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Proof, Logic, and Conjecture

1997-12-15 Mathematics
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Release : 1997-12-15
Genre : Mathematics
Kind : eBook
Book Rating : 507/5 ( reviews)

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Book Synopsis Proof, Logic, and Conjecture by : Robert S. Wolf

Download or read book Proof, Logic, and Conjecture written by Robert S. Wolf. This book was released on 1997-12-15. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed to teach students how to read and write proofs in mathematics and to acquaint them with how mathematicians investigate problems and formulate conjecture.

The Mathematician's Toolbox

1997-12-22
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Release : 1997-12-22
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Kind : eBook
Book Rating : 471/5 ( reviews)

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Book Synopsis The Mathematician's Toolbox by : Robert S Wolf

Download or read book The Mathematician's Toolbox written by Robert S Wolf. This book was released on 1997-12-22. Available in PDF, EPUB and Kindle. Book excerpt:

Conjecture and Proof

2001-12-31 Mathematics
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Release : 2001-12-31
Genre : Mathematics
Kind : eBook
Book Rating : 322/5 ( reviews)

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Book Synopsis Conjecture and Proof by : Miklos Laczkovich

Download or read book Conjecture and Proof written by Miklos Laczkovich. This book was released on 2001-12-31. Available in PDF, EPUB and Kindle. Book excerpt: The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on Conjecture and Proof. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of $e$, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.

Proofs and Refutations

1976 Mathematics
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Release : 1976
Genre : Mathematics
Kind : eBook
Book Rating : 388/5 ( reviews)

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Book Synopsis Proofs and Refutations by : Imre Lakatos

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

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.

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