul University, Chicago, USA.  His research areas include algebraic, enumerative, and topological combinatorics.  He received his PhD in Mathematics from Brandeis University.

Shonkwiler, Ronald W., Mendivil, Franklin
Explorations in Monte Carlo Methods
Springer New York
Seiten xii,243
Erscheinungsjahr 2009
Einband: Hardcover
ISBN 9780387878362
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Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems.

Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.

Ronald Shonkwiler is also publishing Mathematical Biology: An Introduction with Maple and Matlab, that will will be available in 2008. He is professor emeritus at Georgia Institute of Technology School of Mathematics. He received his PhD in 1970. His areas of expertise include: stochastic processes, optimization, computer simulation, Monte Carlo numerical methods, mathematical biology, and reproducing Kernel Hilbert spaces.

Franklin Mendevil is a professor at Acadia University in Nova Scotia. He received his PhD in 1996 at Georgia Institute of Technology. He has co-authored numerous papers and publications, several of which were with Dr. Shonkwiler.


Shonkwiler, Ronald W., Mendivil, Franklin
Explorations in Monte Carlo Methods
Springer New York
Seiten xii,243
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9781489983794
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Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems.

Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.

Ronald Shonkwiler is also publishing Mathematical Biology: An Introduction with Maple and Matlab, that will will be available in 2008. He is professor emeritus at Georgia Institute of Technology School of Mathematics. He received his PhD in 1970. His areas of expertise include: stochastic processes, optimization, computer simulation, Monte Carlo numerical methods, mathematical biology, and reproducing Kernel Hilbert spaces.

Franklin Mendevil is a professor at Acadia University in Nova Scotia. He received his PhD in 1996 at Georgia Institute of Technology. He has co-authored numerous papers and publications, several of which were with Dr. Shonkwiler.


de Haan, Laurens, Ferreira, Ana
Extreme Value Theory
An Introduction
Springer New York
Seiten xviii,418
Erscheinungsjahr 2006
Einband: Hardcover
ISBN 9780387239460
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Focuses on theoretical results along with applications

All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion

Concentration is on the probabilistic and statistical aspects of extreme values

Excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity


de Haan, Laurens, Ferreira, Ana
Extreme Value Theory
An Introduction
Springer New York
Seiten xviii,418
Erscheinungsjahr 2006
Einband: Softcover
ISBN 9781441920201
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Focuses on theoretical results along with applications

All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion

Concentration is on the probabilistic and statistical aspects of extreme values

Excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity


Akiyama, Jin, Kano, Mikio
Factors and Factorizations of Graphs
Proof Techniques in Factor Theory
Springer Berlin Heidelberg
Seiten xii,353
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9783642219184
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This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

Audin, Michèle
Fatou, Julia, Montel,
le grand prix des sciences mathématiques de 1918, et après...
Springer Berlin Heidelberg
Seiten vi,276
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9783642004452
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Comment Fatou et Julia ont inventé ce que l’on appelle aujourd’hui les ensembles de Julia, avant, pendant et après la première guerre mondiale? L’histoire est racontée, avec ses mathématiques, ses conflits, ses personnalités. Elle est traitée à partir de sources nouvelles, et avec rigueur. On pourra s’y initier à l’itération des fractions rationnelles et à la dynamique complexe (ensembles de Julia, de Mandelbrot, ensembles-limites). Qui étaient Pierre Fatou, Gaston Julia, Paul Montel? On y trouvera en particulier des informations sur un mathématicien mal connu, Pierre Fatou. On découvrira aussi quelques incidences de la blessure reçue par Julia pendant la guerre sur la vie mathématique en France au vingtième siècle.

How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources.Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the serious injury of Julia during WWI influence mathematical life in France?

Michèle Audin is professor at Strasbourg (Université Louis Pasteur). She uses to lecture on geometry all university levels, but also happens to teach various topics, such as complex analysis, Galois theory or algebraic topology.

As a researcher, she is a specialist of symplectic geometry, a subject on which she has published research articles and a few books, especially on spinning tops and integrable systems.


