Probability and random number: a first guide to randomness
This is a book of elementary probability theory that includes a chapter on algorithmic randomness. It rigorously presents definitions and theorems in computation theory, and explains the meanings of the theorems by comparing them with mechanisms of the computer, which is very effective in the curren...
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| Format: | Buch |
| Sprache: | English |
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New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2018]
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| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Zusammenfassung: | This is a book of elementary probability theory that includes a chapter on algorithmic randomness. It rigorously presents definitions and theorems in computation theory, and explains the meanings of the theorems by comparing them with mechanisms of the computer, which is very effective in the current computer age. Random number topics have not been treated by any books on probability theory, only some books on computation theory. However, the notion of random number is necessary for understanding the essential relation between probability and randomness. The field of probability has changed very much, thus this book will make and leave a big impact even to expert probabilists. Readers from applied sciences will benefit from this book because it presents a very proper foundation of the Monte Carlo method with practical solutions, keeping the technical level no higher than 1st year university calculus. ... |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xi, 125 Seiten Illustrationen, Diagramme |
| ISBN: | 9789813228252 |
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Datensatz im Suchindex
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|---|---|
| adam_text | PROBABILITY AND RANDOM NUMBER
/ SUGITA, HIROSHIYYD1958-YYEAUTHOR
: 2017
TABLE OF CONTENTS / INHALTSVERZEICHNIS
MATHEMATICS OF COIN TOSSING
RANDOM NUMBER
LIMIT THEOREM
MONTE CARLO METHOD
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
Contents Preface Notations and symbols.................... Table of Greek letters.................................................................... 1. Mathematics of coin tossing 1.1 1.2 1.3 1.4 1.5 2. v viii viii 1 Mathematical model............................................................ 1.1.1 Probability space ................................................... 1.1.2 Random variable...................................................... Random number ................................................................. Limit theorem ........................................................................ 1.3.1 Analysis of randomness.......................................... 1.3.2 Mathematical statistics.......................................... Monte Carlo method....................... Infinite coin tosses...............՝..................... .. .................... 1.5.1 Borel’s normal number theorem........................... 1.5.2 Construction of Brownianmotion......................... 1 4 6 10 12 12 15 16 18 19 19 Random number 23 2.1 24 25 2.2 Recursive function.............................................................. 2.1.1 Computable function............................................. 2.1.2 Primitive recursive functionand partial recursive function.............................. ...................................... 2.1.3 Kleene’s normal format3....................................... 2.1.4 Enumeration theorem.......................... Kolmogorov complexity and random number .................. 3The subsections with (*) can be skipped. ix 26 29 31 33
x Contents 2.2.1 2.2.2 2.2.3 3. 34 37 38 Limit theorem 42 3.1 3.2 42 47 48 54 57 60 60 61 65 75 80 86 86 88 3.3 3.4 3.5 4. Kolmogorov complexity.......................................... Random number................. Application: Distribution of prime numbers^*) . . Bernoulli’s theorem............................................................... Law of large numbers ............................................................ 3.2.1 Sequence of independent random variables .... 3.2.2 Chebyshev’s inequality...................................... . 3.2.3 Cramér-Chernoff’s inequality................................. De Moivre-Laplace’s theorem............................................. 3.3.1 Binomial distribution............................................. 3.3.2 Heuristic observation............................................. 3.3.3 Taylor’s formula and Stirling’sformula................ 3.3.4 Proof of de Moivre-Laplace’s theorem.................. Central limit theorem ......................................................... Mathematical statistics......................................................... 3.5.1 Inference.................................................................. 3.5.2 Test........................................................................... Monte Carlo method 4.1 4.2 4.3 4.4 Monte Carlo method as gambling....................................... 4.1.1 Purpose..................................................................... 4.1.2 Exercise I, revisited................................................ Pseudorandom
generator...................................................... 4.2.1 Definition.................................................................. 4.2.2 Security............................. Monte Carlo integration............................. 4.3.1 Mean and integral................................................... 4.3.2 Estimation of mean . . . ....................................... 4.3.3 Random Weyl sampling.......................................... From the viewpoint of mathematical statistics.................. 91 91 91 93 94 94 95 96 96 97 98 104 Appendix A 105 A.l 105 105 106 108 Symbols and terms . ................................. A. 1.1 Set and function....................................................... A.1.2 Symbols for sum and product.................................. A.1.3 Inequality symbol ‘ ^ ’...........................................
Contents A.2 A.3 A.4 A.5 xi Binary numeral system......................................................... A.2.1 Binary integers.......................................................... A.2.2 Binary fractions...................................................... Limit of sequence and function.......................................... A.3.1 Convergence of sequence........................................ A.3.2 Continuity of function of one variable................... A.3.3 Continuity of function of several variables............. Limits of exponential function and logarithm.................. C language program............................................................ 108 108 110 Ill Ill 114 115 115 116 List of mathematicians 119 Further reading 120 Bibliography 121 Index 123
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| spelling | Sugita, Hiroshi (DE-588)1028199201 aut Kakuritsu to ransū Probability and random number a first guide to randomness Hiroshi Sugita (Osaka University, Japan) New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2018] © 2018 xi, 125 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index This is a book of elementary probability theory that includes a chapter on algorithmic randomness. It rigorously presents definitions and theorems in computation theory, and explains the meanings of the theorems by comparing them with mechanisms of the computer, which is very effective in the current computer age. Random number topics have not been treated by any books on probability theory, only some books on computation theory. However, the notion of random number is necessary for understanding the essential relation between probability and randomness. The field of probability has changed very much, thus this book will make and leave a big impact even to expert probabilists. Readers from applied sciences will benefit from this book because it presents a very proper foundation of the Monte Carlo method with practical solutions, keeping the technical level no higher than 1st year university calculus. ... Probabilities Random variables Numbers, Random Monte Carlo method Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Zufallszahlen (DE-588)4124968-9 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Zufallszahlen (DE-588)4124968-9 s LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030145516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030145516&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sugita, Hiroshi Probability and random number a first guide to randomness Probabilities Random variables Numbers, Random Monte Carlo method Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Zufallszahlen (DE-588)4124968-9 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4124968-9 (DE-588)4240945-7 |
| title | Probability and random number a first guide to randomness |
| title_alt | Kakuritsu to ransū |
| title_auth | Probability and random number a first guide to randomness |
| title_exact_search | Probability and random number a first guide to randomness |
| title_full | Probability and random number a first guide to randomness Hiroshi Sugita (Osaka University, Japan) |
| title_fullStr | Probability and random number a first guide to randomness Hiroshi Sugita (Osaka University, Japan) |
| title_full_unstemmed | Probability and random number a first guide to randomness Hiroshi Sugita (Osaka University, Japan) |
| title_short | Probability and random number |
| title_sort | probability and random number a first guide to randomness |
| title_sub | a first guide to randomness |
| topic | Probabilities Random variables Numbers, Random Monte Carlo method Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Zufallszahlen (DE-588)4124968-9 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Probabilities Random variables Numbers, Random Monte Carlo method Wahrscheinlichkeitstheorie Zufallszahlen Monte-Carlo-Simulation |
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