Download or read book The Art of Proof written by Matthias Beck and published by Springer Science & Business Media. This book was released on 2010-08-17 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.
Download or read book The Art of Proofing written by Adele Yunck and published by . This book was released on 2008 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proof and the Art of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-02-23 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.
Download or read book Proofs that Really Count written by Arthur T. Benjamin and published by American Mathematical Society. This book was released on 2022-09-21 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
Download or read book Proof of Work written by Rhea Myers and published by MIT Press. This book was released on 2023-04-11 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: A beautifully produced anthology of crypto-artist, writer, and hacker Rhea Myers's pioneering blockchain art, along with a selection of her essays, reviews, and fictions. DAO? BTC? NFT? ETH? ART? WTF? HODL as OG crypto-artist, writer, and hacker Rhea Myers searches for faces in cryptographic hashes, follows a day in the life of a young shibe in the year 2032, and patiently explains why all art should be destructively uploaded to the blockchain. Now an acknowledged pioneer whose work has graced the auction room at Sotheby’s, Myers embarked on her first art projects focusing on blockchain tech in 2011, making her one of the first artists to engage in creative, speculative, and conceptual engagements with "the new internet." Proof of Work brings together annotated presentations of Myers’s blockchain artworks along with her essays, reviews, and fictions—a sustained critical encounter between the cultures and histories of the artworld and crypto-utopianism, technically accomplished but always generously demystifying and often mischievous. Her deep understanding of the technical history and debates around blockchain technology is complemented by a broader sense of the crypto movement and the artistic and political sensibilities that accompanied its ascendancy. Remodeling the tropes of conceptual art and net.art to explore what blockchain technology reveals about our concepts of value, culture, and currency, Myers’s work has become required viewing for anyone interested in the future of art, consensus, law, and collectivity.
Download or read book Rejection Proof written by Jia Jiang and published by Harmony. This book was released on 2015-04-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inspiring, relatable, and sometimes outrageous true story of how one man used 100 days of rejection therapy to overcome fear and dare to live more boldly “Rejection Proof smashes fear in the face with a one-two punch. You’ll laugh out loud at Jia’s crazy social experiments, but you’ll also go away thinking differently about what you can accomplish.”—Chris Guillebeau, New York Times bestselling author of The Happiness Pursuit Jia Jiang’s TEDx Talk, “What I learned from 100 days of rejection,” has amassed over ten million views! Jia Jiang came to the United States with the dream of being the next Bill Gates. But despite early success in the corporate world, his first attempt to pursue his entrepreneurial dream ended in rejection. Jia was crushed and spiraled into a period of deep self-doubt. Jia realized that his fear of rejection was a bigger obstacle than any single rejection would ever be; he needed to find a way to cope with being told “no” that wouldn’t destroy him. Inspired by rejection therapy, which uses similar modalities as exposure therapy to desensitize you to the effects of being rejected, he undertook the “100 days of rejection” experiment, during which he willfully sought out rejection on a daily basis—from requesting a lesson in sales from a car salesman (no) to asking a flight attendant if he could make an announcement on the loud speaker (yes) to his famous request to get Krispy Kreme donuts in the shape of Olympic rings (yes, with a viral video to prove it). Over the course of one hundred rejection attempts, Jia realized that even the most preposterous wish might be granted if you ask the right way. He learned the secrets to making successful requests, tactics for picking the right people to approach at the right time, and strategies for converting an initial no into something positive. More important, Jia discovered ways to steel himself against rejection and live more fearlessly—skills that can’t be derailed by a single setback. The changes Jia experienced from his rejection therapy experiment went far beyond becoming more successful in business; he realized that he could apply these techniques to get more out of his relationships with friends, family, and even casual encounters with strangers. Filled with great stories and valuable insight, Rejection Proof shares the secrets of Jia’s rejection journey, distilling each lesson into a strategy that can be used in any negotiation or pitch.
Download or read book Interactive Theorem Proving and Program Development written by Yves Bertot and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.
