Selected Works Of A N Kolmogorov
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| Author | : Vladimir M. Tikhomirov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 582 |
| Release | : 1991-06-30 |
| Genre | : Science |
| ISBN | : 9789027727961 |
The Praesidium of the USSR Academy of Sciences has decided to publish three volumes of Selected Works of A.N. Kolmogorov, one of the most prominent mathematicians of the 20th century. The creative work of A.N. Kolmogorov is exceptionally versatile. In his studies on trigonometric and orthogonal series, theory of measure and inte gral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in formation theory, many conceptual and fundamental problems were solved and new questions were posed which gave rise to a great number of investigations. A.N. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of basic results, with many applications to mechanics, geophysics, linguistics, biology and other branches of knowledge. This edition includes the most important papers by A.N. Kolmogorov on mathematics and natural science. It does not include philosophical and ped agogical studies of A.N. Kolmogorov, his articles written for the "Bol'shaya Sov'etskaya Entsiklopediya", papers on prosody and various applications of mathematics and publications on general questions. The material of this edition was selected and grouped by A.N. Kolmogorov.
| Author | : |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 242 |
| Release | : 2000 |
| Genre | : Mathematicians |
| ISBN | : 0821829181 |
The editorial board for the History of Mathematics series has selected for this volume a series of translations from two Russian publications, Kolmogorov in Remembrance and Mathematics and its Historical Development. This book, Kolmogorov in Perspective, includes articles written by Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. The articles combine to give an excellent personal and scientific biography of this important mathematician. There is also an extensive bibliography with the complete list of Kolmogorov's work.
| Author | : A.N. Shiryayev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 618 |
| Release | : 1992-02-29 |
| Genre | : Mathematics |
| ISBN | : 902772797X |
The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and integral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of central results, with many applications to mechanics, geophysics, linguistics and biology, among other subjects. This edition includes Kolmogorov's most important papers on mathematics and the natural sciences. It does not include his philosophical and pedagogical studies, his articles written for the "Bolshaya Sovetskaya Entsiklopediya", his papers on prosody and applications of mathematics or his publications on general questions. The material of this edition was selected and compiled by Kolmogorov himself. The first volume consists of papers on mathematics and also on turbulence and classical mechanics. The second volume is devoted to probability theory and mathematical statistics. The focus of the third volume is on information theory and the theory of algorithms.
| Author | : Angelo Vulpiani |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 268 |
| Release | : 2003-12-02 |
| Genre | : Science |
| ISBN | : 9783540203070 |
The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance.
| Author | : A. N. Kolmogorov |
| Publisher | : Courier Corporation |
| Total Pages | : 418 |
| Release | : 1975-06-01 |
| Genre | : Mathematics |
| ISBN | : 0486612260 |
Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.
| Author | : Ming Li |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 655 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475726066 |
Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
| Author | : A N Shiryayev |
| Publisher | : Springer |
| Total Pages | : 304 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9789401729741 |
This volume is the second of three volumes devoted to the work of one of the most prominent twentieth-century mathematicians. Throughout his mathematical work, A.N. Kolmogorov (1903-1987) showed great creativity and versatility and his wide-ranging studies in many different areas led to the solution of conceptual and fundamental problems and the posing of new, important questions. His lasting contributions embrace probability theory and statistics, the theory of dynamical systems, mathematical logic, geometry and topology, the theory of functions and functional analysis, classical mechanics, the theory of turbulence, and information theory. This second volume contains papers on probability theory and mathematical statistics, and embraces topics such as limit theorems, axiomatics and logical foundations of probability theory, Markov chains and processes, stationary processes and branching processes. The material appearing in each volume was selected by A.N. Kolmogorov himself and is accompanied by short introductory notes and commentaries which reflect upon the influence of this work on the development of modern mathematics. All papers appear in English - some for the first time -- and in chronological order. This volume contains a significant legacy which will find many grateful beneficiaries amongst researchers and students of mathematics and mechanics, as well as historians of mathematics.
| Author | : Vladimir I. Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 500 |
| Release | : 2009-10-22 |
| Genre | : Mathematics |
| ISBN | : 3642017428 |
Vladimir Arnold is one of the greatest mathematical scientists of our time, as well as one of the finest, most prolific mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics and KAM theory.
| Author | : Wolfgang Doeblin |
| Publisher | : Springer |
| Total Pages | : 748 |
| Release | : 2020-11-06 |
| Genre | : Mathematics |
| ISBN | : 9783319418803 |
This book contains all of Wolfgang Doeblin's publications. In addition, it includes a reproduction of the pli cacheté on l'équation de Kolmogoroff and previously unpublished material that Doeblin wrote in 1940. The articles are accompanied by commentaries written by specialists in Doeblin's various areas of interest. The modern theory of probability developed between the two World Wars thanks to the very remarkable work of Kolmogorov, Khinchin, S.N. Bernstein, Romanovsky, von Mises, Hostinsky, Onicescu, Fréchet, Lévy and others, among whom one name shines particularly brightly, that of Wolfgang Doeblin (1915–1940). The work of this young mathematician, whose life was tragically cut short by the war, remains even now, and indeed will remain into the future, an exemplar of originality and of mathematical power. This book was conceived and in essence brought to fruition by Marc Yor before his death in 2014. It is dedicated to him.
| Author | : Yakov G. Sinai |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 148 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 366202845X |
Sinai's book leads the student through the standard material for ProbabilityTheory, with stops along the way for interesting topics such as statistical mechanics, not usually included in a book for beginners. The first part of the book covers discrete random variables, using the same approach, basedon Kolmogorov's axioms for probability, used later for the general case. The text is divided into sixteen lectures, each covering a major topic. The introductory notions and classical results are included, of course: random variables, the central limit theorem, the law of large numbers, conditional probability, random walks, etc. Sinai's style is accessible and clear, with interesting examples to accompany new ideas. Besides statistical mechanics, other interesting, less common topics found in the book are: percolation, the concept of stability in the central limit theorem and the study of probability of large deviations. Little more than a standard undergraduate course in analysis is assumed of the reader. Notions from measure theory and Lebesgue integration are introduced in the second half of the text. The book is suitable for second or third year students in mathematics, physics or other natural sciences. It could also be usedby more advanced readers who want to learn the mathematics of probability theory and some of its applications in statistical physics.
