Foundations of Mathematical Analysis

Автор: Khinchin, A. Ya.
Название: Mathematical Foundations of Statistical Mechanics
ISBN: 0486601471 ISBN-13(EAN): 9780486601472
Издательство: Dover
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Цена: 1855.00 р.
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Описание: The translation of this important book brings to the English-speaking mathematician and mathematical physicist a thoroughly up-to-date introduction to statistical mechanics.
It offers a precise and mathematically rigorous formulation of the problems of statistical mechanics, as opposed to the non-rigorous discussion presented in most other works. It provides analytical tools needed to replace many of the cumbersome concepts and devices commonly used for establishing basic formulae, and it furnishes the mathematician with a logical step-by-step introduction, which will enable him to master the elements of statistical mechanics in the shortest possible time.
After a historical sketch, the author discusses the geometry and kinematics of the phase space, with the theorems of Liouville and Birkhoff; the ergodic problem (in the sense of replacing time averages by phase averages); the theory of probability; central limit theorem; ideal monatomic gas; foundation of thermodynamics, and dispersion and distribution of sum functions.
"An excellent introduction to the difficult and important discipline of Statistical Mechanics. It is clear, concise, and rigorous. There is a very good chapter on the ergodic theorem (with a complete proof ) and . . . a highly lucid chapter on statistical foundations of thermodynamics . . . useful to teachers . . . and to mathematicians." ― M. Kac, "Quarterly of Applied Mathematics. "

Автор: Khinchin, A. Ya.
Название: Mathematical Foundations of Information Theory
ISBN: 0486604349 ISBN-13(EAN): 9780486604343
Издательство: Dover
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Цена: 1359.00 р.
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Описание: The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein, and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists, and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.
In his first paper, Dr. Khinchin develops the concept of entropy in probability theory as a measure of uncertainty of a finite "scheme," and discusses a simple application to coding theory. The second paper investigates the restrictions previously placed on the study of sources, channels, and codes and attempts "to give a complete, detailed proof of both ... Shannon theorems, assuming any ergodic source and any stationary channel with a finite memory."
Partial Contents: I. The Entropy Concept in Probability Theory -- Entropy of Finite Schemes. The Uniqueness Theorem. Entropy of Markov chains. Application to Coding Theory. II. On the Fundamental Theorems of Information Theory -- Two generalizations of Shannon's inequality. Three inequalities of Feinstein. Concept of a source. Stationarity. Entropy. Ergodic sources. The E property. The martingale concept. Noise. Anticipation and memory. Connection of the channel to the source. Feinstein's Fundamental Lemma. Coding. The first Shannon theorem. The second Shannon theorem.