The Magic of Numbers

Download or read book The Magic of Numbers written by Benedict H. Gross and published by Prentice Hall. This book was released on 2004 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.