Statistical Independence in Probability, Analysis and Number Theory (eBook)

Mark Kac (Autor)

eBook Download: EPUB

2018
112 Seiten
Dover Publications (Verlag)
978-0-486-83340-8 (ISBN)

Infos

This concise monograph by a well-known mathematician shows how probability theory, in its simplest form, arises in a variety of contexts and in many different mathematical disciplines. 1959 edition.

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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 "e;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."e; 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.

Autor

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.

Inhalt

Contents Chapter 1. From Vieta to the Notion of Statistical IndependenceChapter 2. Borel and AfterChapter 3.The Normal LawChapter 4. Primes Play a Game of ChanceChapter 5. From Kinetic Theory to Continued Fractions

Produkt-Details

• Erscheint lt. Verlag: 15.8.2018
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Schlagworte: abraham de moivre • andrey markov • Applied mathematics • Continued fractions • Emile Borel • fourier integrals • Kinetic Theory • laws of large numbers • Math • Mathematics • measure and integration • normal law • Normal numbers • number theoretic functions • Number Theory • Probability • Pure Mathematics • Science • science and math • statistical independence • Statistics • vieta
• ISBN-10: 0-486-83340-2 / 0486833402
• ISBN-13: 978-0-486-83340-8 / 9780486833408