The Resource Statistical independence in probability analysis and number theory, by Mark Kac

Statistical independence in probability analysis and number theory, by Mark Kac

Label
Statistical independence in probability analysis and number theory
Title
Statistical independence in probability analysis and number theory
Statement of responsibility
by Mark Kac
Creator
Author
Subject
Genre
Language
  • eng
  • eng
Summary
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. Born in Poland, he studied with Hugo Steinhaus at Lwów earning his doctorate in 1936. He had a long and productive career in the United States, serving on the faculties of Cornell University (1939-1961), Rockefeller University (1961-1982), and the University of Southern California (1982 until his death in 1984)
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Kac, Mark
Dewey number
519.1
Illustrations
illustrations
Index
no index present
Language note
English
LC call number
QA273
LC item number
.K25 1959
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Carus Mathematical Monographs
Series volume
Number 12
http://library.link/vocab/subjectName
  • Probabilities
  • Mathematical statistics
Label
Statistical independence in probability analysis and number theory, by Mark Kac
Instantiates
Publication
Copyright
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • ""cover ""; ""Statistical Independence in Probability, Analysis and Number Theory""; ""Copyright Page""; ""Contents""; ""Chapter 1. From Vieta to the Notion of Statistical Independence""; ""1. A formula of Vieta""; ""2. Another look at Vieta's formula""; ""3. An accident or a beginning of something deeper?""; ""4. (1/2)n = 1/2â€?1/2 (n times)""; ""5. Heads or tails""; ""6. Independence and ""Independence""""; ""Problems""; ""Chapter 2. Borel and After""; ""1. ""Laws of large numbers""""; ""2. Borel and ""normal numbers""""; ""Problems""; ""3. ""Heads or Tails""â€?a more abstract formulation""
  • ""4. What price abstraction?""""5. Example 1. Convergence of series with random signs""; ""6. Example 2. Divergence of series with random signs""; ""Problems""; ""Bibliography""; ""Chapter 3. The Normal Law""; ""1. De Moivre""; ""2. The idea""; ""3. Markoff's method made rigorous""; ""Problems""; ""4. A closer look at the method""; ""Problems""; ""5. A law of nature or a mathematical theorem?""; ""Problems""; ""Bibliography""; ""Chapter 4. Primes Plat a Game of Chance""; ""1. Number theoretic functions, density, independence""; ""2. The statistics of the Euler Ñ?-function""; ""Problems""
  • ""3. Another application""""4. Almost every integer m has approximately log log m prime divisors""; ""Problems""; ""5. The normal law in number theory""; ""Problems""; ""Bibliography""; ""Chapter 5. From Kinetic Theory to Continued Fractions""; ""1. Paradoxes of kinetic theory""; ""2. Preliminaries""; ""3. Boltzmann's reply""; ""4. The abstract formulation""; ""5. The ergodic theorem and continued fractions""; ""Problems""; ""Bibliography""
Dimensions
unknown
Extent
1 online resource (109 p.)
Form of item
online
Isbn
9781614440123
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2560000000141404
  • (EBL)3330465
  • (SSID)ssj0000577751
  • (PQKBManifestationID)11347712
  • (PQKBTitleCode)TC0000577751
  • (PQKBWorkID)10576763
  • (PQKB)11764120
  • (UkCbUP)CR9781614440123
  • (MiAaPQ)EBC3330465
  • (EXLCZ)992560000000141404
Label
Statistical independence in probability analysis and number theory, by Mark Kac
Publication
Copyright
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • ""cover ""; ""Statistical Independence in Probability, Analysis and Number Theory""; ""Copyright Page""; ""Contents""; ""Chapter 1. From Vieta to the Notion of Statistical Independence""; ""1. A formula of Vieta""; ""2. Another look at Vieta's formula""; ""3. An accident or a beginning of something deeper?""; ""4. (1/2)n = 1/2â€?1/2 (n times)""; ""5. Heads or tails""; ""6. Independence and ""Independence""""; ""Problems""; ""Chapter 2. Borel and After""; ""1. ""Laws of large numbers""""; ""2. Borel and ""normal numbers""""; ""Problems""; ""3. ""Heads or Tails""â€?a more abstract formulation""
  • ""4. What price abstraction?""""5. Example 1. Convergence of series with random signs""; ""6. Example 2. Divergence of series with random signs""; ""Problems""; ""Bibliography""; ""Chapter 3. The Normal Law""; ""1. De Moivre""; ""2. The idea""; ""3. Markoff's method made rigorous""; ""Problems""; ""4. A closer look at the method""; ""Problems""; ""5. A law of nature or a mathematical theorem?""; ""Problems""; ""Bibliography""; ""Chapter 4. Primes Plat a Game of Chance""; ""1. Number theoretic functions, density, independence""; ""2. The statistics of the Euler Ñ?-function""; ""Problems""
  • ""3. Another application""""4. Almost every integer m has approximately log log m prime divisors""; ""Problems""; ""5. The normal law in number theory""; ""Problems""; ""Bibliography""; ""Chapter 5. From Kinetic Theory to Continued Fractions""; ""1. Paradoxes of kinetic theory""; ""2. Preliminaries""; ""3. Boltzmann's reply""; ""4. The abstract formulation""; ""5. The ergodic theorem and continued fractions""; ""Problems""; ""Bibliography""
Dimensions
unknown
Extent
1 online resource (109 p.)
Form of item
online
Isbn
9781614440123
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2560000000141404
  • (EBL)3330465
  • (SSID)ssj0000577751
  • (PQKBManifestationID)11347712
  • (PQKBTitleCode)TC0000577751
  • (PQKBWorkID)10576763
  • (PQKB)11764120
  • (UkCbUP)CR9781614440123
  • (MiAaPQ)EBC3330465
  • (EXLCZ)992560000000141404

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