Statistical Independence in Probability Analysis and Number Theory (Carus Mathematical Monographs) - Softcover

Mark Kac (author)

Softcover

ISBN 10: 0883850257 ISBN 13: 9780883850251

Publisher: American Mathematical Society, 1959

Synopsis

Professor Kac's monograph is designed to illustrate how simple observations can be made the starting point of rich and fruitful theories and how the same theme recurs in seemingly unrelated disciplines. An elementary but thorough discussion of the game of ""heads or tails,"" including the normal law and the laws of large numbers, is presented in a setting in which a variety of purely analytic results appear natural and inevitable. The chapter ""Primes Play a Game of Chance"" uses the same setting in dealing with problems of the distribution of values of arithmetic functions. The final chapter ""From Kinetic Theory to Continued Fractions"" deals with a spectacular application of the ergodic theorems to continued fractions. Mark Kac conveyed his infectious enthusiasm for mathematics and its applications in his lectures, papers, and books. Two of his papers won Chauvenet awards for expository excellence.

About this title

Review

Terrific, friendly and profound."" - Persi Diaconis ""This is a splendid book. It ranges from the primitive idea of statistical independence to applications of the most diverse sort: coin-tossing, anharmonic oscillations, prime numbers, and continued fractions. And it does all that with Kac.s customary clarity and charm. Every friend of probability should have it."" - Henry McKeon

About the Author

Mark Kac (1914-1984) was born in Poland and came to the United States in the 1930s. He taught at Cornell and later served on the faculties of Rockefeller University in New York and the University of Southern California. His main focus was probability theory, and Dover also publishes his Mathematics and Logic, co-written with S. M. Ulam.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1959
• ISBN 10: 0883850257
• ISBN 13: 9780883850251
• Binding: Paperback
• Language: English
• Number of pages: 94