Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Why Prove it Again? PDF full book. Access full book title Why Prove it Again? by John W. Dawson, Jr.. Download full books in PDF and EPUB format.
Author: John W. Dawson, Jr. Publisher: Birkhäuser ISBN: 3319173685 Category : Mathematics Languages : en Pages : 211
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
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
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
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
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: Ruchika Tulshyan Publisher: MIT Press ISBN: 0262380609 Category : Business & Economics Languages : en Pages : 305
Book Description
How organizations can foster diversity, equity, and inclusion: taking action to address and prevent workplace bias while centering women of color. Few would disagree that inclusion is both the right thing to do and good for business. Then why are we so terrible at it? If we believe in the morality and the profitability of including people of diverse and underestimated backgrounds in the workplace, why don't we do it? Because, explains Ruchika Tulshyan in this eye-opening book, we don't realize that inclusion takes awareness, intention, and regular practice. Inclusion doesn't just happen; we have to work at it. Tulshyan presents inclusion best practices, showing how leaders and organizations can meaningfully promote inclusion and diversity. Tulshyan centers the workplace experience of women of color, who are subject to both gender and racial bias. It is at the intersection of gender and race, she shows, that we discover the kind of inclusion policies that benefit all. Tulshyan debunks the idea of the “level playing field” and explains how leaders and organizations can use their privilege for good by identifying and exposing bias, knowing that they typically have less to lose in speaking up than a woman of color does. She explains why “leaning in” doesn't work—and dismantling structural bias does; warns against hiring for “culture fit,” arguing for “culture add” instead; and emphasizes the importance of psychological safety in the workplace—you need to know that your organization has your back. With this important book, Tulshyan shows us how we can make progress toward inclusion and diversity—and we must start now.
Author: Monica Biernat Publisher: Wiley-Blackwell ISBN: 9781405130486 Category : Psychology Languages : en Pages : 248
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
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: Elizabeth Lennox Publisher: Elizabeth Lennox Books (www.ElizabethLennox.com) ISBN: 1940134919 Category : Fiction Languages : en Pages : 98
Book Description
Ella is young and impressionable, and awed by Zayn who comes back into her life like a returning hero. After one night of passion, not only has her hero fallen, but so has she. Pregnant and terrified, Ella realizes that Zayn has disappeared for the second time in her life with no explanation and no clues as to where he’s gone. But she works hard and survives, raising her son on her own. When she sees Zayn again six years later, she is determined not to be blinded by his overwhelming presence again. She can’t trust him this time. Unfortunately, nor can she ignore the fiery passion that seems to flare up whenever Zayn comes close to her. She’s a fighter, though. And she won’t give in to that passion like she did the last time he swooped into her life. She is stronger, she can push him away. Can’t she? Zayn can’t believe he’s finally found Ella again! An emergency took him away from her years ago and she disappeared. But this time, he won’t lose her! When he discovers that he also has a five year old son, Zayn is thrilled, eager to bring both of them back to his country. He doesn’t understand Ella’s resistance to him. Gone is the soft, vivacious woman he remembers holding in his arms. But this Ella is even more beautiful, more lush and sensuous. And he refuses to believe that what they felt for each other the last time can’t be revived. He won’t lose her a second time! He can’t!
Author: John W. Dawson, Jr.
Author: John W. Dawson, Jr.
Author: Joan C. Williams
Author: Joan C. Williams
Author: Daniel J. Velleman
Author: Ruchika Tulshyan
Author: Monica Biernat
Author: Adam Grant
Author: Blaire Palmer
Author: Elizabeth Lennox
Author: United States. Congress