Agarwal, Ravi P., KARAPINAR, Erdal, O’Regan, Donal, Roldán-López-de-Hierro, Antonio Francisco
Fixed Point Theory in Metric Type Spaces
Springer International Publishing
Seiten xvii,385
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319240800
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Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology.

The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework.

Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed point theory is an important area of study in pure and applied mathematics and it is a flourishing area of research.
Ravi P. Agarwal
Department of Mathematics
Texas A&M University
Kingsville, Texas
USA

Erdal Karap?nar 
At?l?m University
Department of Mathematics
K?z?lça?ar Köyü
06836 ?ncek ANKARA
Turkey 

Donal O’Regan 
Department of Mathematics
University of Galway
Galway
Ireland

Antonio F. Roldán-López-de-Hierro
Department of Mathematics
University of Granada
Granada

Ratcliffe, John
Foundations of Hyperbolic Manifolds
Springer New York
Seiten xii,782
Erscheinungsjahr 2006
Einband: Hardcover
ISBN 9780387331973
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This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.


Ratcliffe, John
Foundations of Hyperbolic Manifolds
Springer New York
Seiten xii,782
Erscheinungsjahr 2006
Einband: Softcover
ISBN 9781441922021
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This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.


Pedersen, Steen
From Calculus to Analysis
Springer International Publishing
Seiten xix,342
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319381367
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This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers. In addition to the standard results of advanced calculus, the book contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section.
Steen Pedersen, Ph.D. is a Professor of Mathematics at Wright State University in Dayton, Ohio, USA.  His research interests include fractals, metric geometry, fourier analysis, spectral theory, and operator algebras.

Pedersen, Steen
From Calculus to Analysis
Springer International Publishing
Seiten xix,342
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319136400
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This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers. In addition to the standard results of advanced calculus, the book contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section.
Steen Pedersen, Ph.D. is a Professor of Mathematics at Wright State University in Dayton, Ohio, USA.  His research interests include fractals, metric geometry, fourier analysis, spectral theory, and operator algebras.

Lytton, William W.
From Computer to Brain
Foundations of Computational Neuroscience
Springer New York
Seiten xx,364
Erscheinungsjahr 2002
Einband: Hardcover
ISBN 9780387955285
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Biology undergraduates, medical students and life-science graduate students often have limited mathematical skills. Similarly, physics, math and engineering students have little patience for the detailed facts that make up much of biological knowledge. Teaching computational neuroscience as an integrated discipline requires that both groups be brought forward onto common ground. This book does this by making ancillary material available in an appendix and providing basic explanations without becoming bogged down in unnecessary details. The book will be suitable for undergraduates and beginning graduate students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system.

Lytton, William W.
From Computer to Brain
Foundations of Computational Neuroscience
Springer New York
Seiten xx,364
Erscheinungsjahr 2002
Einband: Softcover
ISBN 9780387955261
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Biology undergraduates, medical students and life-science graduate students often have limited mathematical skills. Similarly, physics, math and engineering students have little patience for the detailed facts that make up much of biological knowledge. Teaching computational neuroscience as an integrated discipline requires that both groups be brought forward onto common ground. This book does this by making ancillary material available in an appendix and providing basic explanations without becoming bogged down in unnecessary details. The book will be suitable for undergraduates and beginning graduate students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system.

Gomes, Jonas, Velho, Luiz
From Fourier Analysis to Wavelets
Springer International Publishing
Seiten xiii,210
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319220741
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This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed.

Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets.  Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable.

This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.


Holden, Helge, Risebro, Nils Henrik
Front Tracking for Hyperbolic Conservation Laws
Springer Berlin Heidelberg
Seiten xiv,517
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783662475065
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This is the second edition of a well-received book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions and the detailed solution of the Riemann problem for the Euler equations.

Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included.

From the reviews of the first edition:

`It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style.` D. Serre, MathSciNet

`I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course.` S. Noelle, Book review, German Math. Soc.

`Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws.` M. Laforest, Comp. Phys. Comm.

Helge Holden is professor of mathematics at the Norwegian University of Science and Technology and an adjunct professor at the Center of Mathematics for Applications, part of the University of Oslo.  He has done extensive research in stochastic analysis, in particular in its application to flow in porous media.

Nils Henrik Risebro is professor of mathematics at the University of Oslo. His research interests are mainly nonlinear partial differential equations and numerical methods for these. He has also worked on conservation laws with discontinuous coefficients in a variety of applications.


Yosida, Kosaku
Functional Analysis
Springer Berlin Heidelberg
Seiten xvi,504
Erscheinungsjahr 1995
Einband: Softcover
ISBN 9783540586548
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The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo­ logical Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SOBOLEV and L. SCHWARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathe­ maticians, both pure and applied. The reader may pass, e. g. , from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution). Such materials as `Weak Topologies and Duality in Locally Convex Spaces` and `Nuclear Spaces` are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

Biography of Kôsaku Yosida

Kôsaku Yosida (7.2.1909-20.6.1990) was born in Hiroshima, Japan. After studying mathematics a the University of Tokyo he held posts at Osaka and Nagoya Universities before returning to the University of Tokyo in 1955.

Yosida obtained important and fundamental results in functional analysis and probability. He is best remembered for his joint work with E. Hille which brought forth a theory of semigroups of operators successfully applied to diffusion equations, Markov processes, hyperbolic equations and potential theory. His famous textbook on Functional Analysis was published in 6 distinct editions between 1965 and 1980.


Brezis, Haim
Functional Analysis, Sobolev Spaces and Partial Differential Equations
Springer New York
Seiten xiv,600
Erscheinungsjahr 2011
Einband: Softcover
ISBN 9780387709130
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This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.


Small, Christopher G.
Functional Equations and How to Solve Them
Springer New York
Seiten xii,131
Erscheinungsjahr 2007
Einband: Softcover
ISBN 9780387345390
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Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.


Small, Christopher G.
Functional Equations and How to Solve Them
Springer New York
Seiten xii,131
Erscheinungsjahr 2007
Einband: Hardcover
ISBN 9780387345345
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Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.


Christensen, Ole
Functions, Spaces, and Expansions
Mathematical Tools in Physics and Engineering
Birkhäuser Boston
Seiten xix,266
Erscheinungsjahr 2010
Einband: Hardcover
ISBN 9780817649791
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This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering.

Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.


Ortner, Norbert, Wagner, Peter
Fundamental Solutions of Linear Partial Differential Operators
Theory and Practice
Springer International Publishing
Seiten xii,398
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319201399
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This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions.

The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals.

In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics, for Maxwell’s system and others.

The book mainly addresses researchers and lecturers who work with partial differential equations. However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.


Underwood, Robert G.
Fundamentals of Hopf Algebras
Springer International Publishing
Seiten xiv,150
Erscheinungsjahr 2015
Einband: Softcover
ISBN 9783319189901
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This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras and Hopf algebras. The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author’s 2011 publication, An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary text for a graduate algebra course.  Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields and linearly recursive sequences.

The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforward applications of the theory to problems that are devised to challenge the reader. Questions for further study are provided after selected exercises. Most proofs are given in detail, though a few proofs are omitted since they are beyond the scope of this book.

Robert G. Underwood, MS, PhD, is a professor of Mathematics at Auburn University at Montgomery and author of Introduction to Hopf Algebras © Springer 2011. The author`s course notes which contribute strongly to this present book have been used in his modern algebra class since 2008.

Mariano, Paolo Maria, Galano, Luciano
Fundamentals of the Mechanics of Solids
Springer New York
Seiten xxiii,422
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9781493931323
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This distinctive textbook aims to introduce readers to the basic structures of the mechanics of deformable bodies, with a special emphasis on the description of the elastic behavior of simple materials and structures composed by elastic beams.  The authors take a deductive rather than inductive approach and start from a few first, foundational principles.  A wide selection of exercises, many with hints and solutions, are provided throughout and organized in a way that will allow readers to form a link between abstract mathematical concepts and real-world applications.

