Statistical Independence in Probability, Analysis and Number Theory (Dover Books on Mathematics)

Kac, Mark

ISBN 10: 0486821587 / ISBN 13: 9780486821580

Published by Dover Publications, Incorporated, 2018

About this Item

pp. 112.

Seller Inventory # 381483460

Bibliographic Details

• Title: Statistical Independence in Probability, Analysis and Number Theory (Dover Books on Mathematics)
• Publisher: Dover Publications, Incorporated
• Publication Date: 2018
• Language: English
• ISBN 10: 0486821587
• ISBN 13: 9780486821580
• Binding: Soft cover
• Condition: New

About this title

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 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.