# Publication list for Tabachnikov, Serge

## Latest Titles

• Base Product Code Keyword List: mbk; MBK; mbk/86; MBK/86; mbk-86; MBK-86
Print Product Code: MBK/86
Online Product Code: MBK/86.E
Title (HTML): ARNOLD: Swimming Against the Tide
Author/Editor Label (optional): Edited by
Author(s) (Product display): Boris A. Khesin; Serge L. Tabachnikov
Affiliation(s) (HTML): University of Toronto, Toronto, Ontario, Canada; ICERM, Brown University, Providence, RI and Pennsylvania State University, State College, PA
Abstract:

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.

Publication Month and Year: 2014-09-10
Page Count: 224
Cover Type: Softcover
Print ISBN-13: 978-1-4704-1699-7
Online ISBN 13: 978-1-4704-1934-9
Primary MSC: 01
Textbook?: False
Applied Math?: False
Sample?: true
Reference?: false
Electronic Media?: False
SXG Subject: GI
Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/mbk-86
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Mathematicians of all levels: teachers, researchers, graduate and undergraduate students, and other scientists interested in the recent history and ideology of mathematics.

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• Base Product Code Keyword List: mbk; MBK; mbk/46; MBK/46; mbk-46; MBK-46
Print Product Code: MBK/46
Online Product Code: MBK/46.E
Title (HTML): Mathematical Omnibus: Thirty Lectures on Classic Mathematics
Author(s) (Product display): Dmitry Fuchs; Serge Tabachnikov
Affiliation(s) (HTML): University of California, Davis, CA; Pennsylvania State University, University Park, PA
Abstract:

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 award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

Publication Month and Year: 2007-10-10
Page Count: 463
Cover Type: Hardcover
Print ISBN-13: 978-0-8218-4316-1
Online ISBN 13: 978-1-4704-1812-0
Primary MSC: 00
Textbook?: False
Applied Math?: False
Sample?: false
Reference?: false
Electronic Media?: False
SXG Subject: GI
Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/mbk-46
Online Price 1 Label: List
Online Price 1: 65.00
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Print Price 1: 65.00
Online Price 2 Label: Individual Member
Online Price 2: 52.00
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Print Price 2: 52.00
Print Add to Cart URL: /some/url/at/AMS/MBK-46
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Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1812-0&pisbn=978-0-8218-4316-1&epc=MBK/46.E&ppc=MBK/46&title=Mathematical%20Omnibus%3A%20Thirty%20Lectures%20on%20Classic%20Mathematics&author=Dmitry%20Fuchs%3B%20Serge%20Tabachnikov&type=R

Reviews:

The authors manage to breathe new life into topics that at first glance appear to be old hat.

MAA Reviews

This is an enjoyable book with suggested uses ranging from a text for a undergraduate Honors Mathematics Seminar to a coffee table book. It is appropriate for either It could also be used as a starting point for undergraduate research topics or a place to find a short undergraduate seminar talk. This is a wonderful book that is not only fun to read, but gives the reader new ideas to think about.

Dmitry Fuchs and Serge Tabachnikov display impeccable taste in their choice of the material, level of exposition, and the balance between concrete and more conceptual mathematical themes. Each of the thirty lectures tells a unique mathematical story, each with a display of mathematical narrative art, with great care for the details, revealing masters of their craft at work. Both novice and more experienced readers will find many pleasant surprises at all levels of exposition. ...[A] book suitable for such a noble and demanding goal to serve as an introduction to the world of 'serious mathematics' for new generations of mathematicians. ...[E]very page has one or more diagrams, graphs, and pictures illustrating the material. ...[T]he special artistic spirit and atmosphere the book owes to numerous, witty, humorous, and mysterious illustrations of the artist Sergey Ivanov. Without much exaggeration, one may say that these provocative, yet mathematically correct drawings can alone serve as a layman's guide to the beauty and mystery of mathematics. Summarizing, we can say that Mathematical Omnibus is a 'desert island book,' a 'coffee table book,' a book to share with friends, colleagues, and students, a gift for a beginner and an expert alike. In short, it is a wonderful addition to our personal, school, and university libraries.