The text begins with the definition of bodies and deformations, keeping the kinematics of rigid bodies as a special case; the authors also distinguish between material and spatial metrics, defining each one in the pertinent space.  Subsequent chapters cover observers and classes of possible changes; forces, torques, and related balances, which are derived from the invariance under classical changes in observers of the power of the external actions over a body, rather than postulated a priori; constitutive structures; variational principles in linear elasticity; the de Saint-Venant problem; yield criteria and a discussion of their role in the representation of material behavior; and an overview of some bifurcation phenomena, focusing on the Euler rod.  An appendix on tensor algebra and tensor calculus is included for readers who need a brief refresher on these topics.

Fundamentals of the Mechanics of Solids is primarily intended for graduate and advanced undergraduate students in various fields of engineering and applied mathematics.  Prerequisites include basic courses in calculus, mathematical analysis, and classical mechanics.

Prof. Dr. Paolo Maria Mariano teaches Mechanics of Solids and Theoretical Mechanics in the School of Engineering at the University of Florence. He is also coordinator of the Research Group in Theoretical Mechanics of the Mathematics Research Center “E. De Giorgi” of the Scuola Normale Superiore in Pisa. His research interests cover continuum mechanics of simple and complex materials, thermodynamics, applied calculus of variations, and applied differential geometry.

Prof. Dr. Luciano Galano is a senior researcher in the School of Engineering at the University of Florence, where he teaches Mechanics of Masonry. His research interests cover the mechanics of masonry structures, the dynamics of structures subjected to earthquakes, the mechanics of concrete, and computational mechanics.



Ion, P., Serre, Jean-Pierre
Galois Cohomology
Springer Berlin Heidelberg
Seiten x,211
Erscheinungsjahr 1997
Einband: Hardcover
ISBN 9783540421924
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This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.


Ion, P., Serre, Jean-Pierre
Galois Cohomology
Springer Berlin Heidelberg
Seiten x,211
Erscheinungsjahr 1997
Einband: Softcover
ISBN 9783642638664
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This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.


Rotman, Joseph
Galois Theory
Springer New York
Seiten xiv,176
Erscheinungsjahr 1998
Einband: Softcover
ISBN 9780387985411
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A clear, efficient exposition of this topic with complete proofs and exercises, covering cubic and quartic formulas; fundamental theory of Galois theory; insolvability of the quintic; Galoiss Great Theorem; and computation of Galois groups of cubics and quartics. Suitable for first-year graduate students, either as a text for a course or for study outside the classroom, this new edition has been completely rewritten in an attempt to make proofs clearer by providing more details. It now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups - an analogy which serves to help readers organise the various field theoretic definitions and constructions. The text is rounded off by appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. The exposition has been redesigned so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included.

Weintraub, Steven H.
Galois Theory
Springer New York
Seiten xiv,212
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9780387875743
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Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text `Galois Theory,` and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.

Steven H. Weintraub is a Professor of Mathematics at Lehigh University and author of seven books. This book grew out of a graduate course he taught at Lehigh. He is also the author of Algebra: An Approach via Module Theory (with W. A. Adkins).


Schulz, Andreas S., Skutella, Martin, Stiller, Sebastian, Wagner, Dorothea
Gems of Combinatorial Optimization and Graph Algorithms
Springer International Publishing
Seiten x,150
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9783319249704
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Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory?  Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar?  Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science?  

Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas.  Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks.  

This volume is aimed at readers with some familiarity of combinatorial optimization, and appeals to researchers, graduate students, and advanced undergraduate students alike.

