Experimental Mathematics in Action

Description

contains a good philosophical introduction

• C. S. Peirce, like J. S. Mill, considered mathematics an experimental science; cf. Philosophy of Math: Selected Writings §14 "The Logic of Quantity" (PDF pp. 152ff.).
• cf. "Which philosophers considered mathematics an experimental science?"
• ref. to this book courtesy this comment
• cf. the Princeton Companion to Mathematics p. 991 (PDF p. 1014)

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.

Publisher's description: "The last twenty years have been witness to a fundamental shift in the way mathematics is practiced. 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 that can really take advantage of computer-aided research especially given the scope and availability of modern computational packages such as Maple, Mathematica, and MATLAB. The authors provide a coherent variety of accessible examples of modern mathematics subjects in which intelligent computing plays a significant role.''
Contents: 1. A philosophical introduction; 2. Algorithms for experimental mathematics I; 3. Algorithms for experimental mathematics II; 4. Exploration and discovery in inverse scattering; 5. Exploring strange functions on the computer; 6. Random vectors and factoring integers: a case study; 7. A selection of integrals from a popular table; 8. Experimental mathematics: a computational conclusion; 9. Exercises.