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Mathematics by Experiment: Plausible Reasoning in the 21st Century 2nd edition [Hardback]

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(Coventry University, London, UK), (University of Newcastle, Callaghan, Australia)
  • Formāts: Hardback, 394 pages, height x width: 229x152 mm, weight: 680 g
  • Izdošanas datums: 27-Oct-2008
  • Izdevniecība: A K Peters
  • ISBN-10: 1568814429
  • ISBN-13: 9781568814421
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  • Hardback
  • Cena: 145,75 €
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Mathematics by Experiment: Plausible Reasoning in the 21st Century 2nd editionPalielināt
  • Formāts: Hardback, 394 pages, height x width: 229x152 mm, weight: 680 g
  • Izdošanas datums: 27-Oct-2008
  • Izdevniecība: A K Peters
  • ISBN-10: 1568814429
  • ISBN-13: 9781568814421
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781568814421.html
Keywords:
This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational Paths to Discovery is a highly recommended companion.

Recenzijas

"... experimental mathematics is here to stay. The reader who wants to get an introduction to this exciting approach to doing mathematics can do no better than [ this book]." - Notices of the AMS "Let me cut to the chase: every mathematics library requires a copy of this book.... Every supervisor of higher degree students requires a copy on their shelf. Welcome to the rich world of computer-supported mathematics!" - Mathematical Reviews "These are such fun books to read!... You are going to learn more math (experimental or otherwise) than you ever did from any two single volumes. Not only that, you will learn by osmosis how to become an experimental mathematician." - American Scientist"

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
33
2 Experimental Mathematics in Action 47
2.1 Pascal's Triangle
47
2.2 A Curious Anomaly in the Gregory Series
50
2.3 Bifurcation Points in the Logistic Iteration
52
2.4 Experimental Mathematics and Sculpture
55
2.5 Recognition of Euler Sums
58
2.6 Quantum Field Theory
60
2.7 Definite Integrals and Infinite Series
62
2.8 Prime Numbers and the Zeta Function
65
2.9 Two Observations about square root of 2
74
2.10 Commentary and Additional Examples
76
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
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 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 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 Recent Experiences 243
7.1 Doing What Is Easy
243
7.2 Recursions for Ising Integrals
260
7.3 Euler and Boole Summation Revisited
271
7.4 The QRS Oscillator Constant
283
7.5 Proof Versus Trust
288
7.6 Commentary and Additional Examples
295
Bibliography 349
Subject Index 367
Jonathan M. Borwein, Dalhousie University, Canada; University of Newcastle, Australia. David H. Bailey, Chief Technologist, Computational Research Dept.Lawrence Berkeley National Laboratory. Together, Borwein and Bailey have written Mathematics by Experiment, Experimentation in Mathematics, Experimental Mathematics in Action, and Experiments in Mathematics CD.