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How To Prove It
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Book Synopsis How to Prove It by : Daniel J. Velleman
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: This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
Book Synopsis How to Prove It by : Daniel J. Velleman
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 399 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.
Book Synopsis How to Prove It by : Daniel J. Velleman
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 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
Book Synopsis Proofs from THE BOOK by : Martin Aigner
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.
Book Synopsis 100% Mathematical Proof by : Rowan Garnier
Download or read book 100% Mathematical Proof written by Rowan Garnier and published by . This book was released on 1996-08 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proof" has been and remains one of the concepts which characterises mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principle techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. Many examples from analysis and modern algebra are included. The exceptionally clear style and presentation ensures that the book will be useful and enjoyable to those studying and interested in the notion of mathematical "proof."
Book Synopsis Principia Mathematica by : Alfred North Whitehead
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis We Reason & We Prove for ALL Mathematics by : Fran Arbaugh
Download or read book We Reason & We Prove for ALL Mathematics written by Fran Arbaugh and published by Corwin Press. This book was released on 2018-08-08 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sharpen concrete teaching strategies that empower students to reason-and-prove How do teachers and students benefit from engaging in reasoning-and-proving? What strategies can teachers use to support students’ capacity to reason-and-prove? What does reasoning-and-proving instruction look like? We Reason & We Prove for ALL Mathematics helps mathematics teachers in grades 6-12 engage in the critical practice of reasoning-and-proving and support the development of reasoning-and-proving in their students. The phrase "reasoning-and-proving" describes the processes of identifying patterns, making conjectures, and providing arguments that may or may not qualify as proofs – processes that reflect the work of mathematicians. Going beyond the idea of "formal proof" traditionally relegated only to geometry, this book transcends all mathematical content areas with a variety of activities for teachers to learn more about reasoning-and-proving and about how to support students’ capacities to engage in this mathematical thinking through: Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work that features a range of solution strategies, representations, and misconceptions Modifying tasks from curriculum materials so that they better support students to reason-and-prove Evaluating learning environments and making connections between key ideas about reasoning-and-proving and teaching strategies We Reason & We Prove for ALL Mathematics is designed as a learning tool for practicing and pre-service mathematics teachers and can be used individually or in a group. No other book tackles reasoning-and-proving with such breadth, depth, and practical applicability. Classroom examples, case studies, and sample problems help to sharpen concrete teaching strategies that empower students to reason-and-prove!
Download or read book Prove It! written by Stacey Barr and published by John Wiley & Sons. This book was released on 2017-01-18 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspire performance and prove your leadership impact Prove It! is the executive guide to improving organisational performance through the practice of evidence-based leadership. More than ever before, the world is demanding transparency and accountability from organisational leaders, and there is a growing push to hold leaders responsible for the performance of their organisation. Many executives panic at the thought of what transparency might reveal and how they might be held accountable, but others relish the opportunity to showcase their organisation's performance. The difference is in the leadership methodology. The best leaders already know how their organisation is performing, and that it has improved during their tenure – and they can prove it because they practise evidence-based leadership. This book offers a clear blueprint for building on your existing skills and performance management systems to build a truly high performance organisation. Just three personal leadership habits and three organisation-wide habits can transform your organisation into the powerhouse you know it can be. With a simple methodology and a focus on practical results, this book can help you: Set a strategic direction that really does inspire organisational excellence Gain a true picture of your organisation's performance Master the habits that help you lead a high-performance culture Improve your organisation objectively, measurably and quickly If an organisation can only be as good as its leadership, it's reasonable to place the burden of performance responsibility on those who make the decisions. A leader's job is to inspire, motivate and guide, and those who do it well are already raising the bar. Prove It! gives you a practical model for measurable, real-world results, starting today.
Book Synopsis Introduction · to Mathematical Structures and · Proofs by : Larry Gerstein
Download or read book Introduction · to Mathematical Structures and · Proofs written by Larry Gerstein and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.
Book Synopsis Why Prove it Again? by : John W. Dawson, Jr.
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.
Book Synopsis Book of Proof by : Richard H. Hammack
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.