Download or read book G del s Theorems and Zermelo s Axioms written by Lorenz Halbeisen and published by Springer Nature. This book was released on 2020-10-16 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
Download or read book Robot Proof revised and updated edition written by Joseph E. Aoun and published by MIT Press. This book was released on 2024-10-15 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fresh look at a “robot-proof” education in the new age of generative AI. In 2017, Robot-Proof, the first edition, foresaw the advent of the AI economy and called for a new model of higher education designed to help human beings flourish alongside smart machines. That economy has arrived. Creative tasks that, seven years ago, seemed resistant to automation can now be performed with a simple prompt. As a result, we must now learn not only to be conversant with these technologies, but also to comprehend and deploy their outputs. In this revised and updated edition, Joseph Aoun rethinks the university’s mission for a world transformed by AI, advocating for the lifelong endeavor of a “robot-proof” education. Aoun puts forth a framework for a new curriculum, humanics, which integrates technological, data, and human literacies in an experiential setting, and he renews the call for universities to embrace lifelong learning through a social compact with government, employers, and learners themselves. Drawing on the latest developments and debates around generative AI, Robot-Proof is a blueprint for the university as a force for human reinvention in an era of technological change—an era in which we must constantly renegotiate the shifting boundaries between artificial intelligence and the capacities that remain uniquely human.
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.
Download or read book The Proof written by Frederick Schauer and published by Harvard University Press. This book was released on 2022-05-31 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the Scribes Book Award “Displays a level of intellectual honesty one rarely encounters these days...This is delightful stuff.” —Barton Swaim, Wall Street Journal “At a time when the concept of truth itself is in trouble, this lively and accessible account provides vivid and deep analysis of the practices addressing what is reliably true in law, science, history, and ordinary life. The Proof offers both timely and enduring insights.” —Martha Minow, former Dean of Harvard Law School “His essential argument is that in assessing evidence, we need, first of all, to recognize that evidence comes in degrees...and that probability, the likelihood that the evidence or testimony is accurate, matters.” —Steven Mintz, Inside Higher Education “I would make Proof one of a handful of books that all incoming law students should read...Essential and timely.” —Emily R. D. Murphy, Law and Society Review In the age of fake news, trust and truth are hard to come by. Blatantly and shamelessly, public figures deceive us by abusing what sounds like evidence. To help us navigate this polarized world awash in misinformation, preeminent legal theorist Frederick Schauer proposes a much-needed corrective. How we know what we think we know is largely a matter of how we weigh the evidence. But evidence is no simple thing. Law, science, public and private decision making—all rely on different standards of evidence. From vaccine and food safety to claims of election fraud, the reliability of experts and eyewitnesses to climate science, The Proof develops fresh insights into the challenge of reaching the truth. Schauer reveals how to reason more effectively in everyday life, shows why people often reason poorly, and makes the case that evidence is not just a matter of legal rules, it is the cornerstone of judgment.
Download or read book Strategic Error Proofing written by John J. Casey and published by CRC Press. This book was released on 2010-07-29 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates how the strategic placement of 'error-proofing' devices, which is refered in this book as Success Every Time (SET), drives up industries' profits and throughput. It highlights the deficiencies of Failure Mode Effects Analysis (FMEA) and compares the strategy to the SET.
Download or read book Femme Fatale written by Shuzo Oshimi and published by DENPA, LLC. This book was released on 2021-04-27 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commemorating twenty years of manga, FEMME FATALE showcases of all of the full color artwork from New York Time's Best Selling artist Shuzo Oshimi. Featuring cover art, posters, promotional materials and never before translated comics, this is a definitive compilation of character art from one of the best known manga artists in the 21st Century. Concept art and promotional illustrations from FLOWERS OF EVIL, INSIDE MARI, DRIFTING NET CAFE and BLOOD ON THE RAILS are also included giving readers a deeper look into Oshimi's processes and artistic mind. This collection also includes dozens of never before published in English comic pages that are a must have for Oshimi completionists.
Download or read book Proof written by Adam Rogers and published by Houghton Mifflin Harcourt. This book was released on 2014 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a look at the science of alcohol production and consumption, from the principles behind the fermentation, distillation, and aging of alcoholic beverages, to the psychology and neurobiology of what happens after it is consumed.
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.
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.
Download or read book The Psychology of Proof written by Lance J. Rips and published by MIT Press. This book was released on 1994 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lance Rips describes a unified theory of natural deductive reasoning and fashions a working model of deduction, with strong experimental support, that is capable of playing a central role in mental life.
