Mathematics And Plausible Reasoning V1 2
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| Author | : George Polya |
| Publisher | : |
| Total Pages | : 498 |
| Release | : 2014-01 |
| Genre | : Mathematics |
| ISBN | : 9781614275572 |
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.
| Author | : G. Polya |
| Publisher | : Princeton University Press |
| Total Pages | : 242 |
| Release | : 1990-08-23 |
| Genre | : Mathematics |
| ISBN | : 9780691025100 |
"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 | : G. Polya |
| Publisher | : Princeton University Press |
| Total Pages | : 238 |
| Release | : 2021-08-10 |
| Genre | : Mathematics |
| ISBN | : 1400823722 |
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 | : G. Polya |
| Publisher | : Princeton University Press |
| Total Pages | : 300 |
| Release | : 1990-08-23 |
| Genre | : Mathematics |
| ISBN | : 9780691025094 |
"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 | : George Pólya |
| Publisher | : |
| Total Pages | : 304 |
| Release | : 1954 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : |
| Author | : Sanjoy Mahajan |
| Publisher | : MIT Press |
| Total Pages | : 152 |
| Release | : 2010-03-05 |
| Genre | : Education |
| ISBN | : 0262265591 |
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
| Author | : George Pólya |
| Publisher | : |
| Total Pages | : 208 |
| Release | : 1954 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : |
| Author | : George Polya |
| Publisher | : Courier Corporation |
| Total Pages | : 82 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 048631832X |
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 | : Lyn D. English |
| Publisher | : Routledge |
| Total Pages | : 393 |
| Release | : 2013-04-03 |
| Genre | : Education |
| ISBN | : 1136491074 |
How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied", to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition. This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.
| Author | : Xiao-Shan Gao |
| Publisher | : World Scientific |
| Total Pages | : 338 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9812791965 |
This volume contains selected papers presented at the Fourth Asian Symposium on Computer Mathematics. There are 39 peer-reviewed contributions together with full papers and extended abstracts by the four invited speakers, G.H. Gonnet, D. Lazard, W. McCune and W.-T. Wu, and these cover some of the most significant advances in computer mathematics, including algebraic, symbolic, numeric and geometric computation, automated mathematical reasoning, mathematical software, and computer-aided geometric design.
