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.
Winner of the Scribes Book Award “Displays a level of intellectual honesty one rarely encounters these days...This is delightful stuff.” —Barton Swaim, Wall Street Journal “At a time when the concept of truth itself is in trouble, this lively and accessible account provides vivid and deep analysis of the practices addressing what is reliably true in law, science, history, and ordinary life. The Proof offers both timely and enduring insights.” —Martha Minow, former Dean of Harvard Law School “His essential argument is that in assessing evidence, we need, first of all, to recognize that evidence comes in degrees...and that probability, the likelihood that the evidence or testimony is accurate, matters.” —Steven Mintz, Inside Higher Education “I would make Proof one of a handful of books that all incoming law students should read...Essential and timely.” —Emily R. D. Murphy, Law and Society Review In the age of fake news, trust and truth are hard to come by. Blatantly and shamelessly, public figures deceive us by abusing what sounds like evidence. To help us navigate this polarized world awash in misinformation, preeminent legal theorist Frederick Schauer proposes a much-needed corrective. How we know what we think we know is largely a matter of how we weigh the evidence. But evidence is no simple thing. Law, science, public and private decision making—all rely on different standards of evidence. From vaccine and food safety to claims of election-fraud, the reliability of experts and eyewitnesses to climate science, The Proof develops fresh insights into the challenge of reaching the truth. Schauer reveals how to reason more effectively in everyday life, shows why people often reason poorly, and makes the case that evidence is not just a matter of legal rules, it is the cornerstone of judgment.
What if there was a way of eating that may help us live healthier for longer and protect the future of our planet, too? The good news is that evidence now shows a plant-based diet may offer us exactly that – and straight-talking nutritionist Simon Hill has done the hard work translating the science into actionable advice for everyday life. Before transitioning to a plant-based diet Simon held many of the common misconceptions. But instead he experienced incredible improvements in his energy levels, digestion, mental clarity and post-workout recovery after making the shift. He’d finally understood the power of food and was determined to find out – and share – the agenda-free truth about the optimum diet for human health. By undertaking a master’s degree in nutrition, poring over the latest scientific papers and books, and producing hundreds of hours of his internationally successful Plant Proof podcast, Simon has pursued the answers to all the questions he had about fuelling our bodies with more plants. Now, in his first book, he brings it all together into one inspiring and practical guide. It covers: – The reasons why we’re all so confused about what to eat – The evidence showing how a plant-based diet might reduce risks of heart attacks and strokes, type 2 diabetes, cancer and dementia – The positive impact of plant-based living for the climate and animal welfare – Common myths about a plant-based diet – and what the real facts are – How to build a healthy, satisfying plant-based plate, from macronutrients to micronutrients – Practical tips for making the shift, and much more. If you want to understand and unlock the many benefits of putting more plants on your plate, this book is for you.
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
THE STORY: On the eve of her twenty-fifth birthday, Catherine, a troubled young woman, has spent years caring for her brilliant but unstable father, a famous mathematician. Now, following his death, she must deal with her own volatile emotions; the
A fresh look at a “robot-proof” education in the new age of generative AI. In 2017, Robot-Proof, the first edition, foresaw the advent of the AI economy and called for a new model of higher education designed to help human beings flourish alongside smart machines. That economy has arrived. Creative tasks that, seven years ago, seemed resistant to automation can now be performed with a simple prompt. As a result, we must now learn not only to be conversant with these technologies, but also to comprehend and deploy their outputs. In this revised and updated edition, Joseph Aoun rethinks the university’s mission for a world transformed by AI, advocating for the lifelong endeavor of a “robot-proof” education. Aoun puts forth a framework for a new curriculum, humanics, which integrates technological, data, and human literacies in an experiential setting, and he renews the call for universities to embrace lifelong learning through a social compact with government, employers, and learners themselves. Drawing on the latest developments and debates around generative AI, Robot-Proof is a blueprint for the university as a force for human reinvention in an era of technological change—an era in which we must constantly renegotiate the shifting boundaries between artificial intelligence and the capacities that remain uniquely human.
It’s time to open your eyes to the freeing power of authentic grace—grace that releases us from trying to earn God's favor, grace that enables us to rest in the finished work of Christ, grace that liberates from the tyranny of trying to please others. That's what the theology of Martin Luther and John Calvin did in their own day for the people around them. Time magazine recently dubbed Calvinism as one of the top ten ideas changing the world right now. And yet most of these discussions center on the issue of predestination or on whether particular people agree with the five points of Calvinism. Daniel Montgomery and Timothy Paul Jones think it's time to rescue the theology of the Reformers from such stale scholasticizing and to declare anew the dangerous and intoxicating joy of the gospel that theyproclaimed. PROOF stands for planned grace, resurrecting grace, outrageous grace, overcoming grace, and forever grace. The authors offer proof of God’s grace upon which people can stand against the attacks of legalism that have led many of God's people to lose sight of the freedom and joy of the gospel. And this proof is intoxicating—it’s like a 200-proof drink that will leave you spiritually staggering at its effect on your life. God’s grace not only declares us “not guilty!” in his presence, it changes our relationship with God—forever.?
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.
Presents a look at the science of alcohol production and consumption, from the principles behind the fermentation, distillation, and aging of alcoholic beverages, to the psychology and neurobiology of what happens after it is consumed.
