Mathematical Foundations of Information Theory (Dover Books on Mathematics) [Paperback]

A. Ya. Khinchin (Author), Mathematics (Author)

Book Description

Publication Date: June 1, 1957 | Series: Dover Books on Mathematics

The first comprehensive introduction to information theory, this text explores the work begun by Shannon and continued by McMillan, Feinstein, and Khinchin. Its rigorous treatment addresses the entropy concept in probability theory and fundamental theorems as well as ergodic sources, the martingale concept, anticipation and memory, and other subjects. 1957 edition. 

Product Details

• Paperback: 128 pages
• Publisher: Dover Publications (June 1, 1957)
• Language: English
• ISBN-10: 0486604349
• ISBN-13: 978-0486604343
• Product Dimensions: 7.9 x 5.7 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 Best Sellers Rank: #399,305 in Books (See Top 100 in Books)
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  • #92 in Books > 4-for-3 Books > Science > Mathematics > General

Customer Reviews

Most Helpful Customer Reviews

28 of 29 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 (Boston, MA USA) - See all my reviews
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This review is from: Mathematical Foundations of Information Theory (Dover Books on Mathematics) (Paperback)

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.

26 of 27 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

This review is from: Mathematical Foundations of Information Theory (Dover Books on Mathematics) (Paperback)

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.

5 of 9 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)   

This review is from: Mathematical Foundations of Information Theory (Dover Books on Mathematics) (Paperback)

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.