Mathematics And Plausible Reasoning

Author : George Polya
Publisher : Lushena Books
Page : 0 pages
File Size : 45,5 Mb
Release : 2023-02-08
Category : Computers
ISBN : 1639235663

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Mathematics and Plausible Reasoning by George Polya Pdf

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.

Author : George Pólya
Publisher : Unknown
Page : 0 pages
File Size : 40,8 Mb
Release : 1954
Category : Logic, Symbolic and mathematical
ISBN : OCLC:1087897278

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Mathematics and plausible reasoning. 2. Patterns of plausible inference by George Pólya Pdf

Author : George Pólya
Publisher : Unknown
Page : 200 pages
File Size : 46,5 Mb
Release : 1954
Category : Mathematics
ISBN : 0691080062

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Patterns of Plausible Inference by George Pólya Pdf

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. II, on Patterns of Plausible Inference, attempts to develop a logic of plausibility. What makes some evidence stronger and some weaker? How does one seek evidence that will make a suspected truth more probable? These questions involve philosophy and psychology as well as mathematics.

Author : Jonathan Borwein,David Bailey
Publisher : CRC Press
Page : 393 pages
File Size : 49,8 Mb
Release : 2008-10-27
Category : Mathematics
ISBN : 9781439865361

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Mathematics by Experiment by Jonathan Borwein,David Bailey Pdf

This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational P

Author : George Polya
Publisher : Hassell Street Press
Page : 310 pages
File Size : 41,9 Mb
Release : 2021-09-09
Category : Electronic
ISBN : 1014400325

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Induction_And_Analogy_In_Mathematics_1_ by George Polya Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : G. Polya
Publisher : Princeton University Press
Page : 242 pages
File Size : 48,6 Mb
Release : 1990-08-23
Category : Mathematics
ISBN : 069102510X

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Mathematics and Plausible Reasoning: Patterns of plausible inference by G. Polya Pdf

"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.

Author : Judea Pearl
Publisher : Elsevier
Page : 552 pages
File Size : 47,8 Mb
Release : 2014-06-28
Category : Computers
ISBN : 9780080514895

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Probabilistic Reasoning in Intelligent Systems by Judea Pearl Pdf

Probabilistic Reasoning in Intelligent Systems is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertainty--and offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognition--in short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information. Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Author : Brendan Fong,David I. Spivak
Publisher : Cambridge University Press
Page : 351 pages
File Size : 41,7 Mb
Release : 2019-07-18
Category : Computers
ISBN : 9781108482295

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An Invitation to Applied Category Theory by Brendan Fong,David I. Spivak Pdf

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

Author : George Pólya
Publisher : Unknown
Page : 208 pages
File Size : 46,6 Mb
Release : 1964
Category : Logic, Symbolic and mathematical
ISBN : UOM:39015008206248

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Mathematics and Plausible Reasoning by George Pólya Pdf

Author : George Polya,Jeremy Kilpatrick
Publisher : Courier Corporation
Page : 80 pages
File Size : 41,8 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780486318325

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The Stanford Mathematics Problem Book by George Polya,Jeremy Kilpatrick Pdf

Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Author : David Corfield
Publisher : Cambridge University Press
Page : 300 pages
File Size : 53,6 Mb
Release : 2003-04-24
Category : Philosophy
ISBN : 9781139436397

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Towards a Philosophy of Real Mathematics by David Corfield Pdf

In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.

Author : Randall E. Auxier,Gary L. Herstein
Publisher : Taylor & Francis
Page : 370 pages
File Size : 53,9 Mb
Release : 2017-03-31
Category : Philosophy
ISBN : 9781351792486

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The Quantum of Explanation by Randall E. Auxier,Gary L. Herstein Pdf

The Quantum of Explanation advances a bold new theory of how explanation ought to be understood in philosophical and cosmological inquiries. Using a complete interpretation of Alfred North Whitehead’s philosophical and mathematical writings and an interpretive structure that is essentially new, Auxier and Herstein argue that Whitehead has never been properly understood, nor has the depth and breadth of his contribution to the human search for knowledge been assimilated by his successors. This important book effectively applies Whitehead’s philosophy to problems in the interpretation of science, empirical knowledge, and nature. It develops a new account of philosophical naturalism that will contribute to the current naturalism debate in both Analytic and Continental philosophy. Auxier and Herstein also draw attention to some of the most important differences between the process theology tradition and Whitehead’s thought, arguing in favor of a Whiteheadian naturalism that is more or less independent of theological concerns. This book offers a clear and comprehensive introduction to Whitehead’s philosophy and is an essential resource for students and scholars interested in American philosophy, the philosophy of mathematics and physics, and issues associated with naturalism, explanation and radical empiricism.

Author : Jonathan M. Borwein,David H. Bailey,Roland Girgensohn
Publisher : CRC Press
Page : 372 pages
File Size : 52,9 Mb
Release : 2004-04-12
Category : Mathematics
ISBN : 9781439864197

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Experimentation in Mathematics by Jonathan M. Borwein,David H. Bailey,Roland Girgensohn Pdf

New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of

Author : Nicholas Rescher
Publisher : Unknown
Page : 148 pages
File Size : 55,7 Mb
Release : 1976
Category : Philosophy
ISBN : UCAL:B3161420

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Plausible Reasoning by Nicholas Rescher Pdf

Author : G. Polya
Publisher : Princeton University Press
Page : 300 pages
File Size : 55,7 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9780691218304

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Mathematics and Plausible Reasoning, Volume 1 by G. Polya Pdf

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.