Mathematical Foundations of Information Theory (Paperback)

by A. Ya. Khinchin (Author)

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Product Description

Comprehensive, rigorous introduction to work of Shannon, McMillan, Feinstein and Khinchin. Translated by R. A. Silverman and M. D. Friedman.

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Product Details Paperback: 120 pages Publisher: Dover Publications (June 1, 1957) Language: English ISBN-10: 0486604349 ISBN-13: 978-0486604343 Product Dimensions: 7.8 x 5.4 x 0.3 inches Shipping Weight: 5 ounces (View shipping rates and policies) Average Customer Review: 4.7 out of 5 stars See all reviews (3 customer reviews) Amazon.com Sales Rank: #500,264 in Books (See Bestsellers in Books)

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Front Cover | Table of Contents | First Pages | Back Cover

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Citations (learn more)

69 books cite this book:

• Gamma: Exploring Euler's Constant (Princeton Science Library) by Julian Havil on page 140, and Back Matter
• Probability and Information: An Integrated Approach by David Applebaum in Front Matter, and page 111
• History of Computing in Education (IFIP Advances in Information and Communication Technology) by John Impagliazzo on page 22, and page 25
• Entropy (Princeton Series in Applied Mathematics) by Andreas Greven on page 214, and Back Matter
• Biosemiotics: The Semiotic Web 1991 (Approaches to Semiotics) by Thomas A. Sebeok on page 169

See all 69 books citing this book

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	50% buy the item featured on this page: Mathematical Foundations of Information Theory 4.7 out of 5 stars (3) $9.95
	18% buy An Introduction to Information Theory 4.6 out of 5 stars (18) $7.83
	14% buy Information Theory and Statistics (Dover Books on Mathematics) 4.8 out of 5 stars (4) $12.89
	10% buy Information Theory 4.4 out of 5 stars (7) $12.44

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3 Reviews 5 star:  (2) 4 star:  (1) 3 star:    (0) 2 star:    (0) 1 star:    (0)           Average Customer Review 4.7 out of 5 stars (3 customer reviews)		Share your thoughts with other customers:
Most Helpful Customer Reviews 23 of 24 people found the following review helpful: 5.0 out of 5 stars A clear exposition of Shannon's results by a great mathemati, February 25, 2001 By  anon2001 "anon2001" (Kinross, Western Australia AUSTRALIA) - See all my reviews A Y Khinchin was one of the great mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theory along with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them. He was also famous as a teacher and communicator. The books he wrote on Mathematical Foundations of Information Theory, Statistical Mechanics and Quantum Statistics are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour. In his "Mathematical Foundations" books Khinchin develops a sound mathematical structure for the subject under discussion based on the modern theory of probability. His primary reason for doing this is the lack of mathematically rigorous presentation in many textbooks on these subjects. This book contains two papers written by Khinchin on the concept of entropy in probability theory and Shannon's first and second theorems in information theory - with detailed modern proofs. Like all Khinchin's books, this one is very readable. And unlike many recent books on this subject the price is very cheap. Two minor complaints are: lack of an index, and typesetting could be improved. 23 of 24 people found the following review helpful: 5.0 out of 5 stars More rigorous version of Shannon 1948 paper, January 10, 2000 By  Ryuji Suzuki (Cambridge, MA USA) - See all my reviews (REAL NAME)    Shannon's paper is great. Easy to read (though many people misunderstand many concepts - I may too) but lacks mathematical rigor. This book has redone several points that Shannon made but more accurately. It requires ergodic theory and measure theory to follow every detail, but some parts may be usable even without much background. I don't think the book is perfectly edited, but I know I paid too little for the knowledge I gained from this book. 1 of 3 people found the following review helpful: 4.0 out of 5 stars Mathematical foundation of information theory, May 25, 2007 By  S. M. Jalali "SMJ" (USA) - See all my reviews (REAL NAME)    The main advantage of the book is that it covers the info theory corresponding to different fields of science and art. This is rather interesting and surprizing for EE students and scholars. The mathematics therein however is not rigorous.		Ad feedback   Search Customer Reviews Only search this product's reviews

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Product Details

• Paperback: 120 pages
• Publisher: Dover Publications (June 1, 1957)
• Language: English
• ISBN-10: 0486604349
• ISBN-13: 978-0486604343
• Product Dimensions: 7.8 x 5.4 x 0.3 inches
• Shipping Weight: 5 ounces (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #500,264 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

23 of 24 people found the following review helpful:

5.0 out of 5 stars A clear exposition of Shannon's results by a great mathemati, February 25, 2001

By	anon2001 "anon2001" (Kinross, Western Australia AUSTRALIA) - See all my reviews

A Y Khinchin was one of the great mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theory along with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them. He was also famous as a teacher and communicator. The books he wrote on Mathematical Foundations of Information Theory, Statistical Mechanics and Quantum Statistics are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour.

In his "Mathematical Foundations" books Khinchin develops a sound mathematical structure for the subject under discussion based on the modern theory of probability. His primary reason for doing this is the lack of mathematically rigorous presentation in many textbooks on these subjects.

This book contains two papers written by Khinchin on the concept of entropy in probability theory and Shannon's first and second theorems in information theory - with detailed modern proofs. Like all Khinchin's books, this one is very readable. And unlike many recent books on this subject the price is very cheap. Two minor complaints are: lack of an index, and typesetting could be improved.

23 of 24 people found the following review helpful:

5.0 out of 5 stars More rigorous version of Shannon 1948 paper, January 10, 2000

By	Ryuji Suzuki (Cambridge, MA USA) - See all my reviews (REAL NAME)

Shannon's paper is great. Easy to read (though many people misunderstand many concepts - I may too) but lacks mathematical rigor. This book has redone several points that Shannon made but more accurately. It requires ergodic theory and measure theory to follow every detail, but some parts may be usable even without much background. I don't think the book is perfectly edited, but I know I paid too little for the knowledge I gained from this book.

1 of 3 people found the following review helpful:

4.0 out of 5 stars Mathematical foundation of information theory, May 25, 2007

By	S. M. Jalali "SMJ" (USA) - See all my reviews (REAL NAME)

The main advantage of the book is that it covers the info theory corresponding to different fields of science and art. This is rather interesting and surprizing for EE students and scholars. The mathematics therein however is not rigorous.