Yu I Manin's Books

Cubic Forms

Algebra, Geometry, Arithmetic

By: Yu.I. Manin

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Cubic Forms

Algebra, Geometry, Arithmetic

By: Yu.I. Manin

Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references.The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the theory of the descent and obstructions to the Hasse principle on rational varieties, and recent applications of K-theory to arithmetic.

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337

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Elsevier

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ISBN 10

0080963161

ISBN 13

9780080963167

A Course in Mathematical Logic

By: Yu.I. Manin

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A Course in Mathematical Logic

By: Yu.I. Manin

1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presenta tion here is fairly standard, except that semantics occupies a very domi nant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax.

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296

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Springer Science & Business Media

Published Date

ISBN 10

1475743858

ISBN 13

9781475743852

Number Theory I

Fundamental Problems, Ideas and Theories

By: Yu. I. Manin,Alexei A. Panchishkin

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Number Theory I

Fundamental Problems, Ideas and Theories

By: Yu. I. Manin,Alexei A. Panchishkin

A unified survey of both the status quo and the continuing trends of various branches of number theory. Motivated by elementary problems, the authors present todays most significant results and methods. Topics covered include non-Abelian generalisations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. The book is rounded off with an overview of the major conjectures, most of which are based on analogies between functions and numbers, and on connections with other branches of mathematics such as analysis, representation theory, geometry and algebraic topology.

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311

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Springer Science & Business Media

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ISBN 10

3662080052

ISBN 13

9783662080054

Introduction to Modern Number Theory

Fundamental Problems, Ideas and Theories

By: Yu. I. Manin,Alexei A. Panchishkin

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Introduction to Modern Number Theory

Fundamental Problems, Ideas and Theories

By: Yu. I. Manin,Alexei A. Panchishkin

This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.

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519

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Springer Science & Business Media

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ISBN 10

3540276920

ISBN 13

9783540276920

Art And Practice Of Mathematics, The: Interviews At The Institute For Mathematical Sciences, National University Of Singapore, 2010-2020

By: Yu Kiang Leong

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Art And Practice Of Mathematics, The: Interviews At The Institute For Mathematical Sciences, National University Of Singapore, 2010-2020

By: Yu Kiang Leong

This book constitutes the second volume of interviews with prominent mathematicians and mathematical scientists who visited the Institute for Mathematical Sciences, National University of Singapore. First published in the Institute's newsletter Imprints during the period 2010-2020, they offer glimpses of an esoteric universe as viewed and experienced by some of the leading and creative practitioners of the craft of mathematics.The topics covered in this volume are wide-ranging, running from pure mathematics (logic, number theory, algebraic geometry) to applied mathematics (mathematical modeling, fluid dynamics) through probability and statistics, mathematical physics, theoretical computer science and financial mathematics. This eclectic mix of the abstract and the concrete should interest those who are enthralled by the mystique and power of mathematics, whether they are students, researchers or the non-specialists.By briefly tracing the paths traveled by the pioneers of different national backgrounds, the interviews attempt to put a cultural face to an intellectual endeavor that is often perceived as dry and austere by the uninitiated. They should also interest those who are intrigued by the influence of the environment on the creative spirit, and, in particular, those who are interested in the psychology and history of ideas.

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442

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World Scientific

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ISBN 10

9811219605

ISBN 13

9789811219603

Classical and Quantum Computation

By: Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi

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Classical and Quantum Computation

By: Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi

An introduction to a rapidly developing topic: the theory of quantum computing. Following the basics of classical theory of computation, the book provides an exposition of quantum computation theory. In concluding sections, related topics, including parallel quantum computation, are discussed.

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274

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American Mathematical Soc.

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ISBN 10

0821832298

ISBN 13

9780821832295

Ultrametric Pseudodifferential Equations and Applications

By: Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo

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Ultrametric Pseudodifferential Equations and Applications

By: Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo

Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.

