99 Variations On A Proof

Author : Philip Ording
Publisher : Princeton University Press
ISBN 13 : 0691218978
Total Pages : 272 pages
Book Rating : 4.77/5 ( download)

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Download or read book 99 Variations on a Proof written by Philip Ording and published by Princeton University Press. This book was released on 2021-10-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3662223430
Total Pages : 194 pages
Book Rating : 4.37/5 ( download)

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Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Richard H. Hammack
Publisher :
ISBN 13 : 9780989472111
Total Pages : 314 pages
Book Rating : 4.16/5 ( download)

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Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jessica Wynne
Publisher : Princeton University Press
ISBN 13 : 0691222827
Total Pages : 248 pages
Book Rating : 4.20/5 ( download)

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Download or read book Do Not Erase written by Jessica Wynne and published by Princeton University Press. This book was released on 2021-06-22 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A photographic exploration of mathematicians’ chalkboards “A mathematician, like a painter or poet, is a maker of patterns,” wrote the British mathematician G. H. Hardy. In Do Not Erase, photographer Jessica Wynne presents remarkable examples of this idea through images of mathematicians’ chalkboards. While other fields have replaced chalkboards with whiteboards and digital presentations, mathematicians remain loyal to chalk for puzzling out their ideas and communicating their research. Wynne offers more than one hundred stunning photographs of these chalkboards, gathered from a diverse group of mathematicians around the world. The photographs are accompanied by essays from each mathematician, reflecting on their work and processes. Together, pictures and words provide an illuminating meditation on the unique relationships among mathematics, art, and creativity. The mathematicians featured in this collection comprise exciting new voices alongside established figures, including Sun-Yung Alice Chang, Alain Connes, Misha Gromov, Andre Neves, Kasso Okoudjou, Peter Shor, Christina Sormani, Terence Tao, Claire Voisin, and many others. The companion essays give insights into how the chalkboard serves as a special medium for mathematical expression. The volume also includes an introduction by the author, an afterword by New Yorker writer Alec Wilkinson, and biographical information for each contributor. Do Not Erase is a testament to the myriad ways that mathematicians use their chalkboards to reveal the conceptual and visual beauty of their discipline—shapes, figures, formulas, and conjectures created through imagination, argument, and speculation.

Author : Imre Lakatos
Publisher : Cambridge University Press
ISBN 13 : 9780521290388
Total Pages : 190 pages
Book Rating : 4.84/5 ( download)

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Download or read book Proofs and Refutations written by Imre Lakatos and published by Cambridge University Press. This book was released on 1976 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.

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 : Raymond Queneau
Publisher : New Directions Publishing
ISBN 13 : 9780811207898
Total Pages : 212 pages
Book Rating : 4.97/5 ( download)

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Download or read book Exercises in Style written by Raymond Queneau and published by New Directions Publishing. This book was released on 1981 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queneau uses a variety of literary styles and forms in ninety-nine exercises which retell the same story about a minor brawl aboard a bus.

Author : Timothy Gowers
Publisher : Princeton University Press
ISBN 13 : 1400830397
Total Pages : 1057 pages
Book Rating : 4.98/5 ( download)

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Download or read book The Princeton Companion to Mathematics written by Timothy Gowers and published by Princeton University Press. This book was released on 2010-07-18 with total page 1057 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger

Author : Chen Chung Chang
Publisher : Princeton University Press
ISBN 13 : 1400882052
Total Pages : 165 pages
Book Rating : 4.52/5 ( download)

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Download or read book Continuous Model Theory. (AM-58), Volume 58 written by Chen Chung Chang and published by Princeton University Press. This book was released on 2016-03-02 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a study of the theory of models with truth values in a compact Hausdorff topological space.

Author : Dr. Jason Lisle
Publisher : New Leaf Publishing Group
ISBN 13 : 1614580987
Total Pages : 289 pages
Book Rating : 4.80/5 ( download)

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Download or read book The Ultimate Proof of Creation written by Dr. Jason Lisle and published by New Leaf Publishing Group. This book was released on 2009-06-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: It's a bold title: The Ultimate Proof of Creation - But is there such a thing? There are many books that contain seemingly powerful arguments for biblical creation. But is there an ultimate proof of creation? There is an argument for creation that is powerful, conclusive, and has no true rebuttal. As such, it is an irrefutable argument - an "ultimate proof " of the Christian worldview biblical creation. Master the method outlined in the following chapters, and you will be able to defend Christianity against all opposition. Learn how to apply the ultimate proof in dialogues with evolutionists, how to spot logical fallacies, and biblical examples of defending the faith Discover the nature of scientific evidence and its proper role in the origins debate Details how to address theistic evolution, "day age" creationism, and other compromised positions of biblical creationism An exceptional book for pastors, ministry leaders, seminary attendees, and students of religion and philosophy This book is a complete guide to defending the Christian faith, emphasizing the defense of the Genesis account of creation, built on techniques that have been developed over many years and presentations. They are not difficult to apply when you learn how to do it properly. Ready to move beyond the circular arguments? It is time to get to the real heart of the issue and rationally resolve the origins debate. It is time to discover The Ultimate Proof of Creation.