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Author: John W. Dawson, Jr.
Publisher: Birkhäuser
ISBN: 3319173685
Category : Mathematics
Languages : en
Pages : 211
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Book Description
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.
Author: John W. Dawson, Jr.
Publisher: Birkhäuser
ISBN: 3319173685
Category : Mathematics
Languages : en
Pages : 211
Get Book Here
Book Description
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.
Author: Joan C. Williams
Publisher: NYU Press
ISBN: 1479871834
Category : Business & Economics
Languages : en
Pages : 396
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Book Description
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
Author: Joan C. Williams
Publisher: Harvard Business Press
ISBN: 1647822734
Category : Business & Economics
Languages : en
Pages : 268
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Book Description
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.
Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521861241
Category : Mathematics
Languages : en
Pages : 401
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Book Description
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.
Author: Monica Biernat
Publisher: Wiley-Blackwell
ISBN: 9781405130486
Category : Psychology
Languages : en
Pages : 248
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Book Description
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.
Author: Adam Grant
Publisher: Random House
ISBN: 0753553902
Category : Business & Economics
Languages : en
Pages : 240
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Book Description
THE MILLION-COPY BESTSELLER If you can change your mind you can do anything. Why do we refresh our wardrobes every year, renovate our kitchens every decade, but never update our beliefs and our views? Why do we laugh at people using computers that are ten years old, but yet still cling to opinions we formed ten years ago? There's a new skill for the modern world that matters more than raw intelligence - the ability to change your mind. To have the edge we all need to develop the flexibility to unlearn old beliefs and adapt when the evidence and the world changes before us. Told through fascinating stories, informed by cutting-edge research and illustratedwith amazing insights from Adam Grant's conversations with people such as Elon Musk, Hilary Clinton's campaign team, top CEOs and leading scientists, this is the ultimate guide to keeping your thinking fresh, learning when to question your ideas and update your own opinions, and how to inspire those around you to do the same.
Author: Benjamin Fine
Publisher: Springer Science & Business Media
ISBN: 1461219280
Category : Mathematics
Languages : en
Pages : 220
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Book Description
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.
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
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Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Author: Stieg Larsson
Publisher: Vintage
ISBN: 0307476154
Category : Blomkvist, Mikael (Fictitious character)
Languages : en
Pages : 738
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Book Description
When the reporters to a sex-trafficking exposé are murdered and computer hacker Lisbeth Salander is targeted as the killer, Mikael Blomkvist, the publisher of the exposé, investigates to clear Lisbeth's name.
Author: David G. Smith
Publisher: Harvard Business Press
ISBN: 1633698734
Category : Business & Economics
Languages : en
Pages : 232
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Book Description
The key to advancing gender equality? Men. Women are at a disadvantage. At home, they often face an unequal division of household chores and childcare, and in the workplace, they deal with lower pay, lack of credit for their contributions, roadblocks to promotion, sexual harassment, and more. And while organizations are looking to address these issues, too many gender-inclusion initiatives focus on how women themselves should respond, reinforcing the perception that these are "women's issues" and that men—often the most influential stakeholders in an organization—don't need to be involved. Gender-in-the-workplace experts David G. Smith and W. Brad Johnson counter this perception. In this important book, they show that men have a crucial role to play in promoting gender equality at work. Research shows that when men are deliberately engaged in gender-inclusion programs, 96 percent of women in those organizations perceive real progress in gender equality, compared with only 30 percent of women in organizations without strong male engagement. Good Guys is the first practical, research-based guide for how to be a male ally to women in the workplace. Filled with firsthand accounts from both men and women, and tips for getting started, the book shows how men can partner with their female colleagues to advance women's leadership and equality by breaking ingrained gender stereotypes, overcoming unconscious biases, developing and supporting the talented women around them, and creating productive and respectful working relationships with women.
