Alex Kasman's Books

Glimpses of Soliton Theory

The Algebra and Geometry of Nonlinear PDEs, Second Edition

By: Alex Kasman

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Glimpses of Soliton Theory

The Algebra and Geometry of Nonlinear PDEs, Second Edition

By: Alex Kasman

This book challenges and intrigues from beginning to end. It would be a treat to use for a capstone course or senior seminar. —William J. Satzer, MAA Reviews on Glimpses of Soliton Theory (First Edition) Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena like rogue waves and DNA transcription. Solitons of light are even used by engineers for data transmission and optical switches. Furthermore, unlike most nonlinear partial differential equations, soliton equations have the remarkable property of being exactly solvable. Explicit solutions to those equations provide a rare window into what is possible in the realm of nonlinearity. Glimpses of Soliton Theory reveals the hidden connections discovered over the last half-century that explain the existence of these mysterious mathematical objects. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra, the book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass $wp$-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Hierarchy, and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make the subject accessible to undergraduates, numerous worked examples and thought-provoking exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of Mathematica® to facilitate computation and animate solutions. The second edition refines the exposition in every chapter, adds more homework exercises and projects, updates references, and includes new examples involving non-commutative integrable systems. Moreover, the chapter on KdV multisolitons has been greatly expanded with new theorems providing a thorough analysis of their behavior and decomposition.

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Page Count

366

Publisher

American Mathematical Society

Published Date

ISBN 10

1470472627

ISBN 13

9781470472627

The Bispectral Problem

By: John P. Harnad,Alex Kasman

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The Bispectral Problem

By: John P. Harnad,Alex Kasman

Comprises 16 papers from the March 1997 meeting on the subject in Montreal. The focus is on the search for solutions to eigenvalue problems that satisfy additional equations in the spectral parameter such as pairs of eigenvalue equations. Among the topics: automorphisms of the weyl algebra and bispectral operators, Huygens Principle, beyond the classical orthogonal polynomials, dual isomonodromic deformations, Darboux transformations, explicit formulas for the Airy and Bessel bispectral involutions in terms of Calogero-Moser pairs, Baker-Akhiezer functions and the bispectral problem in many dimensions, and the geometry of spinors and the multicomponent BKP and DKP hierarchies. Annotation copyrighted by Book News, Inc., Portland, OR

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Page Count

245

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821809490

ISBN 13

9780821809495

The Erdos Distance Problem

By: Julia Garibaldi,Alex Iosevich,Steven Senger

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The Erdos Distance Problem

By: Julia Garibaldi,Alex Iosevich,Steven Senger

Introduces the reader to the techniques, ideas, and consequences related to the Erdős problem. The authors introduce these concepts in a concrete and elementary way that allows a wide audience to absorb the content and appreciate its far-reaching implications. In the process, the reader is familiarized with a wide range of techniques from several areas of mathematics and can appreciate the power of the resulting symbiosis.

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Page Count

166

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821852817

ISBN 13

9780821852811

Introduction to Representation Theory

By: Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina

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Introduction to Representation Theory

By: Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

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Page Count

240

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853511

ISBN 13

9780821853511

A Millennium of Buddhist Logic

By: Alex Wayman

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A Millennium of Buddhist Logic

By: Alex Wayman

This is volume One of texts (from sanskrit and Tibetan sources) of the two planned volumes on Buddhist Ligic (the second volume to be on topics and opponents). This first volumes is in two parts. Part 1 has Asanga`s rules of Debate, Dharmakirti Nyayabindu with Kamalasila commentary and Santi-pa`s treatise on inner pervasion. Part II devoted to the Dignage-Dharmakirti system has five sets of eleven verses then a stydy if Bu-Ston`s commentary ib Dharmakirti`s Pramanaviniscaya and finally Tsong-kha-pa;s Mun sel on the seven books of Dharmakirti.

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Page Count

392

Publisher

Motilal Banarsidass Publ.

Published Date

ISBN 10

8120816463

ISBN 13

9788120816466

Glimpses of Soliton Theory

The Algebra and Geometry of Nonlinear PDEs, Second Edition

By: Alex Kasman

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Glimpses of Soliton Theory

The Algebra and Geometry of Nonlinear PDEs, Second Edition

By: Alex Kasman

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Solve jigsaw puzzle

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Page Count

366

Publisher

American Mathematical Society

Published Date

ISBN 10

1470472627

ISBN 13

9781470472627

Glimpses of Soliton Theory

The Algebra and Geometry of Nonlinear PDEs

By: Alex Kasman

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Glimpses of Soliton Theory

The Algebra and Geometry of Nonlinear PDEs

By: Alex Kasman

Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass -functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Equation and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make this advanced subject accessible to any undergraduate math major, numerous worked examples and thought-provoking but not overly-difficult exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of the software package Mathematica« to facilitate computation and to animate the solutions under study. This book provides the reader with a unique glimpse of the unity of mathematics and could form the basis for a self-study, one-semester special topics, or "capstone" course.

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Page Count

322

Publisher

American Mathematical Soc.

ISBN 10

0821884700

ISBN 13

9780821884706

The Bispectral Problem

By: John P. Harnad,Alex Kasman

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The Bispectral Problem

By: John P. Harnad,Alex Kasman

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Solve jigsaw puzzle

Age

Page Count

245

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821809490

ISBN 13

9780821809495

Book's by Alex Kasman

Glimpses of Soliton Theory

Glimpses of Soliton Theory

The Bispectral Problem

The Bispectral Problem

The Erdos Distance Problem

The Erdos Distance Problem

Introduction to Representation Theory

Introduction to Representation Theory

A Millennium of Buddhist Logic

A Millennium of Buddhist Logic

Glimpses of Soliton Theory

Glimpses of Soliton Theory

Glimpses of Soliton Theory

Glimpses of Soliton Theory

The Bispectral Problem

The Bispectral Problem

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