Download or read book Nothing to Prove written by Jennie Allen and published by WaterBrook. This book was released on 2018-02-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The visionary behind the million-strong IF:Gathering challenges Christian women to discover what it means to do life with God rather than always striving to impress him, in this trade paperback edition of her perspective-shifting work, which now includes bonus material to enhance your book club experience, including discussion questions and easy-to-create recipes. All too many of us struggle under the weight of life, convinced we need to work harder to prove to ourselves, to others, and to God that we are good enough, smart enough, and spiritual enough to do the things we believe we should. Author and Bible teacher Jennie Allen invites us into a different experience, one in which our souls overflow with contentment and joy. In Nothing to Prove she calls us to… * Find freedom from self-induced pressure by admitting we’re not enough—but Jesus is. * Admit our greatest needs and watch them be filled by the only One who can meet them. * Make it our goal to know and love Jesus, then watch what He does in and through us. As you wade into the refreshing truth of the more-than-enough life Jesus offers, you’ll experience the joyous freedom that comes to those who are determined to discover what God can do through a soul completely in love with Him. * * * * * “These pages are what your soul is begging for" —Ann Voskamp “Nothing to Prove takes us on a journey toward freedom from the need to measure up.” —Mark Batterson We love this glorious and universally resounding message.” —Louie and Shelley Giglio “This book will help you take your eyes off your problems and put them back on God’s promises.” —Christine Caine
Download or read book Something to Prove written by Rob Skead and published by Carolrhoda Books ®. This book was released on 2014-01-01 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1936, the New York Yankees wanted to test a hot prospect named Joe DiMaggio to see if he was ready for the big leagues. They knew just the ballplayer to call—Satchel Paige, the best pitcher anywhere, black or white. For the game, Paige joined a group of amateur African American players, and they faced off against a team of white major leaguers plus young DiMaggio. The odds were stacked against the less-experienced black team. But Paige's skillful batting and amazing pitching—with his "trouble ball" and "bat dodger"— kept the game close. Would the rookie DiMaggio prove himself as major league player? Or would Paige once again prove his greatness—and the injustice of segregated baseball?
Download or read book Convinced! written by Jack Nasher and published by Berrett-Koehler Publishers. This book was released on 2018-11-13 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Competence does not speak for itself! You can't simply display it; you have to draw people's attention to it. World-renowned negotiation and deception detection expert, business professor, and mentalist Jack Nasher offers effective, proven techniques to convince others that we are talented, trustworthy, and yes, even brilliant. Nasher offers the example of Joshua Bell, possibly the world's most famous violinist. In January 2007, at rush hour, he stepped into a Washington, DC, subway station, dressed like any street busker, and began to play a $4,000,000 Stradivarius. It was part of an experiment staged by a journalist of the Washington Post, who expected Bell's skill alone to attract an immense, awed crowd. But Bell was generally ignored, and when he stopped, nobody applauded. He made $34.17. The good news is that you don't have to accept obscurity: you can positively affect others' perception of your talent. Whether you're looking for work, giving an important presentation, seeking clients or customers for your business, or vying for a promotion, Nasher explains how to use techniques such as expectation management, verbal and nonverbal communication, the Halo Effect, competence framing, and the power of nonconformity to gain control of how others perceive you. Competence is the most highly valued professional trait. But it's not enough to be competent, you have to convey your competence. With Nasher's help you can showcase your expertise, receive the recognition you deserve, and achieve lasting success.
Book Synopsis 99 Variations on a Proof by : Philip Ording
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.
Book Synopsis What We Believe but Cannot Prove by : John Brockman
Download or read book What We Believe but Cannot Prove written by John Brockman and published by Harper Collins. This book was released on 2009-10-13 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than one hundred of the world's leading thinkers write about things they believe in, despite the absence of concrete proof Scientific theory, more often than not, is born of bold assumption, disparate bits of unconnected evidence, and educated leaps of faith. Some of the most potent beliefs among brilliant minds are based on supposition alone -- yet that is enough to push those minds toward making the theory viable. Eminent cultural impresario, editor, and publisher of Edge (www.edge.org), John Brockman asked a group of leading scientists and thinkers to answer the question: What do you believe to be true even though you cannot prove it? This book brings together the very best answers from the most distinguished contributors. Thought-provoking and hugely compelling, this collection of bite-size thought-experiments is a fascinating insight into the instinctive beliefs of some of the most brilliant minds today.
Download or read book Proofs and Ideas written by B. Sethuraman and published by American Mathematical Society. This book was released on 2021-12-02 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proofs and Ideas serves as a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. It is intended to ease the student's transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts. The spirit of the book is that the basic tools of abstract mathematics are best developed in context and that creativity and imagination are at the core of mathematics. So, while the book has chapters on statements and sets and functions and induction, the bulk of the book focuses on core mathematical ideas and on developing intuition. Along with chapters on elementary combinatorics and beginning number theory, this book contains introductory chapters on real analysis, group theory, and graph theory that serve as gentle first exposures to their respective areas. The book contains hundreds of exercises, both routine and non-routine. This book has been used for a transition to advanced mathematics courses at California State University, Northridge, as well as for a general education course on mathematical reasoning at Krea University, India.
