Serge Tabachnikov's Books

Kvant Selecta: Algebra and Analysis, I

Algebra and Analysis, I

By: Serge Tabachnikov

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Kvant Selecta: Algebra and Analysis, I

Algebra and Analysis, I

By: Serge Tabachnikov

This volume contains translated articles originally published from 1970 to 1990 in the Russian journal "Kvant." The influence of this magazine on mathematics and physics education in Russia is unmatched. This volume initiates a collection that represents the Russian tradition of expository mathematical writing at its best. Written by leading Russian mathematicians and expositors, these articles present mathematics in a conceptual, entertaining, and accessible way. This volume is designed for students and teachers who love mathematics, and can expand on local school curriculum subjects. This first volume addresses various topics in number theory.

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Page Count

172

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821810022

ISBN 13

9780821810026

Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

D.B. Fuchs' 60th anniversary collection

By: Alexander Astashkevich,Serge Tabachnikov

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Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

D.B. Fuchs' 60th anniversary collection

By: Alexander Astashkevich,Serge Tabachnikov

This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs, and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics.

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Page Count

362

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082182032X

ISBN 13

9780821820322

Geometry and Billiards

By: Serge Tabachnikov

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Geometry and Billiards

By: Serge Tabachnikov

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. Topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course. Minimum prerequisites are the standard material covered in the first two years of college mathematics (the entire calculus sequence, linear algebra). However, readers should show some mathematical maturity and rely on their mathematical common sense. A unique feature of the book is the coverage of many diverse topics related to billiards, for example, evolutes and involutes of plane curves, the four-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincare recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others. There are approximately 100 illustrations. The book is suitable for advanced undergraduates, graduate students, and researchers interested in ergodic theory and geometry. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State.

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Page Count

192

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839195

ISBN 13

9780821839195

Mathematical Omnibus

Thirty Lectures on Classic Mathematics

By: D. B. Fuks,Serge Tabachnikov

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Mathematical Omnibus

Thirty Lectures on Classic Mathematics

By: D. B. Fuks,Serge Tabachnikov

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

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Page Count

482

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821843168

ISBN 13

9780821843161

Kvant Selecta: Combinatorics, I

Combinatorics, I

By: Serge Tabachnikov

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Kvant Selecta: Combinatorics, I

Combinatorics, I

By: Serge Tabachnikov

This volume is a collection of articles translated from Russian editions of the journal "Kvant"--T.p. verso.

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Page Count

148

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821821717

ISBN 13

9780821821718

American Mathematical Society Translations

By: American Mathematical Society

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American Mathematical Society Translations

By: American Mathematical Society

Translations of articles on mathematics appearing in various Russian mathematical serials.

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Page Count

304

Published Date

ISBN 10

0821813544

ISBN 13

9780821813546

Geometry and Billiards

By: Serge Tabachnikov

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Geometry and Billiards

By: Serge Tabachnikov

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Page Count

192

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839195

ISBN 13

9780821839195

Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

D.B. Fuchs' 60th anniversary collection

By: Alexander Astashkevich,Serge Tabachnikov

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Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

D.B. Fuchs' 60th anniversary collection

By: Alexander Astashkevich,Serge Tabachnikov

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Page Count

362

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082182032X

ISBN 13

9780821820322

Differential and Symplectic Topology of Knots and Curves

By: Serge Tabachnikov

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Differential and Symplectic Topology of Knots and Curves

By: Serge Tabachnikov

This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory ("quantum" knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is its international significance. The volume successfully embodies a fine collaborative effort by worldwide experts from Belgium, France, Germany, Israel, Japan, Poland, Russia, Sweden, the UK, and the US.

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Page Count

530

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821813544

ISBN 13

9780821813546

ARNOLD: Swimming Against the Tide

Swimming Against the Tide

By: Boris A. Khesin,Serge L. Tabachnikov

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ARNOLD: Swimming Against the Tide

Swimming Against the Tide

By: Boris A. Khesin,Serge L. Tabachnikov

Vladimir Arnold, an eminent mathematician of our time, is known both for his mathematical results, which are many and prominent, and for his strong opinions, often expressed in an uncompromising and provoking manner. His dictum that "Mathematics is a part of physics where experiments are cheap" is well known. This book consists of two parts: selected articles by and an interview with Vladimir Arnold, and a collection of articles about him written by his friends, colleagues, and students. The book is generously illustrated by a large collection of photographs, some never before published. The book presents many a facet of this extraordinary mathematician and man, from his mathematical discoveries to his daredevil outdoor adventures.

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Page Count

221

Publisher

American Mathematical Society

Published Date

ISBN 10

1470416999

ISBN 13

9781470416997

Kvant Selecta: Algebra and Analysis, II

Algebra and Analysis

By: Serge Tabachnikov

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Kvant Selecta: Algebra and Analysis, II

Algebra and Analysis

By: Serge Tabachnikov

This volume and Kvant Selecta: Algebra and Analysis, I (MAWRLD/14) are the first volumes of articles published from 1970 to 1990 in the Russian journal, Kvant. The influence of this magazine on mathematics and physics education in Russia is unmatched. This collection represents the Russian tradition of expository mathematical writing at its best. Articles selected for these two volumes are written by leading Russian mathematicians and expositors. Some articles contain classical mathematical gems still used in university curriculae today. Others feature cutting-edge research from the 20th Century. The articles in these books are written so as to present genuine mathematics in a conceptual, entertaining, and accessible way. The volumes are designed to be used by students and teachers who love mathematics and want to study its various aspects, thus deepening and expanding the school curriculum. The articles in the first volume are mainly devoted to various topics in number theory, whereas the second volume treats diverse aspects of analysis and algebra.

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Page Count

177

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821819151

ISBN 13

9780821819159

Book's by Serge Tabachnikov

Kvant Selecta: Algebra and Analysis, I

Kvant Selecta: Algebra and Analysis, I

Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

Geometry and Billiards

Geometry and Billiards

Mathematical Omnibus

Mathematical Omnibus

Kvant Selecta: Combinatorics, I

Kvant Selecta: Combinatorics, I

American Mathematical Society Translations

American Mathematical Society Translations

Geometry and Billiards

Geometry and Billiards

Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

Differential and Symplectic Topology of Knots and Curves

Differential and Symplectic Topology of Knots and Curves

ARNOLD: Swimming Against the Tide

ARNOLD: Swimming Against the Tide

Kvant Selecta: Algebra and Analysis, II

Kvant Selecta: Algebra and Analysis, II

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