The Magic of Numbers

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9780131777217: The Magic of Numbers

For courses in Liberal Arts Mathematics and Quantitative Literacy. A math book for "non--math" people, this text provides the reader with a mathematical view of the world. Based on the popular Quantitative Reasoning Course at Harvard University, it introduces the reader to the "beauty of numbers", including the patterns in their behavior as well as their application. This text teaches the reader about the mathematical thought--mode: the feeling of exploration, as well as the fascination and joy that can come from learning mathematics. This book is designed for math classes for non--math majors. It can also be used for an introductory course for math majors.

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From the Back Cover:

The Magic of Numbers was written with two goals in mind: first, to introduce the reader to some of the beauty of numbers—the patterns in their behavior that have fascinated mathematicians for millennia, and some surprising applications of those patterns; second, and equally important, to teach the reader something of the mathematical mode of thought: the feeling of exploration, excitement, and discovery that are part of how mathematics is developed.

The book, written originally for the course Quantitative Reasoning 28 that the authors developed and taught at Harvard, draws the reader into the content through an engaging and informal writing style. Example-driven, it reduces to a minimum the abstract notation and formal argument that often creates a barrier between mathematicians and students, focusing more instead on the experimental aspect of the subject. Above all, the authors communicate to the reader a sense of the joy and fascination of learning mathematics.

Additional exercises, problems, and sample exams are available at: www.prenhall.com/gross

Principal topics include:
  • Counting and basic combinatorics, with applications to probability and games
  • The arithmetic of natural numbers: the Euclidean Algorithm and the unique factorization theorem
  • Modular arithmetic, including Fermat's Theorem, Euler's Theorem, and how to take powers and roots
  • Codes: how the special properties of ordinary and modular arithmetic in combination allow us to construct the public-key codes that help make data transmission secure.

About the Author:

Benedict Gross is the Leverett Professor of Mathematics and Dean of Harvard College.

Joe Harris is the Higgins Professor of Mathematics and Chair of the Mathematics Department at Harvard.

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