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Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century [Hardcover]

by Jonathan Borwein, David Bailey
5.0 out of 5 stars  See all reviews (5 customer reviews)

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Book Description

October 27, 2008 1568814429 978-1568814421 2
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.

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Editorial Reviews


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, American Mathematical Society

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

You are going to learn more math (experimental or otherwise). Not only that, you will learn by osmosis how to become an experimental mathematician. --American Scientist

About the Author

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.

Product Details

  • Hardcover: 393 pages
  • Publisher: A K Peters/CRC Press; 2 edition (October 27, 2008)
  • Language: English
  • ISBN-10: 1568814429
  • ISBN-13: 978-1568814421
  • Product Dimensions: 9.3 x 6.2 x 1 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #369,771 in Books (See Top 100 in Books)

More About the Author

Jonathan Michael Borwein, FRSC, FAAAS,FBAS, FAA is currently Laureate Professor in the School of Mathematical and Physical Sciences at the University of Newcastle (NSW). He directs the University's Priority Research Centre in Computer Assisted Research Mathematics and its Applications (CARMA).

A Rhodes Scholar, his research interests span pure (analysis), applied (optimization), computational (numerical and computational analysis) mathematics, and high performance computing. He has authored over a dozen books---most recently four on Experimental Mathematics (, a 2010 prize winning book on Convex Functions and two on Modern mathematical computation---and over 400 refereed publications.

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Most Helpful Customer Reviews
32 of 34 people found the following review helpful
5.0 out of 5 stars A Mathematical Paradigm Shift January 28, 2004
"Mathematics by Experiment" is a ground-breaking book about a new way of doing math that generated so much excitement it was reviewed in "Scientific American" six months before it got into print. The authors are long-time collaborators David Bailey, chief technologist in the Computational Research Department of Lawrence Berkeley National Laboratory, and Jonathan Borwein, professor of science at Simon Fraser University in Vancouver, B.C.
They write that applied mathematicians and many scientists and engineers were quick to embrace computer technology, while pure mathematicians -- whose field gave rise to computers in the first place, through the work of beautiful minds like Alan Turing's -- were slower to see the possibilities. Two decades ago, when Bailey and Borwein started collaborating, "there appeared to be a widespread view in the field that 'real mathematicians don't compute.'"
Their book is testament to a paradigm shift in the making. Hardware has "skyrocketed in power and plummeted in cost," and powerful mathematical software has come on the market. Just as important, "a new generation of mathematicians is eagerly becoming skilled at using these tools" -- people comfortable with the notion that "the computer provides the mathematician with a 'laboratory' in which he or she can perform experiments: analyzing examples, testing out new ideas, or searching for patterns."
In this virtual laboratory Bailey and Borwein, with other colleagues, were among the first to discover a number of remarkable new algorithms, among them an extraordinary, simple formula for finding any hexadecimal or binary digit of pi without knowing any of the preceding digits.
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11 of 12 people found the following review helpful
Format:Hardcover|Verified Purchase
If one peruses the mathematical literature for the last one hundred years one will notice that in most cases no diagrams or pictures appear. The level of rigor in all cases is impressive though, but unfortunately this makes the understanding of the results much more difficult. There seems to be an inverse relationship between rigor and understanding in mathematics, at least for those who are new to the subject at hand. In order to gain this understanding, the drawing of pictures and diagrams is useful, along with a certain amount of experimentation with the concepts at hand. Intuition, how mysterious, and however ill defined, plays a role in both the understanding of mathematical results and in their discovery. Many mathematicians do not want to acknowledge this, as a visitation to a typical conference will readily verify. The attitude has been expressed that mathematics has "always been abstract" and therefore that pictures or diagrams violate its spirit. Even a well-known geometry center whose goal was to use sophisticated computer graphics to visualize complex mathematical objects lost its funding, to the consternation of a few but with glee to most.

Thus the way to discovery of mathematics, i.e. the heavy use of intuition, the disorganized shuffling of concepts, and the experimental doodling, has been masked by the final product of this process: a superb example of logical rigor and organization called modern mathematics. The authors of this book however think otherwise, and they give the best apology for the role of experimental mathematics than anyone else in the literature. The book is packed with highly interesting examples and challenging exercises, all of which are ample proof of the need for doing experimentation in mathematics.
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6 of 10 people found the following review helpful
5.0 out of 5 stars A thoroughly detailed work April 14, 2004
The collaborative work of Jonathan Borwein and David Bailey, Mathematics By Experiment: Plausible Reasoning In The 21st Century provides a complex and informative text for advanced mathematics students which offs an historical context and rationale behind experimental mathematics, as well as how modern technology enables the analysis of new examples and the discovery of patterns in a previously unimaginable "laboratory" of raw processing power. A thoroughly detailed work, Mathematics By Experiment offers a veritable wealth of meticulously presented examples which are most especially recommended for graduate-level mathematics studies.
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4 of 7 people found the following review helpful
5.0 out of 5 stars 'Pure' Mathematics has been slow to embrace computers September 2, 2005
High end mathematical theory has veered away from actually doing arithmetic because most of the problems being addressed required a tremendous amount of calculation and that calculation was difficult in the days of only pen and paper. About twenty years ago the advent of big/fast computers (by the standards of those days) began to allow the ready solution of these problems without requiring large numbers of people doing the computing.

Borwein and Bailey have been pioneers in the exploration of the types of mathematical problems that would lend themselves to solution using digital computational means. This book describes this new approach to mathematics, commonly called 'experimental mathematics.'

Obviously in computer related mathematics it began with a lot of emphasis on prime numbers, on calculating the value of Pi to ever greater precision. It has since moved on to many other classes of problems, and the work of the principle researchers in the field is summarized here.
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