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256

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Cambridge University Press

Published Date

ISBN 10

1108102905

ISBN 13

9781108102902

Linear Algebra and Geometry

By: P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin

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Linear Algebra and Geometry

By: P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin

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320

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CRC Press

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ISBN 10

1466593482

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9781466593480

GRIBOV-80 Memorial Volume

Quantum Chromodynamics and Beyond

By: Yu L. Dokshitzer,P. Levai,J. Nyiri

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GRIBOV-80 Memorial Volume

Quantum Chromodynamics and Beyond

By: Yu L. Dokshitzer,P. Levai,J. Nyiri

Vladimir Naumovich Gribov was one of the most outstanding theoretical physicists, a key figure in the development of modern elementary particle physics. His insights into the physics of quantum anomalies and the origin of classical solutions (instantons), the notion of parton systems and their evolution in soft and hard hadron interactions, the first theory of neutrino oscillations and conceptual problems of quantization of non-Abelian fields uncovered by him, have left a lasting impact on the theoretical physics of the 21st century. Gribov-80 the fourth in a series of memorial workshops for V N Gribov was organized on the occasion of his 80th birthday in May 2010, at the Abdus Salam International Centre for Theoretical Physics. The workshop paid tribute to Gribov's great achievements and brought close colleagues, younger researchers and leading experts together to display the new angles of the Gribov heritage at the new energy frontier opened up by the Large Hadron Collider. The book is a collection of the presentations made at the workshop.

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597

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World Scientific

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ISBN 10

9814350184

ISBN 13

9789814350181

Euclidean Quantum Gravity on Manifolds with Boundary

By: Giampiero Esposito,A.Yu. Kamenshchik,G. Pollifrone

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Euclidean Quantum Gravity on Manifolds with Boundary

By: Giampiero Esposito,A.Yu. Kamenshchik,G. Pollifrone

This book reflects our own struggle to understand the semiclassical behaviour of quantized fields in the presence of boundaries. Along many years, motivated by the problems of quantum cosmology and quantum field theory, we have studied in detail the one-loop properties of massless spin-l/2 fields, Euclidean Maxwell the ory, gravitino potentials and Euclidean quantum gravity. Hence our book begins with a review of the physical and mathematical motivations for studying physical theories in the presence of boundaries, with emphasis on electrostatics, vacuum v Maxwell theory and quantum cosmology. We then study the Feynman propagator in Minkowski space-time and in curved space-time. In the latter case, the corre sponding Schwinger-DeWitt asymptotic expansion is given. The following chapters are devoted to the standard theory of the effective action and the geometric im provement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the problem of boundary conditions in one-loop quantum theory. For this purpose, we study in detail Dirichlet, Neumann and Robin boundary conditions for scalar fields, local and non-local boundary conditions for massless spin-l/2 fields, mixed boundary conditions for gauge fields and gravitation. This is the content of Part I. Part II presents our investigations of Euclidean Maxwell theory, simple super gravity and Euclidean quantum gravity.

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334

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Springer Science & Business Media

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ISBN 10

9401158061

ISBN 13

9789401158060

Autowave Processes in Kinetic Systems

Spatial and Temporal Self-Organisation in Physics, Chemistry, Biology, and Medicine

By: V.A. Vasiliev,Yu.M. Romanovskii,D.S. Chernavskii,V.G. Yakhno

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Autowave Processes in Kinetic Systems

Spatial and Temporal Self-Organisation in Physics, Chemistry, Biology, and Medicine

By: V.A. Vasiliev,Yu.M. Romanovskii,D.S. Chernavskii,V.G. Yakhno

Probably, we are obliged to Science, more than to any other field of the human activity, for the origin of our sense that collective efforts are necessary indeed. F. Joliot-Curie The study of autowave processes is a young science. Its basic concepts and methods are still in the process of formation, and the field of its applications to various domains of natural sciences is expanding continuously. Spectacular examples of various autowave processes are observed experimentally in numerous laboratories of quite different orientations, dealing with investigations in physics, chemistry and biology. It is O1). r opinion, however, that if a history of the discovery of autowaves will he written some day its author should surely mention three fundamental phenomena which were the sources of the domain in view. "Ve mean combustion and phase transition waves, waves in chemical reactors where oxidation-reduction processes take place, and propagation of excitations in nerve fibres. The main tools of the theory of autowave processes are various methods used for investigating nonlinear discrete or distributed oscillating systems, the mathe matical theory of nonlinear parabolic differential equations, and methods of the theory of finite automata. It is noteworthy that the theory of autowave,. , has been greatly contributed to be work of brilliant mathematicians who anticipated the experimental discoveries in their abstract studies. One should mention R. Fishel' (1937), A. N. Kolmogorov, G. 1. Petrovskii, and N. S. Piskunov (1937), N. Wiener and A. Rosenbluth (1946), A. Turing (1952).

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265

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Springer Science & Business Media

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ISBN 10

9400937512

ISBN 13

9789400937512

Differential Geometry For Physicists

By: Bo-yu Hou,Bo-yuan Hou

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Differential Geometry For Physicists

By: Bo-yu Hou,Bo-yuan Hou

This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.

