Experimentation in Mathematics: Computational Paths to Discovery [ILLUSTRATED] (Hardcover)

~ Jonathan Borwein (Author), David Bailey (Author), Roland Girgensohn (Author) "Several years ago I was invited to contemplate being marooned on the proverbial desert island..." (more)
Key Phrases: Numerical Techniques, The Power of Constructive Proofs, American Mathematical Monthly (more...)

Editorial Reviews

Product Description

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 Centur", 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.

Product Details

• Hardcover: 300 pages
• Publisher: AK Peters; 1st edition (March 31, 2004)
• Language: English
• ISBN-10: 1568811365
• ISBN-13: 978-1568811369
• Product Dimensions: 9.2 x 6.2 x 1.1 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #1,138,832 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

4.0 out of 5 stars using computers in pure maths, September 20, 2006

By	W Boudville (Terra, Sol 3) - See all my reviews (TOP 10 REVIEWER)    (REAL NAME)

The book is an advanced text in computational maths. It requires a solid undergraduate background in real analysis. Typically, you'd have this if you are a maths major. Or possibly a theoretical physics major. The level of rigour is unlike most undergrad texts on numerical analyis. The authors strive to demonstrate that even in pure maths, it can be fruitful to have a computer perform computations. The chapters show that often when there are what appear to be pure maths derivations, a context might appear where you can, or perhaps need to, crunch some numbers.

There are many problems; some quite challenging. Not all the computations are numerical. Several involve symbolic algebra. The text leaves it to you to use whatever maths packages you prefer.

10 of 18 people found the following review helpful:

5.0 out of 5 stars Advanced numerical techniques, and mathematical experiments, June 4, 2004

By	Midwest Book Review (Oregon, WI USA) - See all my reviews

The collaboration of Jonathan Borwein, David Bailey, and Roland Girgensohn, Experimentation In Mathematics: Computational Paths To Discovery is a scholarly, college and graduate-studies text discussing the role of computer-based experimental research in the formulation of new hypotheses. Extensive equations, advanced numerical techniques, and mathematical experiments explained in meticulous, step-by-step detail reveal the "new paradigm" in mathematic research, in this solid text especially for expert students and field professionals in cutting-edge mathematical studies.