Mathematics And Plausible Reasoning Induction And Analogy In Mathematics

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Mathematics And Plausible Reasoning Two Volumes In One

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Author : George Polya
language : en
Publisher:
Release Date : 2014-01

Mathematics And Plausible Reasoning Two Volumes In One written by George Polya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01 with Mathematics categories.

2014 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.

Mathematics And Plausible Reasoning Volume 1

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Author : George Polya
language : en
Publisher: Princeton University Press
Release Date : 2020-09-01

Mathematics And Plausible Reasoning Volume 1 written by George Polya and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. I, on Induction and Analogy in Mathematics, covers a wide variety of mathematical problems, revealing the trains of thought that lead to solutions, pointing out false bypaths, discussing techniques of searching for proofs. Problems and examples challenge curiosity, judgment, and power of invention.

The Argument Of Mathematics

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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01

The Argument Of Mathematics written by Andrew Aberdein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Philosophy categories.

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

An Invitation To Applied Category Theory

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Author : Brendan Fong
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-18

An Invitation To Applied Category Theory written by Brendan Fong and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Computers categories.

Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.

How To Solve It

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Author : George Polya
language : en
Publisher: Princeton University Press
Release Date : 2014-10-27

How To Solve It written by George Polya and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-27 with Education categories.

A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

Induction And Analogy In Mathematics

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Author : George Pólya
language : en
Publisher:
Release Date : 1954

Induction And Analogy In Mathematics written by George Pólya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Mathematics categories.

"Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines."--Book cover

Mathematical Discovery On Understanding Learning And Teaching Problem Solving

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Author : George Pólya
language : en
Publisher:
Release Date : 2009

Mathematical Discovery On Understanding Learning And Teaching Problem Solving written by George Pólya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Polya Gyorg. He wrote perhaps the most famous book of mathematics ever written, namely "How to Solve It." However, "How to Solve It" is not strictly speaking a math book. It is a book about how to solve problems of any kind, of which math is just one type of problem. The same techniques could in principle be used to solve any problem one encounters in life (such as how to choose the best wife ). Therefore, Polya wrote the current volume to explain how the techniques set forth in "How to Solve It" can be applied to specific areas such as geometry.

Mathematics And Plausible Reasoning

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Author : G. Pólya
language : en
Publisher:
Release Date : 1973

Mathematics And Plausible Reasoning written by G. Pólya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.

How To Prove It

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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16

How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.

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.

Probability Theory

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Author :
language : en
Publisher: Allied Publishers
Release Date : 2013

Probability Theory written by and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.

Probability theory