Why Prove it Again?
Why Prove it Again?

Author: John W. Dawson, Jr.

Publisher: Birkhäuser

Published: 2015-07-15

Total Pages: 211

ISBN-13: 3319173685

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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.

What Works for Women at Work
What Works for Women at Work

Author: Joan C. Williams

Publisher: NYU Press

Published: 2020-08-25

Total Pages: 396

ISBN-13: 1479871834

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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

Bias Interrupted
Bias Interrupted

Author: Joan C. Williams

Publisher: Harvard Business Press

Published: 2021-11-16

Total Pages: 268

ISBN-13: 1647822734

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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.

How to Prove It
How to Prove It

Author: Daniel J. Velleman

Publisher: Cambridge University Press

Published: 2006-01-16

Total Pages: 401

ISBN-13: 0521861241

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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.

The Maternal Wall
The Maternal Wall

Author: Monica Biernat

Publisher: Wiley-Blackwell

Published: 2004-12-10

Total Pages: 248

ISBN-13: 9781405130486

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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.

Proofs from THE BOOK
Proofs from THE BOOK

Author: Martin Aigner

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 194

ISBN-13: 3662223430

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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.

The Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra

Author: Benjamin Fine

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 220

ISBN-13: 1461219280

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The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.

Incompleteness
Incompleteness

Author: Rebecca Goldstein

Publisher: W. W. Norton & Company

Published: 2006-01-31

Total Pages: 299

ISBN-13: 0393327604

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"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

Book of Proof
Book of Proof

Author: Richard H. Hammack

Publisher:

Published: 2016-01-01

Total Pages: 314

ISBN-13: 9780989472111

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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.

Invisible Women
Invisible Women

Author: Caroline Criado Perez

Publisher: Abrams

Published: 2019-03-12

Total Pages: 434

ISBN-13: 1683353145

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The landmark, prize-winning, international bestselling examination of how a gender gap in data perpetuates bias and disadvantages women. #1 International Bestseller * Winner of the Financial Times and McKinsey Business Book of the Year Award * Winner of the Royal Society Science Book Prize Data is fundamental to the modern world. From economic development to health care to education and public policy, we rely on numbers to allocate resources and make crucial decisions. But because so much data fails to take into account gender, because it treats men as the default and women as atypical, bias and discrimination are baked into our systems. And women pay tremendous costs for this insidious bias: in time, in money, and often with their lives. Celebrated feminist advocate Caroline Criado Perez investigates this shocking root cause of gender inequality in Invisible Women. Examining the home, the workplace, the public square, the doctor’s office, and more, Criado Perez unearths a dangerous pattern in data and its consequences on women’s lives. Product designers use a “one-size-fits-all” approach to everything from pianos to cell phones to voice recognition software, when in fact this approach is designed to fit men. Cities prioritize men’s needs when designing public transportation, roads, and even snow removal, neglecting to consider women’s safety or unique responsibilities and travel patterns. And in medical research, women have largely been excluded from studies and textbooks, leaving them chronically misunderstood, mistreated, and misdiagnosed. Built on hundreds of studies in the United States, in the United Kingdom, and around the world, and written with energy, wit, and sparkling intelligence, this is a groundbreaking, highly readable exposé that will change the way you look at the world.