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Ants, Bikes, & Clocks: Problem Solving for Undergraduates

William Briggs
Publication Date: 
Number of Pages: 
Problem Book
[Reviewed by
Jeffrey A. Graham
, on
Ants, Bikes, & Clocks by William Briggs is a text for an undergraduate problem solving course. It is really more of a book of problems than a text. There are 12 chapters in the book. The first eleven chapters focus on the application of various mathematical techniques to problem solving and the last chapter consists of solutions to most of the odd-numbered problems.

The level of mathematics assumed for the text is quite modest. The reader is assumed to have had two semesters of calculus although much of the book is pitched at a lower level. There is a smattering of topics such as Markov chains that require a bit of matrix background. Chapter Nine explores using a computer as a tool for problem solving. Including this chapter in your syllabus adds some modest programming skills to the assumed knowledge.

Each of the first eleven chapters consists of a brief introduction to a mathematical technique followed by a few worked examples and a generous number of problems. The problem solving advice contained in the book is pretty limited. A brief, one page summary of Polya’s four-step method is about all you will find. It is the problems that make this book worth a look. Nearly every mathematical puzzle that I can recall is represented in this book. If you believe (as I do) that problem solving can only be learned by solving problems, then this is the book for you.

Jeffrey A. Graham teaches at Susquehanna University. His interests include numerical analysis, differential equations, inverse problems, and mathematical biology.

Chapter 1: Introduction; Chapter 2: A Problem Solving Framework; Chapter 3: Problem Solving Strategies; Chapter 4: How Do You Do It? Chapter 5: Parts of the Whole; Chapter 6: A World of Change; Chapter 7: At Any Rate; Chapter 8: Difference Equations; Chapter 9: Insight and Computing; Chapter 10: Take a Chance; Chapter 11: Toward Modeling; Chapter 12: Solutions; Bibliography; Index.