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How to Prove It

How to Prove It
Author: Daniel J. Velleman
Publisher: Cambridge University Press
Total Pages: 401
Release: 2006-01-16
Genre: Mathematics
ISBN: 0521861241

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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.


100% Mathematical Proof

100% Mathematical Proof
Author: Rowan Garnier
Publisher:
Total Pages: 332
Release: 1996-08
Genre: Mathematics
ISBN:

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"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."


Proofs from THE BOOK

Proofs from THE BOOK
Author: Martin Aigner
Publisher: Springer Science & Business Media
Total Pages: 194
Release: 2013-06-29
Genre: Mathematics
ISBN: 3662223430

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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.


Why Prove it Again?

Why Prove it Again?
Author: John W. Dawson, Jr.
Publisher: Birkhäuser
Total Pages: 204
Release: 2015-07-15
Genre: Mathematics
ISBN: 3319173685

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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.


Principia Mathematica

Principia Mathematica
Author: Alfred North Whitehead
Publisher:
Total Pages: 696
Release: 1910
Genre: Logic, Symbolic and mathematical
ISBN:

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Prove It!

Prove It!
Author: Stacey Barr
Publisher: John Wiley & Sons
Total Pages: 216
Release: 2017-01-18
Genre: Business & Economics
ISBN: 0730336247

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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.


Convinced!

Convinced!
Author: Jack Nasher
Publisher: Berrett-Koehler Publishers
Total Pages: 273
Release: 2018-11-13
Genre: Business & Economics
ISBN: 1523095601

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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.


Introduction · to Mathematical Structures and · Proofs

Introduction · to Mathematical Structures and · Proofs
Author: Larry Gerstein
Publisher: Springer Science & Business Media
Total Pages: 355
Release: 2013-11-21
Genre: Science
ISBN: 1468467085

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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 of Proof

Book of Proof
Author: Richard H. Hammack
Publisher:
Total Pages: 314
Release: 2016-01-01
Genre: Mathematics
ISBN: 9780989472111

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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.


Nothing to Prove

Nothing to Prove
Author: Jennie Allen
Publisher: WaterBrook
Total Pages: 258
Release: 2017
Genre: Psychology
ISBN: 1601429614

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"Allen understands the daily struggle so many of us face with the fear that we are not enough. And she invites us into a different experience, one in which our souls overflow with contentment and joy"--Amazon.com.