This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.

A mother-daughter legal scholar team “offers unabashedly straightforward advice in a how-to primer for ambitious women . . . [A]ttention-grabbing revelations” (Debora L. Spar, The New York Times Book Review) What Works for Women at Work is a comprehensive and insightful guide for mastering office politics as a woman. Authored by Joan C. Williams, one of the nation’s most-cited experts on women and work, and her daughter, Rachel Dempsey, this unique book offers a multi-generational perspective into the realities of today’s workplace. Often women receive messages that they have only themselves to blame for failing to get ahead. What Works for Women at Work tells women it’s not their fault. Based on interviews with 127 successful working women, over half of them women of color, What Works for Women at Work presents a toolkit for getting ahead in today’s workplace. Distilling over thirty-five years of research, Williams and Dempsey offer four crisp patterns that affect working women. Each represents different challenges and requires different strategies—which is why women need to be savvier than men to survive and thrive in high-powered careers. Williams and Dempsey’s analysis of working women is nuanced and in-depth, going beyond the traditional one-size-fits-all approaches of most career guides for women. Throughout the book, they weave real-life anecdotes from the women they interviewed, along with advice on dealing with difficult situations such as sexual harassment. An essential resource for any working woman. “Many steps beyond Lean In (2013), Sheryl Sandberg’s prescription for getting ahead . . . .[F]illed with street-smart advice and plain old savvy about the way life works in corporate America.” —Booklist, starred review) “A playbook on how to transcend and triumph.” —O, The Oprah Magazine

A cutting-edge, relentless, objective approach to inclusion. Companies spend billions of dollars annually on diversity efforts with remarkably few results. Too often diversity efforts rest on the assumption that all that's needed is an earnest conversation about "privilege." That's not enough. To truly make progress we need to stop celebrating the problem and instead take effective steps to solve it. In Bias Interrupted, Joan C. Williams shows how it's done, and, reassuringly, how easy it is to get started. One of today's preeminent voices on inclusive workplaces, Williams explains how leaders can use standard business tools—data, metrics, and persistence—to interrupt the bias that is continually transmitted through formal systems like performance appraisals, as well as the informal systems that control access to career-enhancing opportunities. The book presents fresh evidence, based on Williams's exhaustive research and work with companies, that interrupting bias helps every group—including white men. Comprehensive, though compact and straightforward, Bias Interrupted delivers real, practical value in an efficient and accessible manner to an audience that has never needed it more. It's possible to interrupt bias. Here's where you start.

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.

Over the past four or five decades, the feminist revolution has brought a lot of changes. There is a lot of evidence that the glass ceiling is being shattered. For one particular group, however, gender equity remains elusive. That group is working mothers. The problem of the "glass ceiling" has now turned into a related, from different problem: "the maternal wall." In the first Journal of Social Issues (JSI) to deal specifically with the topic of working mothers, scholars from several disciplines discuss a variety of aspects of the problem of the maternal wall.

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.

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.