Andreas S. Schulz currently holds a chaired professorship at the Technische Universität München, where he has a joint appointment at the Center for Mathematics and the School of Management. Previously he was Head of the Operations Research and Statistics Group at the Sloan School of the Massachusetts Institute of Technology. His research interests span the theory and practice of mathematical optimization as well as computational economics and algorithmic game theory.
Martin Skutella is full professor in the Department of Mathematics at TU Berlin and member of the Research Center extsc{Matheon}, “Mathematics for Key Technologies,” in Berlin. His main research interests lie in the area of efficient algorithms and combinatorial optimization, in particular in network optimization and scheduling. From 2009 to 2012, he was Editor-in-Chief of the Notices of the German Mathematical Society (DMV). 
Sebastian Stiller is Professor for Mathematical Optimization at TU Braunschweig, Germany. His research interests include robust optimization, game theory, network flows, and scheduling, with applications mainly in traffic, transport, logistics, and real-time systems. 
Dorothea Wagner heads the Institute of Theoretical Informatics at the Karlsruhe Institute of Technology.  Her research interests are in the field of graph algorithms and algorithm engineering with a focus on traffic optimization, social network analysis and network visualization.  She is currently a member of the German Council of Science and Humanities (Wissenschaftsrat) and served previously, for seven years as Vice President of the German Research Foundation (DFG).






Barnes, John
Gems of Geometry
Springer Berlin Heidelberg
Seiten xiii,325
Erscheinungsjahr 2012
Einband: Hardcover
ISBN 9783642309632
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Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author`s infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein`s Theories of Relativity.

 

Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes` book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment.

 

In this second edition, stimulated by recent lectures at Oxford, further material and extra illustrations have been added on many topics including Coloured Cubes, Chaos and Crystals.

Mr Barnes` principal achievements have been in the area of computer programming language design. He designed the language RTL/2 whilst with ICI. This was widely used in the 1970s and 80s for process control in the UK, the Netherlands and South Africa. It still lingers in use in a number of systems (eg the Thames Barrier). He was a member of the Ada language design teams. Ada is widely used in safety critical applications such as those found in defence systems generally, avionics, air traffic control and railroad signalling. He has published eight books: RTL/2 Design and Philosophy, Heyden, 1976. Programming in Ada, Addison-Wesley, 1982. Programming in Ada 95, Addison-Wesley, 1996. High Integrity Ada, Addison-Wesley, 1997. Ada 95 Rationale, Springer-Verlag, 1997. High Integrity Software, Addison-Wesley, 2003. Programming in Ada 2005, Addison-Wesley, 2006. Ada 2005 Rationale, Springer-Verlag, 2008. Programming in Ada went through four editions and was translated into six other languages. Revised versions are entitled Programming in Ada 95 and Programming in Ada 2005. Combined total sales of these books are over 150,000. Mr Barnes has given many lectures and tutorials on various aspects of programming. Although moving towards retirement he still gives occasional lectures including lectures for postgraduate courses at the University of York. He has published many papers, this list gives just two from his early career in ICI, a milestone paper when Ada emerged, and a pair of recent reflective papers. An algorithm for solving non-linear equations based on the secant method, The Computer Journal, vol 8, no 1 (April 1965). A KDF9 Algol list-processing scheme, The Computer Journal, vol 8, no 2 (July 1965). An overview of Ada, Software Practice and Experience, vol 10, pp851-887 (1980). Half a century of programming and not much progress, Software Focus, vol 2, no 1 (2001). Half a century of programming and a spark of light, Software Focus, vol 2, no 2 (2001). Recently, he has rediscovered an interest in mathematics and has given a number of courses at the University of Reading as part of their Continuing Education program.

Hirschfeld, James, Thas, Joseph A.
General Galois Geometries
Springer London
Seiten xvii,409
Erscheinungsjahr 2016
Einband: Hardcover
ISBN 9781447167884
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This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). 

This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. 

General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.
Both authors have been active in the field for about a half century. They have authored several books and several hundreds of papers in international journals; they have also been keynote speakers at numerous international conferences, as well as having organised such conferences. The standard works on Galois geometries and finite generalised quadrangles are due to them as authors or co-authors.
James Hirschfeld was born and brought up in Sydney, and studied at Sydney and Edinburgh. He has been at Sussex since 1966.
Joseph Thas studied at Ghent University, where he has held positions since 1966. He has been a member of the Royal Flemish Academy of Belgium for Science and the Arts since 1988.

