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El. knyga: Experimental Mathematics in Action [Taylor & Francis e-book]

(Lawrence Berkeley National Laboratory, California, USA), (The German Armed Forces, Muenchen, Germany), (Tulane University, New Orleans, ), (Winthrop University, Rock Hill, South Carolina, USA), (Clemson University, South Carolina, USA),
  • Formatas: 334 pages
  • Išleidimo metai: 31-May-2007
  • Leidėjas: A K Peters
  • ISBN-13: 9780429064357
Kitos knygos pagal šią temą:
  • Taylor & Francis e-book
  • Kaina: 166,18 €*
  • * this price gives unlimited concurrent access for unlimited time
  • Standartinė kaina: 237,40 €
  • Sutaupote 30%
Experimental Mathematics in ActionDidesnis paveikslėlis
  • Formatas: 334 pages
  • Išleidimo metai: 31-May-2007
  • Leidėjas: A K Peters
  • ISBN-13: 9780429064357
Kitos knygos pagal šią temą:
Taylor & Francis e-booksMore info about Taylor & Francis e-books
Partnerių interneto svetainė: https://www.taylorfrancis.com/books/9780429064357
With the continued advance of computing power and accessibility, the view that “real mathematicians don't compute” no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doing to highlight some of the key algorithms and to teach some of the key experimental approaches. This book is an excellent choice for researchers [ in mathematics] interested in exploring new avenues.

Preface xi
A Philosophical Introduction
1(28)
Introduction
1(1)
Mathematical Knowledge as We View It
1(1)
Mathematical Reasoning
2(1)
Philosophy of Experimental Mathematics
3(8)
Our Experimental Mathodology
11(4)
Finding Things versus Proving Things
15(9)
Conclusions
24(5)
Algorithms for Experimental Mathematics I
29(24)
The Poetry of Computation
29(1)
High-Precision Arithmetic
30(1)
Integer Relation Detection
31(2)
Illustrations and Examples
33(10)
Definite Integrals and Infinite Series Summations
43(1)
Computation of Multivariate Zeta Values
44(1)
Ramanujan-Type Elliptic Series
45(8)
Algorithms for Experimental Mathematics II
53(26)
True Scientific Value
53(2)
Prime Number Computations
55(3)
Roots of Polynomials
58(3)
Numerical Quadrature
61(6)
Infinite Series Summation
67(3)
Apery-Like Summations
70(9)
Exploration and Discovery in Inverse Scattering
79(34)
Metaphysics and Mechanics
79(1)
The Physical Experiment
80(3)
The Model
83(7)
The Mathematical Experiment: Qualitative Inverse Scattering
90(17)
Current Research
107(6)
Exploring Strange Functions on the Computer
113(26)
What Is ``Strange''?
113(1)
Nowhere Differentiable Functions
114(12)
Bernoulli Convolutions
126(13)
Random Vectors and Factoring Integers: A Case Study
139(22)
Learning from Experience
139(1)
Integer Factorization
140(3)
Random Models
143(1)
The Main Questions
144(1)
Bounds
145(4)
Which Model Is Best?
149(6)
Experimental Evidence
155(3)
Conclusions
158(3)
A Selection of Integrals from a Popular Table
161(28)
The Allure of the Integral
161(2)
The Project and Its Experimental Nature
163(1)
Families and Individuals
164(3)
An Experimental Derivation of Wallis' Formula
167(3)
A Hyperbolic Example
170(4)
A Formula Hidden in the List
174(3)
Some Experiments on Valuations
177(7)
An Error in the Latest Edition
184(1)
Some Examples Involving the Hurwitz Zeta Function
185(4)
Experimental Mathematics: A Computational Conclusion
189(36)
Mathematicians Are a Kind of Frenchmen
189(1)
Putting Lessons in Action
190(1)
Visual Computing
191(3)
A Preliminary Example: Visualizing DNA Strands
194(1)
What Is a Chaos Game?
195(7)
Hilbert's Inequality and Witten's Zeta Function
202(12)
Computational Challenge Problems
214(8)
Last Words
222(3)
Exercises
225(76)
Exercises for
Chapter 1
225(6)
Exercises for
Chapter 2
231(18)
Exercises for
Chapter 3
249(7)
Exercises for
Chapter 4
256(4)
Exercises for
Chapter 5
260(2)
Exercises for
Chapter 6
262(3)
Exercises for
Chapter 7
265(8)
Exercises for
Chapter 8
273(7)
Additional Exercises
280(21)
Bibliography 301(16)
Index 317


David Bailey, Jonathan Borwein, Neil Calkin, Russell Luke, Roland Girgensohn, Victor Moll
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