According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.

Aerial and on-site photographs made at a classified military site in the Great Salt Lake Desert by David Maisel, author of Black Maps David Maisel's (born 1961) Proving Ground comprises aerial and on-site photographs made at Dugway Proving Ground, a classified military site covering nearly 800,000 acres in Utah's Great Salt Lake Desert. A primary mission of Dugway is to develop, test and implement chemical and biological weaponry and defense programs. After more than a decade of inquiry, Maisel was granted access to this facility in order to photograph the terrain, the testing facilities and other aspects of the site. Maisel began by photographing at ground level, focusing on structures related to the testing of chemical warfare dispersal patterns. He then moved to an aerial perspective to create images that resemble large-scale minimalist drawings inscribed on the land. Maisel's work at Dugway also includes photographs of the newly minted WSLAT (Whole System Live Agent Test) facility, which is devoted to identification and neutralization of chemical and biological toxins that can be weaponized by terrorists or rogue nations.

In honor of the late BYU Professor Eugene England (1933-2001), friends and colleagues have contributed their best original stories, poems, reminiscences, scholarly articles, and essays for this impressive volume. In one essay, "Eugene England Enters Heaven," Robert A. Rees imagines his friend being welcomed into heaven by the Savior. Rees then imagines England "organizing contests between the Telestial and Celestial Kingdoms, leading a theater tour to Kolob, and pleading the cause of friends still struggling in mortality. This," he concludes, "is the image I have of Gene, that I hold in my heart."

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

What would cause a young African American engineer to walk away from a promising career at the world's foremost electronics research and development company to start a business, from scratch, in his basement? David Tarver not only did that, he convinced two African American colleagues to join him in the improbable venture. Twelve years later, he negotiated the sale of that venture, Telecom Analysis Systems Inc., for $30 million. Tarver's business success was accomplished without the help of angel investors, venture capital, government grants, or minority business development programs. Overcoming obstacles related to race, technology, and business, Tarver and his colleagues conceived, designed, engineered, and manufactured sophisticated telecommunications instruments and sold them in more than twenty countries. David Tarver felt he had something important to prove to himself, to his colleagues, and to society. That is why he was willing to risk everything on a roll of the entrepreneuri

*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.