Stan Wagon

David Bressoud

"The accompanying CD-Rom contains Mathematica files with all the commands and programs."--P. [4] of cover.

A Course in Computational Number Theor

Folkmar Bornemann

Dirk Laurie

J?rg Waldvogel

Gives concrete examples of how to justify the validity of every single digit of a numerical answer.

A Study in High-Accuracy Numerical Computing

The SIAM 100-Digit Challenge

Joseph D. E. Konhauser

Dan Velleman

The best problems selected from over 25 years of the Problem of the Week at Macalester College.

And Other Intriguing Mathematical Mysteries

Which Way Did the Bicycle Go?

Grzegorz Tomkowicz

The Banach-Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.

The Banach–Tarski Paradox

Plenty of examples and case studies utilize Mathematica 7's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting. Emphasizes the breadth of Mathematica and the impressive results of combining techniques from different areas. Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, and new and surprising formulas for p. Visualization is emphasized throughout, with finely crafted graphics in each chapter.

Problem Solving Through Visualization and Computation

Mathematica® in Action

Victor Klee

Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.

Stan Wagon

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