-- Rade T. Zivaljevic, The American Mathematical Monthly

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• Base Product Code Keyword List: stml; STML; stml/30; STML/30; stml-30; STML-30
Print Product Code: STML/30
Online Product Code: STML/30.E
Title (HTML): Geometry and Billiards
Author(s) (Product display): Serge Tabachnikov
Affiliation(s) (HTML): Penn State, University Park, PA
Abstract:

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 Poincaré 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 book is published in cooperation with Mathematics Advanced Study Semesters

Book Series Name: Student Mathematical Library
Volume: 30
Publication Month and Year: 2005-09-28
Page Count: 176
Cover Type: Softcover
Print ISBN-13: 978-0-8218-3919-5
Online ISBN 13: 978-1-4704-2141-0
Print ISSN: 1520-9121
Online ISSN: 1520-9121
Primary MSC: 37; 51
Secondary MSC: 49; 70; 78
Textbook?: False
Applied Math?: False
Electronic Media?: False
Publisher (non-AMS): Published in cooperation with Mathematics Advanced Study Semesters
SXG Subject: GT; DE
Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/stml-30
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Online Price 1: 41.00
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Print Add to Cart URL: /some/url/at/AMS/STML-30
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Reviews:

(This book) is very well written, with nice illustrations. The author presents the results very clearly, with interesting digressions and he mentions applications of billiards to various fields.

-- Zentralblatt MATH

• Base Product Code Keyword List: mass; MASS
Print Product Code: MASS
Online Product Code: MASS.E
Author/Editor Label (optional): Edited by
Author(s) (Product display): Svetlana Katok; Alexei Sossinsky; Serge Tabachnikov
Affiliation(s) (HTML): Pennsylvania State University, University Park, PA; Pennsylvania State University, University Park, PA; Pennsylvania State University, University Park, PA
Publisher Blurb: Mathematics Advanced Study Semesters
Abstract:

This book results from a unique and innovative program at Pennsylvania State University. Under the program, the “best of the best” students nationwide are chosen to study challenging mathematical areas under the guidance of experienced mathematicians. This program, Mathematics Advanced Study Semesters (MASS), offers an unparalleled opportunity for talented undergraduate students who are serious in the pursuit of mathematical knowledge.

This volume represents various aspects of the MASS program over its six-year existence, including core courses, summer courses, students' research, and colloquium talks. The book is most appropriate for college professors of mathematics who work with bright and eager undergraduate and beginning graduate students, for such students who want to expand their mathematical horizons, and for everyone who loves mathematics and wants to learn more interesting and unusual material.

The first half of the book contains lecture notes of nonstandard courses. A text for a semester-long course on $$p$$-adic analysis is centered around contrasts and similarities with its real counterpart. A shorter text focuses on a classical area of interplay between geometry, algebra and number theory (continued fractions, hyperbolic geometry and quadratic forms). Also provided are detailed descriptions of two innovative courses, one on geometry and the other on classical mechanics. These notes constitute what one may call the skeleton of a course, leaving the instructor ample room for innovation and improvisation.

The second half of the book contains a large collection of essays on a broad spectrum of exciting topics from Hilbert's Fourth Problem to geometric inequalities and minimal surfaces, from mathematical billiards to fractals and tilings, from unprovable theorems to the classification of finite simple groups and lexicographic codes.

Publication Month and Year: 2003-05-13
Page Count: 313
Cover Type: Hardcover
Print ISBN-13: 978-0-8218-3363-6
Online ISBN 13: 978-1-4704-2491-6
Online ISSN:
Primary MSC: 00
Textbook?: False
Applied Math?: False
Electronic Media?: False
SXG Subject: GI
Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/mass
Online Price 1 Label: List
Online Price 1: 69.00
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Professors of mathematics; general mathematical audience.

• Base Product Code Keyword List: mawrld; MAWRLD; mawrld/17; MAWRLD/17; mawrld-17; MAWRLD-17
Print Product Code: MAWRLD/17
Title (HTML): Kvant Selecta: Combinatorics, I
Author/Editor Label (optional): Edited by
Author(s) (Product display): Serge Tabachnikov
Affiliation(s) (HTML): University of Arkansas at Fayetteville, Fayetteville, AR
Abstract:

There is a tradition in Russia that holds that mathematics can be both challenging and fun. One fine outgrowth of that tradition is the magazine, Kvant, which has been enjoyed by many of the best students since its founding in 1970. The articles in Kvant assume only a minimal background, that of a good high school student, yet are capable of entertaining mathematicians of almost any level. Sometimes the articles require careful thought or a moment's work with a pencil and paper. However, the industrious reader will be generously rewarded by the elegance and beauty of the subjects.

