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Ants, Bikes, and Clocks: Problem Solving for Undergraduates

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by William Briggs


2005 / vi + 170 pages / Softcover / ISBN: 978-0-898715-74-3 / List Price $61.00 / SIAM Member Price $42.70 / Order Code OT90

"Briggs's book is in some sense an update of Polya's classic, How to Solve It. Certainly Briggs pays due homage to the master, cites his four main principles of problem solving, and organizes his text in a manner that at least pays homage to Polya. But Briggs goes much further. His writing style is lively and attractive. He gets in the reader's face and stays in his/her face from page one. He does this in a friendly way, one that gets the reader involved and keeps him/her involved as the work progresses. The student will be carried along by this book, and ever anxious to learn the next new idea. I like Briggs's book so well that I would certainly make considerable use of his text the next time that I teach problem-solving."
-- Steven G. Krantz, Washington University in St. Louis.

Mathematics educators agree that problem solving is one of the essential skills their students should possess, yet few mathematics courses or textbooks are devoted entirely to developing this skill. Supported by narrative, examples, and exercises, Ants, Bikes, and Clocks: Problem Solving for Undergraduates is a readable and enjoyable text designed to strengthen the problem-solving skills of undergraduate students. The book, which provides hundreds of mathematical problems, gives special emphasis to problems in context, often called story problems or modeling problems, that require mathematical formulation as a preliminary step. Both analytical and computational approaches, as well as the interplay between them, are included.

With its lively and engaging writing style and interesting and entertaining problems, Ants, Bikes, and Clocks will strengthen students' mathematical skills, introduce them to new mathematical ideas, demonstrate for them the connectedness of mathematics, and improve both their analytical and computational problem solving. One of the remarkable and unusual features of this text is that it encourages students to use the computer for experimentation. In fact, Briggs uses a variety of tricks that encourage students to use any tool at hand to test their ideas.

Ants, Bikes, and Clocks is an excellent text for an undergraduate problem-solving course or as a resource for mathematics educators, providing hundreds of mathematical problems that can be used in any course. Mathematically the book relies on two semesters of calculus, although much of the book requires only precalculus skills.

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.

ISBN: 9780898715743

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