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Author: Robert S. Wolf
Publisher: W. H. Freeman
Published: 1997-12-15
Total Pages: 4
ISBN-13: 9780716730507
DOWNLOAD EBOOKThis 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.
Author: Robert S Wolf
Publisher: W.H. Freeman
Published: 1997-12-22
Total Pages:
ISBN-13: 9780716732471
DOWNLOAD EBOOKAuthor: Miklos Laczkovich
Publisher: American Mathematical Soc.
Published: 2001-12-31
Total Pages: 118
ISBN-13: 1470458322
DOWNLOAD EBOOKThe 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.
Author: Imre Lakatos
Publisher: Cambridge University Press
Published: 1976
Total Pages: 190
ISBN-13: 9780521290388
DOWNLOAD EBOOKProofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Author: Daniel J. Velleman
Publisher: Cambridge University Press
Published: 2006-01-16
Total Pages: 401
ISBN-13: 0521861241
DOWNLOAD EBOOKMany 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.
Author: Imre Lakatos
Publisher: Cambridge University Press
Published: 2015-10-15
Total Pages: 197
ISBN-13: 1107113466
DOWNLOAD EBOOKThis influential book discusses the nature of mathematical discovery, development, methodology and practice, forming Imre Lakatos's theory of 'proofs and refutations'.
Author: Martin Aigner
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 194
ISBN-13: 3662223430
DOWNLOAD EBOOKAccording 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.
Author: David M. Bressoud
Publisher: Cambridge University Press
Published: 1999-08-13
Total Pages: 292
ISBN-13: 1316582752
DOWNLOAD EBOOKThis is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While apparent that the conjecture must be true, the proof was elusive. Researchers became drawn to this problem, making connections to aspects of invariant theory, to symmetric functions, to hypergeometric and basic hypergeometric series, and, finally, to the six-vertex model of statistical mechanics. All these threads are brought together in Zeilberger's 1996 proof of the original conjecture. The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something new here.
Author: Diane Driscoll Schwartz
Publisher: Brooks/Cole Publishing Company
Published: 1997
Total Pages: 419
ISBN-13: 9780030983382
DOWNLOAD EBOOKAuthor: George Polya
Publisher:
Published: 2014-01
Total Pages: 498
ISBN-13: 9781614275572
DOWNLOAD EBOOK2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket.
