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The Resource Statistical independence in probability analysis and number theory, by Mark Kac
Statistical independence in probability analysis and number theory, by Mark Kac
Resource Information
The item Statistical independence in probability analysis and number theory, by Mark Kac represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Statistical independence in probability analysis and number theory, by Mark Kac represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 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 (19391961), Rockefeller University (19611982), and the University of Southern California (1982 until his death in 1984)
 Language

 eng
 eng
 Extent
 1 online resource (109 p.)
 Note
 Description based upon print version of record
 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""
 Isbn
 9781614440123
 Label
 Statistical independence in probability analysis and number theory
 Title
 Statistical independence in probability analysis and number theory
 Statement of responsibility
 by Mark Kac
 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 (19391961), Rockefeller University (19611982), and the University of Southern California (1982 until his death in 1984)
 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
 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
 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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