Why Prove It Again
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Why Prove It Again
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Author : John W. Dawson, Jr.
language : en
Publisher: Birkhäuser
Release Date : 2015-07-15
Why Prove It Again written by John W. Dawson, Jr. and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Mathematics categories.
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.
Why Prove It Again
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Author : Dawson, Jr. (John W.)
language : en
Publisher:
Release Date : 2015
Why Prove It Again written by Dawson, Jr. (John W.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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.
Why Prove It Again
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Author : John W. Dawson, Jr.
language : en
Publisher: Birkhäuser
Release Date : 2016-10-22
Why Prove It Again written by John W. Dawson, Jr. and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-22 with Mathematics categories.
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.
How To Prove It
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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16
How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.
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.
How To Prove It
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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-18
How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Computers categories.
Helps students transition from problem solving to proving theorems, with a new chapter on number theory and over 150 new exercises.
The South Has Risen Again
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Author : Ray Mead
language : en
Publisher: Page Publishing Inc
Release Date : 2018-09-10
The South Has Risen Again written by Ray Mead and has been published by Page Publishing Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-10 with Fiction categories.
The south has risen again and brought death, destruction, and a devastating futuristic battlefield with it. This compendium tells the story of population control, government conspiracy, and most of all, brutalities of war. Many years into the future, an epic conflict floods the country within a bloodbath of endless carnage. In a pollution-ravaged, overpopulated time, the United States wages its second civil war filled with massive death machines, power armor, and catastrophic weaponry. The South Has Risen Again chronicles several years where genocidal battles slaughter millions in an attempt to save the nation's dwindling supplies of fresh water. The vanguard for the Northern Army is made up solely of conscripted-prisoner battalions that get utilized as cannon fodder more than anything else. This time line follows along as Fexter, a defiant young drug dealer, is thrown into military service, where he enters a hellish life of pain, prejudice, brotherhood, and extreme violence. Through his rough years at war, he learns harsh lessons on how to grow up, find love, and deal with the aftermath of lost friends.
Why We Hate Us
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Author : Dick Meyer
language : en
Publisher: Crown
Release Date : 2008-08-05
Why We Hate Us written by Dick Meyer and has been published by Crown this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-05 with Social Science categories.
Americans are as safe, well fed, securely sheltered, long-lived, free, and healthy as any human beings who have ever lived on the planet. But we are down on America. So why do we hate us? According to Dick Meyer, the following items on this (much abbreviated) list are some of the contributors to our deep disenchantment with our own culture: Cell-phone talkers broadcasting the intimate details of their lives in public spaces Worship of self-awareness, self-realization, and self-fulfillment T-shirts that read, “Eat Me” Facebook, MySpace, and kids being taught to market themselves High-level cheating in business and sports Reality television and the cosmetic surgery boom Multinational corporations that claim, “We care about you.” The decline of organic communities A line of cosmetics called “S.L.U.T.” The phony red state–blue state divide The penetration of OmniMarketing into OmniMedia and the insinuation of both into every facet of our lives You undoubtedly could add to the list with hardly a moment’s thought. In Why We Hate Us, Meyer absolutely nails America’s early-twenty-first-century mood disorder. He points out the most widespread carriers of the why-we-hate-us germs, including the belligerence of partisan politics that perverts our democracy, the decline of once common manners, the vulgarity of Hollywood entertainment, the superficiality and untrustworthiness of the news media, the cult of celebrity, and the disappearance of authentic neighborhoods and voluntary organizations (the kind that have actual meetings where one can hobnob instead of just clicking in an online contribution). Meyer argues—with biting wit and observations that make you want to shout, “Yes! I hate that too!”—that when the social, spiritual, and political turmoil that followed the sixties collided with the technological and media revolution at the turn of the century, something inside us hit overload. American culture no longer reflects our own values. As a result, we are now morally and existentially tired, disoriented, anchorless, and defensive. We hate us and we wonder why. Why We Hate Us reveals why we do and also offers a thoughtful and uplifting prescription for breaking out of our current morass and learning how to hate us less. It is a penetrating but always accessible Culture of Narcissism for a new generation, and it carries forward ideas that resounded with readers in bestsellers such as On Bullshit and Bowling Alone.
Building Arguments
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Author : Drew Hinderer
language : en
Publisher: Wipf and Stock Publishers
Release Date : 2005-01-28
Building Arguments written by Drew Hinderer and has been published by Wipf and Stock Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-28 with Social Science categories.
'Building Arguments' offers a fresh new approach to informal logic - successfully combining an accessible style with a rigorous, systematic treatment of argument: -It integrates reasoning and writing, teaching readers to argue effectively and communicate ideas in persuasive prose. -It combines fundamental topics of critical thinking into broader discussions of reasoning. So where other books may treat fallacy identification and avoidance, induction and deduction, and validity and soundness as ends in themselves, 'Building Arguments' presents these topics in a practical yet philosophically sound context. -It includes entertaining and relevant examples and exercises drawn from sports, popular advertising, current events, and many academic areas. -'Building Arguments' is unique in its emphasis on helping readers to develop their own persuasive arguments as well as to evaluate arguments from other sources. Using a writing level and organization guided by the principles of reading development, the author introduces material gradually - moving from a very accessible level to a more rigorous one. The result? A book unique in its ability to foster philosophically-based argument analysis while promoting reasoning and writing skills across the curriculum.
The Traveling Salesman Problem And Its Variations
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Author : G. Gutin
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-02
The Traveling Salesman Problem And Its Variations written by G. Gutin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-02 with Computers categories.
A brilliant treatment of a knotty problem in computing. This volume contains chapters written by reputable researchers and provides the state of the art in theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, and includes a thorough computational analysis of heuristic and metaheuristic algorithms.
Passions Of The Mind
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Author : Harold N. Boris
language : en
Publisher: NYU Press
Release Date : 1993-10
Passions Of The Mind written by Harold N. Boris and has been published by NYU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10 with History categories.
Passions of the mind advances the view that, as social animals, we are only partly understandable in terms of individual psychodynamics. Within us, another principle is at work - to preserve the Group, even at the expense of the individual. As we pursue our own individual courses in life, seeking egoistic satisfactions, we are bound by countervailing forces, biologically rooted, social in nature, which cause us to identify with the aims of the Group, even if that requires of us a failure to thrive - indeed our very deaths. In this three-way synthesis of classical psychoanalysis, recent interpersonal and object relations psychology, and current selectivistic evolutionary biology, Professor Harold N. Boris draws on the work of Melanie Klein and Wilfred R. Bion and provides a bridge between the personal and biosocial psychologies of which we are made up. He elaborates on his concepts of the Couple, which involves the pleasure principle and egoistic identity, and the Pair, which enlists his newly proposed selection principle in representing social identity and biological imperatives. Professor Boris shows how these two states of mind, each with its own characteristic themes and variations, feelings and fantasies, and presences and absences, at once compete, conjoin, and intertwine in the paradoxical dialectic of psychoanalysis. In the latter half of the book, Professor Boris provides a transcript of an "analysis," a composite of what the experience in the consulting room is both for the patient and analyst. These illustrative sessions, complete with commentary, give the reader a rare glimpse of a living psychoanalysis in process. In addition to his day-to-day work in the psychoanalytic consulting room, Boris brings to this subtle and scholarly book his analytic work in many other settings - in day and overnight schools for normal and disturbed children, in rural villages and urban centers, and with individuals and groups.