Hardcover ISBN:  9780883850251 
Product Code:  CAR/12 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
eBook ISBN:  9781614440123 
Product Code:  CAR/12.E 
List Price:  $40.00 
MAA Member Price:  $30.00 
AMS Member Price:  $30.00 
Hardcover ISBN:  9780883850251 
eBook: ISBN:  9781614440123 
Product Code:  CAR/12.B 
List Price:  $85.00 $65.00 
MAA Member Price:  $63.75 $48.75 
AMS Member Price:  $63.75 $48.75 
Hardcover ISBN:  9780883850251 
Product Code:  CAR/12 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
eBook ISBN:  9781614440123 
Product Code:  CAR/12.E 
List Price:  $40.00 
MAA Member Price:  $30.00 
AMS Member Price:  $30.00 
Hardcover ISBN:  9780883850251 
eBook ISBN:  9781614440123 
Product Code:  CAR/12.B 
List Price:  $85.00 $65.00 
MAA Member Price:  $63.75 $48.75 
AMS Member Price:  $63.75 $48.75 

Book DetailsThe Carus Mathematical MonographsVolume: 12; 1959; 94 pp
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.

Table of Contents

Chapters

Chapter 1. From Vieta to the notion of statistical independence

Chapter 2. Borel and after

Chapter 3. The normal law

Chapter 4. Primes play a game of chance

Chapter 5. From kinetic theory to continued fractions


Additional Material

Reviews

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: cointossing, 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


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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.

Chapters

Chapter 1. From Vieta to the notion of statistical independence

Chapter 2. Borel and after

Chapter 3. The normal law

Chapter 4. Primes play a game of chance

Chapter 5. From kinetic theory to continued fractions

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: cointossing, 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