An irreverent and accessible explanation of challenging puzzles within the world of mathematics considers such topics as the link between a pineapple's spirals and the famous Fibonacci numbers, the shape of the universe as reflected by a twisted strip of paper, and the parallels between the Lincoln and Kennedy assassinations. Reprint.
Designed for undergraduate students and lecturers, this text guides its users to develop the skills, attitudes, and habits of mind of a mathematician. It presents a carefully designed sequence of exercises and theorems so that its readers will be directed to discover mathematical ideas, strategies of proof, and strategies of thinking. Through the exploration of interesting mathematical content including graphs, groups, and calculus, this book helps to foster habits of inquiry. This book can be used by instructors as a text for an inquiry-based introduction to proof course, or as an independent study guide for mathematics students. The three core mathematical topics are presented separately, and each helps students develop theorem-proving skills and strategies of thinking whilst also providing an organised set of challenges that lead students to understand the process of mathematical creativity and development.
Chaos: The Science of Predictable Random Motion bridges the gap between introductions for the layman and college-level texts with an account of chaos theory based on elementary mathematics. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by numerousfigures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory.
Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Includes, beginning Sept. 15, 1954 (and on the 15th of each month, Sept.-May) a special section: School library journal, ISSN 0000-0035, (called Junior libraries, 1954-May 1961). Also issued separately.