Nikolai Konstantinovich Vereshchagin's Books

Basic Set Theory

By: Nikolai Konstantinovich Vereshchagin,Alexander Shen

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Basic Set Theory

By: Nikolai Konstantinovich Vereshchagin,Alexander Shen

The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.

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Page Count

130

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827316

ISBN 13

9780821827314

Computable Functions

By: Nikolai Konstantinovich Vereshchagin,Alexander Shen

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Computable Functions

By: Nikolai Konstantinovich Vereshchagin,Alexander Shen

Based on the lectures for undergraduates at Moscow State University, this book presents a lively and concise introduction to the central facts and basic notions of the general theory of computation. It begins with the definition of a computable function and an algorithm, and discusses decidability, enumerability, universal functions, numberings and their properties, the fixed point theorem, arithmetical hierarchy, oracle computations, and degrees.

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Page Count

178

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827324

ISBN 13

9780821827321

Basic Set Theory

By: Nikolai Konstantinovich Vereshchagin,Alexander Shen

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Basic Set Theory

By: Nikolai Konstantinovich Vereshchagin,Alexander Shen

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Solve jigsaw puzzle

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Page Count

130

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827316

ISBN 13

9780821827314

Computable Functions

By: Nikolai Konstantinovich Vereshchagin,Alexander Shen

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Computable Functions

By: Nikolai Konstantinovich Vereshchagin,Alexander Shen

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Solve jigsaw puzzle

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Page Count

178

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827324

ISBN 13

9780821827321

Kolmogorov Complexity and Algorithmic Randomness

By: A. Shen,V. A. Uspensky,N. Vereshchagin

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Kolmogorov Complexity and Algorithmic Randomness

By: A. Shen,V. A. Uspensky,N. Vereshchagin

Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.

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Page Count

534

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470431823

ISBN 13

9781470431822

Book's by Nikolai Konstantinovich Vereshchagin

Basic Set Theory

Basic Set Theory

Computable Functions

Computable Functions

Basic Set Theory

Basic Set Theory

Computable Functions

Computable Functions

Kolmogorov Complexity and Algorithmic Randomness

Kolmogorov Complexity and Algorithmic Randomness

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