Statistical Independence in Probability Analysis and Number Theory (Carus Mathematical Monographs, No 12) - Softcover

Kac, Marc

Softcover

ISBN 10: 0883850125 ISBN 13: 9780883850121

Publisher: Mathematical Assn of Amer, 1969

Synopsis

This concise monograph in probability by Mark Kac, a well-known mathematician, presumes a familiarity with Lebesgue's theory of measure and integration, the elementary theory of Fourier integrals, and the rudiments of number theory. Readers may then follow Dr. Kac's attempt "to rescue statistical independence from the fate of abstract oblivion by showing how in its simplest form it arises in various contexts cutting across different mathematical disciplines."
The treatment begins with an examination of a formula of Vieta that extends to the notion of statistical independence. Subsequent chapters explore laws of large numbers and Émile Borel's concept of normal numbers; the normal law, as expressed by Abraham de Moivre and Andrey Markov's method; and number theoretic functions as well as the normal law in number theory. The final chapter ranges in scope from kinetic theory to continued fractions. All five chapters are enhanced by problems.

About this title

About the Author

Marc Kac, born in Poland, studied with Hugo Steinhaus at Lwow earning his doctorate in 1936. He had a long and productive career in the United States, serving on the faculities, of Cornell University, Rockefeller University, and he University of Southern California.

Review

A masterly celebration of the unity of mathemtics. -- Ian Stewart

Terrific, friendly, and profound. -- Persi Diaconis

Edition details

• Publisher: Mathematical Assn of Amer
• Publication date: 1969
• ISBN 10: 0883850125
• ISBN 13: 9780883850121
• Binding: Paperback
• Language: English
• Number of pages: 105