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How to Prove It

2006-01-16 Mathematics
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Release : 2006-01-16
Genre : Mathematics
Kind : eBook
Book Rating : 241/5 ( reviews)

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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. This book was released on 2006-01-16. 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.

How to Prove It

2006-01-16 Mathematics
Download How to Prove It PDF Online Free

Author :
Release : 2006-01-16
Genre : Mathematics
Kind : eBook
Book Rating : 972/5 ( reviews)

GET EBOOK


Book Synopsis How to Prove It by : Daniel J. Velleman

Download or read book How to Prove It written by Daniel J. Velleman. This book was released on 2006-01-16. 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.

How to Prove It

2006-01-16 Computers
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Release : 2006-01-16
Genre : Computers
Kind : eBook
Book Rating : 994/5 ( reviews)

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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. This book was released on 2006-01-16. 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.

Proofs from THE BOOK

2013-06-29 Mathematics
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Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 430/5 ( reviews)

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Book Synopsis Proofs from THE BOOK by : Martin Aigner

Download or read book Proofs from THE BOOK written by Martin Aigner. This book was released on 2013-06-29. 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.

Why Prove it Again?

2015-07-15 Mathematics
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Release : 2015-07-15
Genre : Mathematics
Kind : eBook
Book Rating : 685/5 ( reviews)

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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.. This book was released on 2015-07-15. 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.

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