Download or read book Mathematics and Plausible Reasoning Two Volumes in One written by George Polya and published by . This book was released on 2014-01 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Patterns of Plausible Inference written by George Pólya and published by . This book was released on 1954 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics by Experiment written by Jonathan Borwein and published by CRC Press. This book was released on 2008-10-27 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book What Is Mathematical Logic written by J. N. Crossley and published by Courier Corporation. This book was released on 2012-08-29 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.
Download or read book Street Fighting Mathematics written by Sanjoy Mahajan and published by MIT Press. This book was released on 2010-03-05 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Experimentation in Mathematics written by Jonathan M. Borwein and published by CRC Press. This book was released on 2004-04-12 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Towards a Philosophy of Real Mathematics written by David Corfield and published by Cambridge University Press. This book was released on 2003-04-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability Theory written by and published by Allied Publishers. This book was released on 2013 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory
Download or read book Concepts of Modern Mathematics written by Ian Stewart and published by Courier Corporation. This book was released on 2012-05-23 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.
Download or read book The Argument of Mathematics written by Andrew Aberdein and published by Springer Science & Business Media. This book was released on 2013-07-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Discovery on Understanding Learning and Teaching Problem Solving written by George Pólya and published by . This book was released on 2009 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
Download or read book The Stanford Mathematics Problem Book written by George Polya and published by Courier Corporation. This book was released on 2013-04-09 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Patterns of Plausible Inference written by G. Polya and published by . This book was released on 1968 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plausible Reasoning written by Nicholas Rescher and published by . This book was released on 1976 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophy of Mathematics and Deductive Structure in Euclid s Elements written by Ian Mueller and published by Courier Dover Publications. This book was released on 2006 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions -- rather than focusing strictly on historical and mathematical issues -- and features several helpful appendixes.
Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
