Mathematics by experiment: plausible reasoning in the 21st century
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Natick, Mass.
Peters
2004
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 267-280) and index |
| Beschreibung: | X, 288 S. Ill. |
| ISBN: | 1568812116 |
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Datensatz im Suchindex
| _version_ | 1804132885667512320 |
|---|---|
| adam_text | MATHEMATICS BY EXPERIMENT: PLAUSIBLE REASONING IN THE 21 ST CENTURY
JONATHAN BORWEIN DAVID BAILEY A K PETERS NATICK, MASSACHUSETTS CONTENTS
PREFACE VII 1 WHAT IS EXPERIMENTAL MATHEMATICS? 1 1.1 BACKGROUND 1 1.2
COMPLEXITY CONSIDERATIONS 3 1.3 PROOF VERSUS TRUTH 7 1.4 PARADIGM SHIFTS
10 1.5 GAUSS, THE EXPERIMENTAL MATHEMATICIAN 12 1.6 GEOMETRIC
EXPERIMENTS 16 1.7 SAMPLE PROBLEMS OF EXPERIMENTAL MATH 22 1.8
INTERNET-BASED MATHEMATICAL RESOURCES 26 1.9 COMMENTARY AND ADDITIONAL
EXAMPLES 32 2 EXPERIMENTAL MATHEMATICS IN ACTION 45 2.1 PASCAL S
TRIANGLE 45 2.2 A CURIOUS ANOMALY IN THE GREGORY SERIES 48 2.3
BIFURCATION POINTS IN THE LOGISTIC ITERATION 50 2.4 EXPERIMENTAL
MATHEMATICS AND SCULPTURE 53 2.5 RECOGNITION OF EULER SUMS 56 2.6
QUANTUM FIELD THEORY 58 2.7 DEFINITE INTEGRALS AND INFINITE SERIES 60
2.8 PRIME NUMBERS AND THE ZETA FUNCTION 63 2.9 TWO OBSERVATIONS ABOUT
[2 72 2.10 COMMENTARY AND ADDITIONAL EXAMPLES 74 3 PI AND ITS FRIENDS
103 3.1 A SHORT HISTORY OF PI . . . . 103 3.2 FASCINATION WITH PI 115
3.3 BEHIND THE CUBIC AND QUARTIC ITERATIONS 117 3.4 COMPUTING INDIVIDUAL
DIGITS OF PI 118 3.5 UNPACKING THE BBP FORMULA FOR PI 125 3.6 OTHER
BBP-TYPE FORMULAS 127 VI CONTENTS 3.7 DOES PI HAVE A NONBINARY BBP
FORMULA? 131 3.8 COMMENTARY AND ADDITIONAL EXAMPLES 133 4 NORMALITY OF
NUMBERS 143 4.1 NORMALITY: A STUBBORN QUESTION 143 4.2 BBP CONSTANTS AND
NORMALITY 148 4.3 A CLASS OF PROVABLY NORMAL CONSTANTS 152 4.4 ALGEBRAIC
IRRATIONALS 156 4.5 PERIODIC ATTRACTORS AND NORMALITY 159 4.6 COMMENTARY
AND ADDITIONAL EXAMPLES 164 5 THE POWER OF CONSTRUCTIVE PROOFS I 175 5.1
THE FUNDAMENTAL THEOREM OF ALGEBRA 175 5.2 THE UNCERTAINTY PRINCIPLE 183
5.3 A CONCRETE APPROACH TO INEQUALITIES 188 5.4 THE GAMMA FUNCTION 192
5.5 STIRLING S FORMULA 197 5.6 DERIVATIVE METHODS OF EVALUATION 199 5.7
COMMENTARY AND ADDITIONAL EXAMPLES 205 6 NUMERICAL TECHNIQUES I 215 6.1
CONVOLUTIONS AND FOURIER TRANSFORMS 216 6.2 HIGH-PRECISION ARITHMETIC
218 6.3 CONSTANT RECOGNITION 229 6.4 COMMENTARY AND ADDITIONAL EXAMPLES
235 7 MAKING SENSE OF EXPERIMENTAL MATH 243 7.1 INTRODUCTION 243 7.2
EXPERIMENTAL MATHEMATICS 246 7.3 ZEILBERGER AND THE ENCAPSULATION OF
IDENTITY 251 7.4 EXPERIMENT AND THEORY 255 7.5 THEORETICAL
EXPERIMENTATION 256 7.6 A MATHEMATICAL EXPERIMENT 259 7.7 CONCLUSION 262
BIBLIOGRAPHY 267 INDEX 281
|
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| spelling | Borwein, Jonathan M. 1951-2016 Verfasser (DE-588)115617884 aut Mathematics by experiment plausible reasoning in the 21st century Jonathan Borwein ; David Bailey Natick, Mass. Peters 2004 X, 288 S. Ill. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 267-280) and index Dataprocessing gtt Experimenteel onderzoek gtt Mathématiques - Expérimentation Mathématiques - Informatique Wiskundige methoden gtt aMathematics xData processing aMathematics xExperiments Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Experiment (DE-588)4015999-1 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 s Datenverarbeitung (DE-588)4011152-0 s Experiment (DE-588)4015999-1 s DE-604 Mathematik (DE-588)4037944-9 s 1\p DE-604 Bailey, David H. Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012882881&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Borwein, Jonathan M. 1951-2016 Mathematics by experiment plausible reasoning in the 21st century Dataprocessing gtt Experimenteel onderzoek gtt Mathématiques - Expérimentation Mathématiques - Informatique Wiskundige methoden gtt aMathematics xData processing aMathematics xExperiments Angewandte Mathematik (DE-588)4142443-8 gnd Datenverarbeitung (DE-588)4011152-0 gnd Mathematik (DE-588)4037944-9 gnd Experiment (DE-588)4015999-1 gnd |
| subject_GND | (DE-588)4142443-8 (DE-588)4011152-0 (DE-588)4037944-9 (DE-588)4015999-1 |
| title | Mathematics by experiment plausible reasoning in the 21st century |
| title_auth | Mathematics by experiment plausible reasoning in the 21st century |
| title_exact_search | Mathematics by experiment plausible reasoning in the 21st century |
| title_full | Mathematics by experiment plausible reasoning in the 21st century Jonathan Borwein ; David Bailey |
| title_fullStr | Mathematics by experiment plausible reasoning in the 21st century Jonathan Borwein ; David Bailey |
| title_full_unstemmed | Mathematics by experiment plausible reasoning in the 21st century Jonathan Borwein ; David Bailey |
| title_short | Mathematics by experiment |
| title_sort | mathematics by experiment plausible reasoning in the 21st century |
| title_sub | plausible reasoning in the 21st century |
| topic | Dataprocessing gtt Experimenteel onderzoek gtt Mathématiques - Expérimentation Mathématiques - Informatique Wiskundige methoden gtt aMathematics xData processing aMathematics xExperiments Angewandte Mathematik (DE-588)4142443-8 gnd Datenverarbeitung (DE-588)4011152-0 gnd Mathematik (DE-588)4037944-9 gnd Experiment (DE-588)4015999-1 gnd |
| topic_facet | Dataprocessing Experimenteel onderzoek Mathématiques - Expérimentation Mathématiques - Informatique Wiskundige methoden aMathematics xData processing aMathematics xExperiments Angewandte Mathematik Datenverarbeitung Mathematik Experiment |
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