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.
Brian P. Katz,Michael Starbird,Michael P. Starbird
Author: Brian P. Katz,Michael Starbird,Michael P. Starbird
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.
This book is a comprehensive guide for educators and policy makers who are ready to create schools for Latinos (particularly Mexican Americans), such that students will be successful in learning and achieving in K-12 grades and college and help to advance society in the 21st century.
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.
Author: David C. Marshall,Edward Odell,Michael Starbird
This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. The first is to help students develop mathematical thinking skills, particularly theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for independent study, or for a course designed as an introduction to abstract mathematics. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method, which gives students a totally different experience compared to a standard lecture course. Students develop an attitude of personal reliance and a sense that they can think effectively about difficult problems; goals that are fundamental to the educational enterprise within and beyond mathematics.
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.
In this book, author Leonard Valverde contends that it is imperative to reinvent schools in order to provide a viable education for these students. Improving Schools for Latinos starts with the past, points out the present, and speaks to the future. It exposes the negative mental models and practices that must be discarded and proposes what favorable elements need to be put into place. Helpful resources for program assistance, community-based organizations, and funding sources are included.
Blut, Treibstoff, Lebensprinzip - in seinem furiosen Buch erzählt Bestsellerautor James Gleick, wie die Information zum Kernstück unserer heutigen Zivilisation wurde. Beginnend bei den Wörtern, den "sprechenden" Trommeln in Afrika, über das Morsealphabet und bis hin zur Internetrevolution beleuchtet er, wie die Übermittlung von Informationen die Gesellschaften prägten und veränderten. Gleick erläutert die Theorien, die sich mit dem Codieren und Decodieren, der Übermittlung von Inhalten und dem Verbreiten der Myriaden von Botschaften beschäftigen. Er stellt die bekannten und unbekannten Pioniere der Informationsgesellschaft vor: Claude Shannon, Norbert Wiener, Ada Byron, Alan Turing und andere. Er bietet dem Leser neue Einblicke in die Mechanismen des Informationsaustausches. So lernt dieser etwa die sich selbst replizierende Meme kennen, die "DNA" der Informationen. Sein Buch ermöglicht ein neues Verständnis von Musik, Quantenmechanik - und eine gänzlich neue Sicht auf die faszinierende Welt der Informationen.