Viktor Vasil evich Prasolov's Books

Elements of Combinatorial and Differential Topology

By: Viktor Vasilʹevich Prasolov

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Elements of Combinatorial and Differential Topology

By: Viktor Vasilʹevich Prasolov

Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed. One of the maingoals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology. The book contains many problems; almost all of them are suppliedwith hints or complete solutions.

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Page Count

348

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821838091

ISBN 13

9780821838099

Elliptic Functions and Elliptic Integrals

By: Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev

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Elliptic Functions and Elliptic Integrals

By: Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev

This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is self-contained and assumes as prerequisites only the standard one-year courses of algebra and analysis.

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Page Count

202

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821897802

ISBN 13

9780821897805

Problems and Theorems in Linear Algebra

By: Viktor Vasil_evich Prasolov

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Problems and Theorems in Linear Algebra

By: Viktor Vasil_evich Prasolov

There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.

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Page Count

250

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821802364

ISBN 13

9780821802366

Elements of Homology Theory

By: Viktor Vasilʹevich Prasolov

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Elements of Homology Theory

By: Viktor Vasilʹevich Prasolov

The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.

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Page Count

432

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821838121

ISBN 13

9780821838129

Essays on Numbers and Figures

By: Viktor Vasilʹevich Prasolov

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Essays on Numbers and Figures

By: Viktor Vasilʹevich Prasolov

This is the English translation of the book originally published in Russian. It contains 20 essays, each dealing with a separate mathematical topic. The topics range from brilliant mathematical statements with interesting proofs, to simple and effective methods of problem-solving, to interesting properties of polynomials, to exceptional points of the triangle. Many of the topics have a long and interesting history. The author has lectured on them to students worldwide.The essays are independent of one another for the most part, and each presents a vivid mathematical result that led to current research in number theory, geometry, polynomial algebra, or topology.

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Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821819445

ISBN 13

9780821819449

Intuitive Topology

By: Viktor Vasilʹevich Prasolov

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Intuitive Topology

By: Viktor Vasilʹevich Prasolov

This book is an introduction to elementary topology presented in an intuitive way, emphasizing the visual aspect. Examples of nontrivial and often unexpected topological phenomena acquaint the reader with the picturesque world of knots, links, vector fields, and two-dimensional surfaces. The book begins with definitions presented in a tangible and perceptible way, on an everyday level, and progressively makes them more precise and rigorous, eventually reaching the level of fairly sophisticated proofs. This allows meaningful problems to be tackled from the outset. Another unusual trait of this book is that it deals mainly with constructions and maps, rather than with proofs that certain maps and constructions do or do not exist. The numerous illustrations are an essential feature. The book is accessible not only to undergraduates but also to high school students and will interest any reader who has some feeling for the visual elegance of geometry and topology.

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Page Count

106

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821803565

ISBN 13

9780821803561

Knots, Links, Braids and 3-Manifolds

An Introduction to the New Invariants in Low-dimensional Topology

By: Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ

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Knots, Links, Braids and 3-Manifolds

An Introduction to the New Invariants in Low-dimensional Topology

By: Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ

This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.

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Page Count

250

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821808982

ISBN 13

9780821808986

Book's by Viktor Vasil evich Prasolov

Elements of Combinatorial and Differential Topology

Elements of Combinatorial and Differential Topology

Elliptic Functions and Elliptic Integrals

Elliptic Functions and Elliptic Integrals

Problems and Theorems in Linear Algebra

Problems and Theorems in Linear Algebra

Elements of Homology Theory

Elements of Homology Theory

Essays on Numbers and Figures

Essays on Numbers and Figures

Intuitive Topology

Intuitive Topology

Knots, Links, Braids and 3-Manifolds

Knots, Links, Braids and 3-Manifolds

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