Experimentation in Mathematics: Computational Paths to Discovery

ISBN-13: 9781568811369 / Angielski / Twarda / 2004 / 372 str.

Jonathan M. Borwein; David H. Bailey

Opis

New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of experimental research in the statement of new hypotheses and the discovery of new results that chart the road to future developments. Following the lead of Mathematics by Experiment: Plausible Reasoning in the 21st Century this book gives numerous additional case studies of experimental mathematics in action, ranging from sequences, series, products, integrals, Fourier series, zeta functions, partitions, primes and polynomials. Some advanced numerical techniques are also presented. To get a taste of the material presented in both books view the condensed version.

Spis treści

Preface, 1 Sequences, Series, Products and Integrals, 2 Fourier Series and Integrals, 3 Zeta Functions and Multizeta Functions, 4 Partitions and Powers, 5 Primes and Polynomials, 6 The Power of Constructive Proofs II, 7 Numerical Techniques II, Bibliography, Index

O autorze

Jonathan M. Borwein, David H. Bailey, Roland Girgensohn, David H. Bailey, Jonathan M. Borwein