For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its...

This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers. While keeping the mathematics to a simple level with few formulas, the reader is introduced to an area of current scientific research that was scarcely possible until the availability of computers. The book is divided into two main parts; the first provides the most interesting problems, each with a solution in a computer program format. Numerous exercises enable the reader to conduct his or her own experimental work. The second part provides sample programs for specific machine and operating...

Peppered with wit and controversial topics, this is a refreshing new look at the co-evolution of mind and culture. Bestselling authors Ian Stewart and Jack Cohen (The Collapse of Chaos, 1994) eloquently argue that our minds evolved within an inextricable link with culture and language. They go beyond conventional views of the function and purpose of the mind to look at the ways that the mind is the response of an evolving brain that is constantly adjusting to a complex environment. Along the way they develop new and intriguing insights into the nature of evolution, science, and humanity that...

Since the dramatic discovery of the mathematical concept of chaos in 1989, the controversy of its contents has settled down. This revised edition of Does God Play Dice? takes a fresh look at its achievements and potential. With a new preface and three completely new chapters, it includes the latest practical applications of chaos theory, such as developing intelligent heart pacemakers. All this provides a fascinating new answer to Einstien's question which provided the title of this book.

Why do many flowers have five or eight petals, but very few six or seven? Why do snowflakes have sixfold symmetry? Why do tigers have stripes but leopards have spots? Mathematics is to nature as Sherlock Holmes is to evidence. Mathematics can look at a single snowflake and deduce the atomic geometry of its crystals; it can start with a violin string and uncover the existence of radio waves. And mathematics still has the power to open our eyes to new and unsuspected regularities the secret structure of a cloud or the hidden rhythms of the weather. There are patterns in the world we are now...

Vivid accounts of the lives of 25 of the world's greatest mathematicians with clear descriptions of their far-reaching discoveries

In this book, Stewart explores the history and mathematics of uncertainty, which lurks in every consideration of the future. Touching on gaming, probability, statistics, financial and weather forecasts, censuses, medical studies, chaos, quantum physics and climate, he makes one thing clear: a reasonable probability is the only certainty.