Why Prove It Again

Author : John W. Dawson, Jr.
Publisher : Birkhäuser
ISBN 13 : 3319173685
Total Pages : 204 pages
Book Rating : 4.89/5 ( download)

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Download or read book Why Prove it Again? written by John W. Dawson, Jr. and published by Birkhäuser. This book was released on 2015-07-15 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 1479835455
Total Pages : 405 pages
Book Rating : 4.54/5 ( download)

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Download or read book What Works for Women at Work written by Joan C. Williams and published by NYU Press. This book was released on 2014-01-17 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Up-beat, pragmatic, and chock full of advice, What Works for Women at Work is an indispensable guide for working women. An essential resource for any working woman, 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, writer 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—Negotiate more! Stop being such a wimp! Stop being such a witch! What Works for Women at Work tells women it’s not their fault. The simple fact is that office politics often benefits men over women. 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 35 years of research, Williams and Dempsey offer four crisp patterns that affect working women: Prove-It-Again!, the Tightrope, the Maternal Wall, and the Tug of War. 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 far beyond the traditional cookie-cutter, 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 quick kernels of advice like a “New Girl Action Plan,” ways to “Take Care of Yourself”, and even “Comeback Lines” for dealing with sexual harassment and other difficult situations.

Author : Dawson, Jr. (John W.)
Publisher :
ISBN 13 : 9783319173696
Total Pages : pages
Book Rating : 4.93/5 ( download)

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Download or read book Why Prove it Again? written by Dawson, Jr. (John W.) and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Harvard Business Press
ISBN 13 : 1647822734
Total Pages : 268 pages
Book Rating : 4.36/5 ( download)

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Download or read book Bias Interrupted written by Joan C. Williams and published by Harvard Business Press. This book was released on 2021-11-16 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Adam Grant
Publisher : Penguin
ISBN 13 : 1984878123
Total Pages : 321 pages
Book Rating : 4.20/5 ( download)

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Download or read book Think Again written by Adam Grant and published by Penguin. This book was released on 2023-12-26 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: #1 New York Times Bestseller “THIS. This is the right book for right now. Yes, learning requires focus. But, unlearning and relearning requires much more—it requires choosing courage over comfort. In Think Again, Adam Grant weaves together research and storytelling to help us build the intellectual and emotional muscle we need to stay curious enough about the world to actually change it. I’ve never felt so hopeful about what I don’t know.” —Brené Brown, Ph.D., #1 New York Times bestselling author of Dare to Lead The #1 New York Times bestselling author of Hidden Potential, Originals, and Give and Take examines the critical art of rethinking: learning to question your opinions and open other people's minds, which can position you for excellence at work and wisdom in life Intelligence is usually seen as the ability to think and learn, but in a rapidly changing world, there's another set of cognitive skills that might matter more: the ability to rethink and unlearn. In our daily lives, too many of us favor the comfort of conviction over the discomfort of doubt. We listen to opinions that make us feel good, instead of ideas that make us think hard. We see disagreement as a threat to our egos, rather than an opportunity to learn. We surround ourselves with people who agree with our conclusions, when we should be gravitating toward those who challenge our thought process. The result is that our beliefs get brittle long before our bones. We think too much like preachers defending our sacred beliefs, prosecutors proving the other side wrong, and politicians campaigning for approval--and too little like scientists searching for truth. Intelligence is no cure, and it can even be a curse: being good at thinking can make us worse at rethinking. The brighter we are, the blinder to our own limitations we can become. Organizational psychologist Adam Grant is an expert on opening other people's minds--and our own. As Wharton's top-rated professor and the bestselling author of Originals and Give and Take, he makes it one of his guiding principles to argue like he's right but listen like he's wrong. With bold ideas and rigorous evidence, he investigates how we can embrace the joy of being wrong, bring nuance to charged conversations, and build schools, workplaces, and communities of lifelong learners. You'll learn how an international debate champion wins arguments, a Black musician persuades white supremacists to abandon hate, a vaccine whisperer convinces concerned parents to immunize their children, and Adam has coaxed Yankees fans to root for the Red Sox. Think Again reveals that we don't have to believe everything we think or internalize everything we feel. It's an invitation to let go of views that are no longer serving us well and prize mental flexibility over foolish consistency. If knowledge is power, knowing what we don't know is wisdom.

Author : Ruchika Tulshyan
Publisher : MIT Press
ISBN 13 : 0262380609
Total Pages : 305 pages
Book Rating : 4.07/5 ( download)

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Download or read book Inclusion on Purpose written by Ruchika Tulshyan and published by MIT Press. This book was released on 2024-04-16 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Daniel J. Velleman
Publisher : Cambridge University Press
ISBN 13 : 0521861241
Total Pages : 401 pages
Book Rating : 4.43/5 ( download)

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Download or read book How to Prove It written by Daniel J. Velleman and published by Cambridge University Press. This book was released on 2006-01-16 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Björn Lundgren
Publisher : Springer Nature
ISBN 13 : 3030752674
Total Pages : 264 pages
Book Rating : 4.75/5 ( download)

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Download or read book Philosophy of Computing written by Björn Lundgren and published by Springer Nature. This book was released on 2022-05-04 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a unique selection of works presented at the 2019 annual international conference of the International Association for Computing and Philosophy (IACAP). Every contribution has been peer-reviewed, revised, and extended. The included chapters are thematically diverse; topics include epistemology, dynamic epistemic logic, topology, philosophy of science and computation, game theory and abductive inferences, automated reasoning and mathematical proofs, computer simulations, scientific modelling, applied ethics, pedagogy, human-robot interactions, and big data, algorithms, and artificial intelligence. The volume is a testament to the value of interdisciplinary approaches to the computational and informational turn. We live in a time of tremendous development, which requires rigorous reflection on the philosophical nature of these technologies and how they are changing the world. How can we understand these technologies? How do these technologies change our understanding of the world? And how do these technologies affect our place as humans in the world? These questions, and more, are addressed in this volume which is of interest to philosophers, engineers, and computer scientists alike.

Author : Craig Bauer
Publisher : CRC Press
ISBN 13 : 0429682883
Total Pages : 668 pages
Book Rating : 4.89/5 ( download)

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Download or read book Discrete Encounters written by Craig Bauer and published by CRC Press. This book was released on 2020-05-14 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers’ appreciation of mathematics. This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers’ attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy. Highlights: Features fascinating historical context to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text’s narrative style is that of a popular book, not a dry textbook Includes the work of many living mathematicians Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses Contains many open problems Profusely illustrated

Author : Blaire Palmer
Publisher : A&C Black
ISBN 13 : 1408105063
Total Pages : 188 pages
Book Rating : 4.61/5 ( download)

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Download or read book The Recipe for Success written by Blaire Palmer and published by A&C Black. This book was released on 2009-05-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the secrets of the most successful high flyers and use them to help reach your own goals.