Verfügbarkeit: Mathematics by experiment | Technische Universität München

Mathematics by experiment: plausible reasoning in the 21st century

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Bibliographische Detailangaben
Beteilige Person:	Borwein, Jonathan M. 1951-2016 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Natick, Mass. Peters 2004
Schlagwörter:	Dataprocessing Experimenteel onderzoek Mathématiques - Expérimentation Mathématiques - Informatique Wiskundige methoden aMathematics > xData processing aMathematics > xExperiments Angewandte Mathematik Datenverarbeitung Mathematik Experiment
Links:	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
Beschreibung:	Includes bibliographical references (p. 267-280) and index
Umfang:	X, 288 S. Ill.
ISBN:	1568812116

Internformat

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Datensatz im Suchindex

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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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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
url	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
work_keys_str_mv	AT borweinjonathanm mathematicsbyexperimentplausiblereasoninginthe21stcentury AT baileydavidh mathematicsbyexperimentplausiblereasoninginthe21stcentury

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