Vladimir Zorich's Books

Mathematical Analysis I

By: Vladimir A. Zorich

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This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions.

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610

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Springer Science & Business Media

Published Date

ISBN 10

3540403868

ISBN 13

9783540403869

Mathematical Analysis II

By: Vladimir A. Zorich

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Mathematical Analysis II

By: Vladimir A. Zorich

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708

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Springer Science & Business Media

Published Date

ISBN 10

3540406336

ISBN 13

9783540406334

Mathematical Aspects of Classical and Celestial Mechanics

By: Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt

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Mathematical Aspects of Classical and Celestial Mechanics

By: Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt

The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

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505

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Springer Science & Business Media

Published Date

ISBN 10

3540489266

ISBN 13

9783540489269

Topological Methods in Hydrodynamics

By: Vladimir I. Arnold,Boris A. Khesin

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Topological Methods in Hydrodynamics

By: Vladimir I. Arnold,Boris A. Khesin

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

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376

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Springer Science & Business Media

Published Date

ISBN 10

0387225897

ISBN 13

9780387225890

The Beltrami Equation

A Geometric Approach

By: Vladimir Gutlyanskii,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov

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The Beltrami Equation

A Geometric Approach

By: Vladimir Gutlyanskii,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov

This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.

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309

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Springer Science & Business Media

Published Date

ISBN 10

1461431913

ISBN 13

9781461431916

Lectures on Partial Differential Equations

By: Vladimir I. Arnold

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Lectures on Partial Differential Equations

By: Vladimir I. Arnold

Choice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.

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168

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Springer Science & Business Media

Published Date

ISBN 10

3662054418

ISBN 13

9783662054413

Lectures on Advances in Combinatorics

By: Rudolf Ahlswede,Vladimir Blinovsky

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Lectures on Advances in Combinatorics

By: Rudolf Ahlswede,Vladimir Blinovsky

The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].

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324

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Springer Science & Business Media

Published Date

ISBN 10

3540786023

ISBN 13

9783540786023

Moduli in Modern Mapping Theory

By: Olli Martio,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov

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Moduli in Modern Mapping Theory

By: Olli Martio,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov

Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

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368

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Springer Science & Business Media

Published Date

ISBN 10

0387855882

ISBN 13

9780387855882

Measure Theory

By: Vladimir I. Bogachev

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Measure Theory

By: Vladimir I. Bogachev

This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.

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1075

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Springer Science & Business Media

Published Date

ISBN 10

3540345140

ISBN 13

9783540345145

Topology, Ergodic Theory, Real Algebraic Geometry

Rokhlin's Memorial

By: Vladimir G. Turaev,Anatoliĭ Moiseevich Vershik

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Topology, Ergodic Theory, Real Algebraic Geometry

Rokhlin's Memorial

By: Vladimir G. Turaev,Anatoliĭ Moiseevich Vershik

This volume is dedicated to the memory of the Russian mathematician, V.A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmuller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles which should prove of historical interest.

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300

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827405

ISBN 13

9780821827406

Real and Functional Analysis

By: Vladimir I. Bogachev,Oleg G. Smolyanov

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Real and Functional Analysis

By: Vladimir I. Bogachev,Oleg G. Smolyanov

This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.

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602

Publisher

Springer Nature

Published Date

ISBN 10

3030382192

ISBN 13

9783030382193

Weak Convergence of Measures

By: Vladimir I. Bogachev

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Weak Convergence of Measures

By: Vladimir I. Bogachev

This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.

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301

Publisher

American Mathematical Society

Published Date

ISBN 10

147047798X

ISBN 13

9781470477981

The Arnoldfest

Proceedings of a Conference in Honour of V.I. Arnold for His Sixtieth Birthday

By: Vladimir Igorevich Arnolʹd

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The Arnoldfest

Proceedings of a Conference in Honour of V.I. Arnold for His Sixtieth Birthday

By: Vladimir Igorevich Arnolʹd

This volume presents articles originating from invited talks at an exciting international conference held at The Fields Institute in Toronto celebrating the sixtieth birthday of the renowned mathematician, Vladimir Arnold. Experts from the world over--including several from "Arnold's school"--gave illuminating talks and lively poster sessions. The presentations focused on Arnold's main areas of interest: singularity theory, the theory of curves, symmetry groups, dynamical systems, mechanics, and related areas of mathematics. The book begins with notes of three lectures by V. Arnold given in the framework of the Institute's Distinguished Lecturer program. The topics of the lectures are: (1) From Hilbert's Superposition Problem to Dynamical Systems (2) Symplectization, Complexification, and Mathematical Trinities (3) Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. Arnold's three articles include insightful comments on Russian and Western mathematics and science. Complementing the first is Jurgen Moser's "Recollections", concerning some of the history of KAM theory.

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575

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American Mathematical Soc.

Published Date

ISBN 10

0821809458

ISBN 13

9780821809457

Condenser Capacities and Symmetrization in Geometric Function Theory

By: Vladimir N. Dubinin

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Condenser Capacities and Symmetrization in Geometric Function Theory

By: Vladimir N. Dubinin

This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original – the main part has not been covered by existing textbooks and monographs. After an introduction to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others) is established, followed by various types of symmetrization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problems are solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven. This book will be a valuable source for current and future researchers in various branches of complex analysis and potential theory.

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352

Publisher

Springer

Published Date

ISBN 10

3034808437

ISBN 13

9783034808439

Mathematical Analysis of Problems in the Natural Sciences

By: Vladimir Zorich

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Mathematical Analysis of Problems in the Natural Sciences

By: Vladimir Zorich

Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric. It includes problems, historical remarks, and Zorich's popular article, "Mathematics as language and method.

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133

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Springer Science & Business Media

Published Date

ISBN 10

3642148131

ISBN 13

9783642148132

Mathematical Analysis II

By: V. A. Zorich

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Mathematical Analysis II

By: V. A. Zorich

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

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729

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Springer

Published Date

ISBN 10

3662489937

ISBN 13

9783662489932

Pseudoperiodic Topology

By: Vladimir Igorevich Arnolʹd,Maxim Kontsevich,Anton Zorich

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Pseudoperiodic Topology

By: Vladimir Igorevich Arnolʹd,Maxim Kontsevich,Anton Zorich

This volume offers an account of the present state of the art in pseudoperiodic topology--a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors ... have done much to show how modern mathematics begets, from this sea of pathological counterexamples, remarkable general and universal laws, whose discovery would be unthinkable and whose formulation would be impossible in the naive set-theoretical setting.

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Page Count

196

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082182094X

ISBN 13

9780821820940

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