Sherman K. Stein

'Some topics in advanced mathematics require nothing more than arithmetic and common sense. How the Other Half Thinks makes use of this phenomenon to offer both the mathematically adept and mathematical beginner eight fascinating illustrations of the mathematical way. Each chapter starts with a question about strings made up of nothing more than two letters. This question in turn suggests thought-provoking problems. After these problems are explored and solved, the author shows how the related mathematics has been applied in areas as varied as computers, cell phones, measurement of astronomical distances, and cell growth.An experienced educator, prize-winning expositor, and researcher, Stein engagingly presents each concept. The leisurely pace allows a reader to move slowly through each chapter, omitting no steps. This approach makes complex concepts like topology, set theory, and probability accessible and exciting. The book creates a bridge across the gulf between the two cultures: humanities and the sciences. Stein shows how the mathematical style of thinking is one that everyone can use to understand the world. This charming book speaks to both those who employ the intuitive, creative right half of the brain, and to those who rely more on the analytical, numerical left half. How the Other Half Thinks is for the novice and the skilled, the poet and the scientist, the left-brained and the right-brained. When you read this book, you are immersed in the world of mathematics, not as a spectator, but as an involved participant."Occasionally, in some difficult musical compositions there are beautiful, but easy parts­­"so simple a beginner could play them. So it is with mathematics as well. There are some discoveries in advanced mathematics that do not depend on specialized knowledge, not even on algebra, geometry, or trigonometry. Instead they may involve, at most, a little arithmetic, such as 'the sum of two odd numbers is even,' and common sense. As I wrote, I kept in mind two types of readers: those who enjoyed mathematics until they were turned off by an unpleasant episode, usually around fifth grade; and mathematics aficionados, who will find much that is new throughout the book.' Sherman Stein

The Carus Mathematical Monographs are an expression of the desire of Mrs. Mary Hegeler Carus and of her son, Dr. Edward H. Carus, to contribute to the dissemination of mathematical knowledge by making accessible at nominal cost a series of expository presentations of the best thoughts and keenest researches in pure and applied mathematics. The publication of the first four of these monographs was made possible by Mrs. Carus as sole trustee of the Edward C. Hegeler Trust Fund. The sales from these have resulted in the Carus Monograph Fund, and the Mathematical Association of America has used this as a revolving book fund to publish the succeeding monographs. The expositions of mathematical subjects that the monographs contain are set forth in a manner comprehensible not only to teachers and students specializing in mathematics, but also to scientific workers in other fields. More generally, the monographs are intended for the wide circle of thoughtful people familiar with basic graduate or advanced undergraduate mathematics, encountered in the study of mathematics itself or in the context of related disciplines, who wish to extend their knowledge without prolonged and critical study of the mathematical journals and treatises. -- from dust jacket.

Includes short stories and discussions which present such mathematical concepts as decimals, tangrams, number lines, and fractals.

"Mathematics: The New Golden Age offers a glimpse of the extraordinary vistas and bizarre universes opened up by contemporary mathematicians: Hilbert's tenth problem and the four-color theorem, Gaussian integers, chaotic dynamics and the Mandelbrot set, infinite numbers, and strange number systems. Why a "new golden age"? According to Keith Devlin, we are currently witnessing an astronomical amount of mathematical research. Charting the most significant developments that have taken place in mathematics since 1960, Devlin expertly describes these advances for the interested layperson and adroitly summarizes their significance as he leads the reader into the heart of the most interesting mathematical perplexities - from the biggest known prime number to the Shimura-Taniyama conjecture for Fermat's Last Theorem."--BOOK JACKET.

Presents mathematical ideas through poetic dialogues intended to be read by two people.

Rate of change of a function - Derivatives - Applications and derivatives - Integration - Transcendental functions - Techniques of integration - Infinite series - Vectors - Conic sections, polar coordinates - Functions of two or more variables - Multiple integrals - Differential equations.

Penrose the cat explores and experiences a variety of mathematical concepts, including infinity, the golden rectangle, and impossible figures.