Bourbaki, N.
General Topology
Chapters 5–10
Springer Berlin Heidelberg
Seiten iv,363
Erscheinungsjahr 1989
Einband: Softcover
ISBN 9783540645634
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This is the softcover reprint of the 1974 English translation of the later chapters of Bourbaki’s Topologie Generale. Initial chapters study subgroups and quotients of R, real vector spaces and projective spaces, and additive groups Rn. Analogous properties are then studied for complex numbers. Later chapters illustrate the use of real numbers in general topology and discuss various topologies of function spaces and approximation of functions.


Bourbaki, N.
General Topology
Chapters 1-4
Springer Berlin Heidelberg
Seiten vii,437
Erscheinungsjahr 1995
Einband: Softcover
ISBN 9783540642411
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This is the softcover reprint of the 1971 English translation of the first four chapters of Bourbaki’s Topologie Generale. It gives all basics of the subject, starting from definitions. Important classes of topological spaces are studied, and uniform structures are introduced and applied to topological groups. In addition, real numbers are constructed and their properties established.


Krantz, Steven G., Parks, Harold R.
Geometric Integration Theory
Birkhäuser Boston
Seiten xvi,340
Erscheinungsjahr 2008
Einband: Hardcover
ISBN 9780817646769
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This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.


Mumford, David, Fogarty, John, Kirwan, Frances
Geometric Invariant Theory
Springer Berlin Heidelberg
Seiten xiv,294
Erscheinungsjahr 1994
Einband: Hardcover
ISBN 9783540569633
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This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.


Mumford, David, Fogarty, John, Kirwan, Frances
Geometric Invariant Theory
Springer Berlin Heidelberg
Seiten xiv,294
Erscheinungsjahr 1994
Einband: Softcover
ISBN 9783642634000
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80.24
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This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.


Federer, Herbert
Geometric Measure Theory
Springer Berlin Heidelberg
Seiten iv,677
Erscheinungsjahr 1996
Einband: Softcover
ISBN 9783540606567
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26.74
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`This book is a major treatise in mathematics and is essential in the working library of the modern analyst.` (Bulletin of the London Mathematical Society)

Biography of Herbert Federer

Herbert Federer was born on July 23, 1920, in Vienna. After emigrating to the US in 1938, he studied mathematics and physics at the University of California, Berkeley. Affiliated to Brown University, Providence since 1945, he is now Professor Emeritus there.
The major part of Professor Federer`s scientific effort has been directed to the development of the subject of Geometric Measure Theory, with its roots and applications in classical geometry and analysis, yet in the functorial spirit of modern topology and algebra. His work includes more than thirty research papers published between 1943 and 1986, as well as this book.


Fenn, Roger
Geometry
Springer London
Seiten xii,313
Erscheinungsjahr 2001
Einband: Softcover
ISBN 9781852330583
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18.18
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Intended to introduce readers to the major geometrical topics taught at undergraduate level in a manner that is both accessible and rigorous, the author uses world measurement as a synonym for geometry - hence the importance of numbers, coordinates and their manipulation - and has included over 300 exercises, with answers to most of them.

Jost, Jürgen
Geometry and Physics
Springer Berlin Heidelberg
Seiten xiv,217
Erscheinungsjahr 2009
Einband: Softcover
ISBN 9783642420702
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26.74
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`Geometry and Physics` addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.


Jost, Jürgen
Geometry and Physics
Springer Berlin Heidelberg
Seiten xiv,217
Erscheinungsjahr 2009
Einband: Hardcover
ISBN 9783642005404
Yellow Sale Preis
26.74
(inkl. 7% Mwst)
Lieferstatus  
 

`Geometry and Physics` addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.


Cecil, Thomas E., Ryan, Patrick J.
Geometry of Hypersurfaces
Springer New York
Seiten xi,596
Erscheinungsjahr 2015
Einband: Hardcover
ISBN 9781493932450
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64.19
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