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561

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World Scientific Publishing Company

Published Date

ISBN 10

9813105097

ISBN 13

9789813105096

Methods of Noncommutative Analysis

Theory and Applications

By: Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin

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Methods of Noncommutative Analysis

Theory and Applications

By: Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

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385

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Walter de Gruyter

Published Date

ISBN 10

3110813548

ISBN 13

9783110813548

Geometry of Vector Fields

By: Yu. Aminov

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Geometry of Vector Fields

By: Yu. Aminov

Presenting a classical approach to the foundations and development of the geometry of vector fields, this volume space, three orthogonal systems, and applications in mechanics. Other topics, including vector fields, Pfaff forms and systems in n-dimensional space, foliations and Godbillon-Vey invariant, are also considered. There is much interest in the study of geometrical objects in n-dimensional Euclidean space, and this volume provides a useful and comprehensive presentation.

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190

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CRC Press

Published Date

ISBN 10

9056992015

ISBN 13

9789056992019

Borel-Laplace Transform and Asymptotic Theory

Introduction to Resurgent Analysis

By: Boris Yu. Sternin,Victor E. Shatalov

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Borel-Laplace Transform and Asymptotic Theory

Introduction to Resurgent Analysis

By: Boris Yu. Sternin,Victor E. Shatalov

The resurgent function theory introduced by J. Ecalle is one of the most interesting theories in mathematical analysis. In essence, the theory provides a resummation method for divergent power series (e.g., asymptotic series), and allows this method to be applied to mathematical problems. This new book introduces the methods and ideas inherent in resurgent analysis. The discussions are clear and precise, and the authors assume no previous knowledge of the subject. With this new book, mathematicians and other scientists can acquaint themselves with an interesting and powerful branch of asymptotic theory - the resurgent functions theory - and will learn techniques for applying it to solve problems in mathematics and mathematical sciences.

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284

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CRC Press

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ISBN 10

084939435X

ISBN 13

9780849394355

Geometry of Defining Relations in Groups

By: A.Yu. Ol'shanskii

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Geometry of Defining Relations in Groups

By: A.Yu. Ol'shanskii

The main feature of this book is a systematic application of elementary geometric and topological techniques for solving problems that arise naturally in algebra. After an account of preliminary material, there is a discussion of a geometrically intuitive interpretation of the derivation of consequences of defining relations of groups. A study is made of planar and certain other two-dimensional maps connected with well-known problems in general group theory, such as the problems of Burnside and O. Yu. Schmidt. The method of cancellation diagrams developed here is applied to these and to a series of other problems. This monograph is addressed to research workers and students in universities, and may be used as a basis for a series of specialized lectures or seminars.

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540

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Springer Science & Business Media

Published Date

ISBN 10

0792313941

ISBN 13

9780792313946

Quasiconformal Mappings and Sobolev Spaces

By: V.M. Gol'dshtein,Yu.G. Reshetnyak

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Quasiconformal Mappings and Sobolev Spaces

By: V.M. Gol'dshtein,Yu.G. Reshetnyak

Ht moi ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'~re of this series

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389

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Springer Science & Business Media

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ISBN 10

9400919220

ISBN 13

9789400919228

General Theory of Irregular Curves

By: V.V. Alexandrov,Yu.G. Reshetnyak

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General Theory of Irregular Curves

By: V.V. Alexandrov,Yu.G. Reshetnyak

One service mathematics has rendered the "Et moi ... si j'a\'ait su comment en revenir, human race. It has put common sense back je n'y scrais point alit: Jules Verne where it belongs, on the topmost shelf next to the dusty canister labc\led 'discarded non The series is divergent; therefore we may be sense'. Eric T. 8c\l able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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298

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Springer Science & Business Media

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ISBN 10

9400925913

ISBN 13

9789400925915

Stochastic Equations and Differential Geometry

By: Ya.I. Belopolskaya,Yu.L. Dalecky

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Stochastic Equations and Differential Geometry

By: Ya.I. Belopolskaya,Yu.L. Dalecky

Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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274

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Springer Science & Business Media

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ISBN 10

9400922159

ISBN 13

9789400922150

Self-Assembled Nanostructures

By: Jin Zhang,Zhong-lin Wang,Jun Liu,Shaowei Chen,Gang-yu Liu

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Self-Assembled Nanostructures

By: Jin Zhang,Zhong-lin Wang,Jun Liu,Shaowei Chen,Gang-yu Liu

Nanostructures refer to materials that have relevant dimensions on the nanometer length scales and reside in the mesoscopic regime between isolated atoms and molecules in bulk matter. These materials have unique physical properties that are distinctly different from bulk materials. Self-Assembled Nanostructures provides systematic coverage of basic nanomaterials science including materials assembly and synthesis, characterization, and application. Suitable for both beginners and experts, it balances the chemistry aspects of nanomaterials with physical principles. It also highlights nanomaterial-based architectures including assembled or self-assembled systems. Filled with in-depth discussion of important applications of nano-architectures as well as potential applications ranging from physical to chemical and biological systems, Self-Assembled Nanostructures is the essential reference or text for scientists involved with nanostructures.