This book is the third collection of articles from Kvant to be published by the AMS. The volume is devoted mainly to combinatorics and discrete mathematics. Several of the topics are well known: nonrepeating sequences, detecting a counterfeit coin, and linear inequalities in economics, but they are discussed here with the entertaining and engaging style typical of the magazine. The two previous collections treat aspects of algebra and analysis, including connections to number theory and other topics. They were published as Volumes 14 and 15 in the Mathematical World series.

The articles are written so as to present genuine mathematics in a conceptual, entertaining, and accessible way. The books are designed to be used by students and teachers who love mathematics and want to study its various aspects, deepening and expanding upon the school curriculum.

Book Series Name: Mathematical World
Volume: 17
Publication Month and Year: 2001-11-05
Page Count: 131
Cover Type: Softcover
Print ISBN-13: 978-0-8218-2171-8
Print ISSN: 1055-9426
Primary MSC: 00
Secondary MSC: 97
Textbook?: False
Applied Math?: False
Electronic Media?: False
SXG Subject: GI; DM
Print Price 1 Label: List
Print Price 1: 36.00
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Print Price 2: 28.80
Print Add to Cart URL: /some/url/at/AMS/MAWRLD-17
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Graduate students and research mathematicians interested in combinatorics and discrete mathematics.

Cover Image URL: ~~FreeAttachments/mawrld-17-cov.jpg
• Base Product Code Keyword List: mawrld; MAWRLD; mawrld/15; MAWRLD/15; mawrld-15; MAWRLD-15
Print Product Code: MAWRLD/15
Title (HTML): Kvant Selecta: Algebra and Analysis, II
Author/Editor Label (optional): Edited by
Author(s) (Product display): Serge Tabachnikov
Affiliation(s) (HTML): University of Arkansas at Fayetteville, Fayetteville, AR
Book Series Name: Mathematical World
Volume: 15
Publication Month and Year: 1999-08-05
Page Count: 165
Cover Type: Softcover
Print ISBN-13: 978-0-8218-1915-9
Print ISSN: 1055-9426
Primary MSC: 00
Textbook?: False
Applied Math?: False
Electronic Media?: False
SXG Subject: GI
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Print Price 1: 29.00
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Print Price 2: 23.20
Print Add to Cart URL: /some/url/at/AMS/MAWRLD-15
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Advanced high school and undergraduate students interested in mathematics; mathematics teachers in high schools and colleges.

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 curricula today. Others feature cutting-edge research from the twentieth 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 first volume is mainly devoted to various topics in number theory, whereas the second volume treats diverse aspects of analysis and algebra.

Published in the very popular and relatively basic-level Mathematical World series. Features a low price and a colorful cover. This is kind of a “What's Happening in Russian Mathematics” (Russian mathematics are still considered to be among the best in the world). Second of two volumes on the topic.

Zentralblatt MATH

The slate of the authors is most impressive … It is most impressive and commendable that these ‘serious’ mathematicians went out of their way to make their sophisticated material understandable by a broad readership … a welcome edition to mathematics literature where rigor co-exists with fun and accessibility.

