Books on Experimental Mathematics

Bailey and Borwein have written several references works on experimental mathematics, which we feature here. As other books are published in this general area, we will feature them here also.

• Mathematics by Experiment: Plausible Reasoning in the 21st Century. "Experimental mathematics" means using advanced computing technology as a "laboratory" for mathematical research. This book presents the rationale and historical context of experimental mathematics, and includes a series of examples that best portray the experimental methodology, together with some of the numerical techniques used in this research. Numerous historical and biographical notes are also included. Available at: AK Peters | Amazon.com
• Experimentation in Mathematics: Computational Paths to Discovery. Following the lead of the first volume, 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. Available at: AK Peters | Amazon.com
• Experiments in Mathematics This is a CD-ROM with a hyperlinked, searchable PDF files of the above two books. This is the first time a major work of mathematics has appeared in this format. Available at: AK Peters | Amazon.com
• Experimental Mathematics in Action. This new book, published in May 2007 by AK Peters, is the companion volume to the MAA Short Course conducted at the San Antonio AMS-MAA meeting in Jan 2006. The authors are David Bailey, Jonathan Borwein, Neil Calkin, Roland Girgensohn, Russell Luke and Victor Moll. Each chapter presents some case studies of experimental mathematics being used in real problems of mathematical research, both pure and applied:
  1. Jonathan M. Borwein, "A Philosophical Introduction".
  2. David H. Bailey, "Algorithms I"
  3. David H. Bailey, "Algorithms II"
  4. Russell Luke, "Inverse Scattering"
  5. Roland Girgensohn, "Strange Functions"
  6. Neil Calkin, "Factoring Integers"
  7. Victor Moll, "Integrals"
  8. Jonathan M. Borwein, "A Computational Conclusion"
  9. "Exercises"
  Press release: AKP press release
  Available at: AK Peters | Amazon.com

Other books in the area of experimental mathematics

• Fernando Villegas, Experimental Number Theory. This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, along with exercises and selected solutions. Sample programs are written in GP, the scripting language for the computational package PARI, and are available for download from the author's website. Available at: Oxford University Press

Book Reviews

1. Review of Experimental Mathematics in Action in Zenmtralblatt-Math 1127: PDF
   We agree with the reviewer that in some cases more historical references would have been appropriate: but the book was written as a short course and more detailed references were always available in articles cited in the book.
2. Review of Experimental Mathematics in Action in the Gazette of the Australian Mathematical Society (see pg. 290) (Nov 2007): PDF
3. BookNews.com review of Experimental Mathematics in Action (see pg. 16): PDF
4. MAA Online book review of Experimenal Mathematics in Action: HTML
5. Experimental Math in Action is included by Science News in a listing of "new and notable" science books (Aug 2007): PDF
6. ACM Computing Reviews review of Mathematics by Experiment, Experimentation in Mathematics, and CD-ROM version (2 Mar 2007): PDF
7. Review of Mathematics by Experiment and Experimentation in Mathematics in Notes of the Canadian Mathematical Society, by Richard Crandall (vol. 38, no. 4, 2006): PDF
8. Review of Mathematics by Experiment and Experimentation in Mathematics in Notices of the American Mathematical Society, by Jeffrey Shallit (Sep 2005 issue): PDF
9. Review of Expermentation in Mathematics in Math Reviews, by Frits Beukers (May 2005): PDF
10. Article in Pour La Science (French), by Jean-Paul Delahaye (Apr 2005): PDF
11. Review of Mathematics by Experiment and Experimentation in Mathematics in Gazette of the Australian Mathematical Society, vol. 32, no. 3, pg. 199 (2005), by Andrew Rechnitzer: PDF
12. Review of Mathematics by Experiment and Experimentation in Mathematics in SIAM Review, by Reuben Hersh and Robin Frye (vol. 47 no. 4, 2005): PDF
13. MAA online book review of Mathematics by Experiment and Experimentation in Mathematics, by David P. Roberts (2005): HTML
14. Review of Mathematics by Experiment and Experimentation in Mathematics in American Scientist, by Doron Zeilberger (Mar-Apr 2005 issue): HTML
15. Review of Mathematics by Experiment in Mathematics Magazine, by Paul J. Campbell (2005): HTML
16. Zentralblatt review of Mathematics by Experiment and Experimentation in Mathematics, by Gunter M. Ziegler (2004): PDF
17. Review of Mathematics by Experiment in Math Reviews, by John H. Mason (Nov 2004): PDF
18. Review of Mathematics by Experiment and Experimentation in Mathematics in European Mathematical Society Review, by Ivan Netuka and Vladimir Soucek (Sept 2004): PDF
19. Citation in the National Academy of Science report "Getting Up to Speed: The Future of Supercomputing" (June 2004): PDF
20. Berkeley Science Review article, by Padraig Murphy (June 2004): PDF

Supplementary Information for the Books

1. A "Reader's Digest" version of "Mathematics by Experiment" and "Experimentation in Mathematics" is freely available here: PDF
2. Citation errors in Mathematics by Experiment
3. Ten Sample Problems of Experimental Math
4. Errata in Mathematics by Experiment
5. Errata in Experimentation in Mathematics
6. Errata in Mathematics by Experiment and Experiments in Mathematics (CD-ROM edition)
7. Errata in Experimental Mathematics in Action

Author Websites

1. Borwein's website: http://www.cs.dal.ca/~jborwein
2. Bailey's website: http://crd.lbl.gov/~dhbailey
3. Girgensohn's email: zzzzzz@mytum.de. To obtain the real address, replace "zzzzzz" by "girgen".