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327

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Springer Science & Business Media

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ISBN 10

0306479419

ISBN 13

9780306479410

The Geometry of Submanifolds

By: Yu. Aminov

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The Geometry of Submanifolds

By: Yu. Aminov

This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects. Discussions include submanifolds in Euclidean states and Riemannian space, minimal submanifolds, Grassman mappings, multi-dimensional regular polyhedra, and isometric immersions of Lobachevski space into Euclidean spaces. This volume also highlights the contributions made by great geometers to the geometry of submanifolds and its areas of application.

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392

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CRC Press

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ISBN 10

905699087X

ISBN 13

9789056990879

Buy A Husband and Get Rich

Volume 12

By: Xiao Yu

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Buy A Husband and Get Rich

Volume 12

By: Xiao Yu

As Su Qinghuan put her hands on her hips, she said, "With medical skills in hand, I have all the skills in the world!" What? You're accusing me of not marrying seventeen? No problem, buy a sickly guy, sit and wait to become a widow, earn a chastity memorial archway! However, with a change in his bearing, how did he become a powerful general? Su Qing Huan: Hey, hey, hey. You took the wrong script. This is Tian Wen! The female lead likes to take off the tease, kind-hearted and tough; the male lead is overbearing and affectionate, playing the pig to eat the tiger; Joy and tears, sorrow and joy, but deep love never let down.

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694

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Funstory

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ISBN 10

1636892310

ISBN 13

9781636892313

Beyond the Arab Awakening

Policies and Investments for Poverty Reduction and Food Security

By: Breisinger, Clemens,Ecker, Olivier,Al-Riffai, Perrihan,Yu, Bingxin

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Beyond the Arab Awakening

Policies and Investments for Poverty Reduction and Food Security

By: Breisinger, Clemens,Ecker, Olivier,Al-Riffai, Perrihan,Yu, Bingxin

This report aims to inform and stimulate the debate on key policy priorities for poverty reduction and food security in light of the Arab Awakening. Its findings are based on an innovative combination of datasets and rigorous economic analysis. Results suggest that poverty and income inequality in the Arab world are likely higher than official numbers have long suggested. Given that poverty indicators seem to be misleading for many countries in the region, the report introduces a new welfare measure reflecting food insecurity risks at both national and household levels to classify Arab countries into five risk groups. Regression analyses further show that, unlike in the rest of the world, manufacturing- and service sectorled growth, rather than agriculture-led growth, is most pro-poor in Arab countries. In addition, high levels of public spending in the Arab world do not do as much to stimulate growth as in other world regions, particularly in the case of education. Three key policy recommendations emerge from this report: (1) improve data and capacity as the basis for evidence-based decisionmaking, (2) foster growth that enhances food security at national and household levels, and (3) significantly enhance the efficiency and retool the allocation of public spending. More generally, the report argues that the region urgently needs national dialogues about societies' joint vision and economic development strategies. Successful design and implementation of these strategies will require visionary leadership, sound laws and institutions, politicians who are accountable and listen to the voices of the people, and civil society that is patient and accepts the tenets of democracy. The Arab world is awakeit is time to move forward.

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Intl Food Policy Res Inst

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ISBN 10

0896295451

ISBN 13

9780896295452

Tauberian Theorems for Generalized Functions

By: V.S. Vladimirov,Yu.N. Drozzinov,O.I. Zavialov

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Tauberian Theorems for Generalized Functions

By: V.S. Vladimirov,Yu.N. Drozzinov,O.I. Zavialov

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. The Scandal of Father G. K. Chesterton. 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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308

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Springer Science & Business Media

Published Date

ISBN 10

9400928319

ISBN 13

9789400928312

Statistical Theory of Open Systems

By: Yu.L. Klimontovich

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Statistical Theory of Open Systems