Supplementary Reading Cover art created by Sergei Ivanov. Used with permission. MAWRLD/14 Binomial coefficients, polynomials, and sequences (Several approaches to a certain problem) V. N. Vaguten Vaguten V. N. Formulas for prime numbers Yu. V. Matiyasevich Matiyasevich Yu. V. Fermat's theorem for polynomials B. Martynov Martynov B. Commuting polynomials I. Yantarov Yantarov I. On the removal of parentheses, on Euler, Gauss, and Macdonald, and on missed opportunities D. B. Fuchs Fuchs D. B. Chebyshev polynomials and recurrence relations N. Vasil'ev Vasil'ev N. A. Zelevinskii Zelevinskii A. Why resistance does not decrease O. V. Lyashko Lyashko O. V. Evolution processes and ordinary differential equations V. I. Arnol'd Arnol'd V. I. Irrationality and irreducibility V. A. Oleinikov Oleinikov V. A. Irreducibility and irrationality V. A. Oleinikov Oleinikov V. A. The arithmetic of elliptic curves Yu. P. Solov'ev Solov'ev Yu. P. Pascal's hexagrams and cubic curves N. B. Vasil'ev Vasil'ev N. B. Kepler's second law and the topology of abelian integrals (According to Newton) V. I. Arnol'd Arnol'd V. I. Partitions of integers F. V. Vainstein Vainstein F. V. On the Denogardus great number and Hooke's law V. Yu. Ovsienko Ovsienko V. Yu. Polynomials having least deviation from zero S. Tabachnikov Tabachnikov S.
Cover Image URL: ~~FreeAttachments/mawrld-15-cov.jpg
• Base Product Code Keyword List: mawrld; MAWRLD; mawrld/14; MAWRLD/14; mawrld-14; MAWRLD-14
Print Product Code: MAWRLD/14
Title (HTML): Kvant Selecta: Algebra and Analysis, I
Author/Editor Label (optional): Edited by
Author(s) (Product display): Serge Tabachnikov
Affiliation(s) (HTML): University of Arkansas at Fayetteville, Fayetteville, AR
Abstract:

This volume and Kvant Selecta: Algebra and Analysis, II (MAWRLD/15) 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 curricula today. Others feature cutting-edge research from the twentieth 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 first volume is mainly devoted to various topics in number theory, whereas the second volume treats diverse aspects of analysis and algebra.

Book Series Name: Mathematical World
Volume: 14
Publication Month and Year: 1999-08-03
Page Count: 155
Cover Type: Softcover
Print ISBN-13: 978-0-8218-1002-6
Print ISSN: 1055-9426
Primary MSC: 00
Textbook?: False
Applied Math?: False
Electronic Media?: False
SXG Subject: GI
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Print Price 1: 29.00
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Print Price 2: 23.20
Print Add to Cart URL: /some/url/at/AMS/MAWRLD-14
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Advanced high school and undergraduate students interested in mathematics; mathematics teachers in high schools and colleges.

Reviews:

The slate of the authors is most impressive … It becomes even more impressive in view of the fact that these ‘serious’ mathematicians went out of their way to make their sophisticated material understandable by a broad readership … a welcome edition to mathematics literature where rigor co-exists with fun and accessibility.

-- Zentralblatt MATH

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• Base Product Code Keyword List: trans2; TRANS2; trans2/194; TRANS2/194; trans2-194; TRANS2-194
Print Product Code: TRANS2/194
Online Product Code: TRANS2/194.E
Title (HTML): Differential Topology, Infinite-Dimensional Lie Algebras, and Applications: D. B. Fuchs’ 60th Anniversary Collection
Author/Editor Label (optional): Edited by
Author(s) (Product display): Alexander Astashkevich; Serge Tabachnikov
Affiliation(s) (HTML): Renaissance Technologies, East Setauket, NY; University of Arkansas, Fayetteville, AR
Abstract:

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.

The main topics addressed in this unique work are infinite-dimensional Lie algebras with applications (vertex operator algebras, conformal field theory, quantum integrable systems, etc.) and differential topology. The volume provides an excellent introduction to current research in the field.

Book Series Name: American Mathematical Society Translations - Series 2
Publication Month and Year: 1999-08-10
Page Count: 313
Cover Type: Hardcover
Print ISBN-13: 978-0-8218-2032-2
Online ISBN 13: 978-1-4704-3405-2
Print ISSN: 0065-9290
Online ISSN: 0065-9290
Primary MSC: 14; 17; 58
Textbook?: False
Applied Math?: False
Electronic Media?: False
SXG Subject: AA; GT
Online Price 1 Label: List
Online Price 1: 130.00
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Print Price 1: 130.00
Online Price 2 Label: Individual Member
Online Price 2: 104.00
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Print Price 2: 104.00
Print Add to Cart URL: /some/url/at/AMS/TRANS2-194
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Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3405-2&pisbn=978-0-8218-2032-2&epc=TRANS2/194.E&ppc=TRANS2/194&title=Differential%20Topology%2C%20Infinite-Dimensional%20Lie%20Algebras%2C%20and%20Applications%3A%20D.%20B.%20Fuchs%26rsquo%3B%2060th%20Anniversary%20Collection&author=Alexander%20Astashkevich%3B%20Serge%20Tabachnikov&type=R