By: Yu.L. Klimontovich

This monograph gives a systematic presentation of ideas, methods and results of the modern statistical theory of open systems -- systems capable of exchanging matter, energy and information with the surrounding world. The resulting self-organization can lead to more sophisticated and advanced structures. Central to this work are the statistical criteria of self-organization. The feasibility of a unified description of kinetic, hydrodynamic and diffusion processes in passive and active macroscopic systems without resorting to the methods of perturbation theory is demonstrated. On this basis, a general definition of thermal flux is given in terms of the entropy gradient. Moreover, a consistent method for calculating both kinetic and hydrodynamic fluctuations is proposed. This approach is then used to construct a theory of classical and anomalous Brownian motion in nonlinear media. This theory makes it possible to treat in an original way the phenomenon of turbulence, and to propose a unified kinetic description of laminar and turbulent motion. The proposed methods are also applied to the statistical description of quantum macroscopic open systems. This provides answers as to whether or not the quantum mechanical description is complete, and whether or not there are hidden parameters in quantum mechanics. The book has no analogy in the existing literature. It is both a monograph and a textbook, and is based largely on the author's original research. The book will be useful to postgraduate students and researchers in chemistry, physics, mathematics, economics, sociology, and engineering.

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Page Count

600

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0792332423

ISBN 13

9780792332428

Turbulent Motion and the Structure of Chaos

A New Approach to the Statistical Theory of Open Systems

By: Yu.L. Klimontovich

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Turbulent Motion and the Structure of Chaos

A New Approach to the Statistical Theory of Open Systems

By: Yu.L. Klimontovich

analyzing the experimental data and constructing math.ematical models of the processes under study, one has to rely rather on the physical intuition than on the strict calculations. Now let us go one step higher and explain the main title of the book. The concepts of "laminary" and "turbulent" motions were first introduced in hydrodynamics. Since the old days these concepts have considerably broadened; now the laminar and the turbulent motions have been discovered and investigated at all levels of description of nonequilibrium processes in the open systems, from kinetics to reaction diffusion. In any case, one of the principal characteristics of the turbulent motion is the existence of a large number of well-developed macroscopic degrees of freedom. For this reason the turbulent motion is extremely complicated and to a large extent unpredictable. As the laminar and the turbulent flows play an important role in the processes of evolution in the open systems, and in particular, in the processes of self-organization, the need arises for assessing the relative degree of order of laminar and turbulent motions, and also for comparing the degree of order of various turbulent motions. Without being able to make such estimates it will be impossible to determine whether the evolution is going towards higher or towards lower organization when one turbulent state is replaced by another.

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Page Count

430

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0792311140

ISBN 13

9780792311140

A Course in Mathematical Logic

By: Yu.I. Manin

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A Course in Mathematical Logic

By: Yu.I. Manin

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296

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Springer Science & Business Media

Published Date

ISBN 10

1475743858

ISBN 13

9781475743852

A Course in Mathematical Logic for Mathematicians

By: Yu. I. Manin

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A Course in Mathematical Logic for Mathematicians

By: Yu. I. Manin

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

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Page Count

384

Publisher

Springer

Published Date

ISBN 10

1441906169

ISBN 13

9781441906168

Cubic Forms

Algebra, Geometry, Arithmetic

By: Yu.I. Manin

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Cubic Forms

Algebra, Geometry, Arithmetic

By: Yu.I. Manin

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Page Count

337

Publisher

Elsevier

Published Date

ISBN 10

0080963161

ISBN 13

9780080963167

Number Theory I

Fundamental Problems, Ideas and Theories

By: Yu. I. Manin,Alexei A. Panchishkin

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Number Theory I

Fundamental Problems, Ideas and Theories

By: Yu. I. Manin,Alexei A. Panchishkin

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311

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Springer Science & Business Media

Published Date

ISBN 10

3662080052

ISBN 13

9783662080054

Introduction to Modern Number Theory

Fundamental Problems, Ideas and Theories

By: Yu. I. Manin,Alexei A. Panchishkin

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Introduction to Modern Number Theory

Fundamental Problems, Ideas and Theories

By: Yu. I. Manin,Alexei A. Panchishkin

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519

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540276920

ISBN 13

9783540276920

Linear Algebra and Geometry

By: P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin

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Linear Algebra and Geometry

By: P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin

This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics.

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Page Count

324

Publisher

CRC Press

Published Date

ISBN 10

2881246834

ISBN 13

9782881246838

Homological Algebra

By: S.I. Gelfand,Yu.I. Manin

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Homological Algebra

By: S.I. Gelfand,Yu.I. Manin

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.

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Page Count

222

Publisher

Springer

Published Date

ISBN 10

3540653783

ISBN 13

9783540653783

Book's by Yu I Manin

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