Mathematics and Plausible Reasoning [Two Volumes in One]

Author: George Polya
Publisher:
ISBN: 9781614275572
Category : Mathematics
Languages : en
Pages : 498

Book Description
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 2

Author: G. Polya
Publisher: Princeton University Press
ISBN: 1400823722
Category : Mathematics
Languages : en
Pages : 238

Book Description
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.

Mathematics and Plausible Reasoning, Volume 1

Author: G. Polya
Publisher: Princeton University Press
ISBN: 0691218307
Category : Mathematics
Languages : en
Pages : 300

Book Description
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.

Mathematics by Experiment

Author: Jonathan Borwein
Publisher: CRC Press
ISBN: 1439865361
Category : Mathematics
Languages : en
Pages : 393

Book Description
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

Famous Puzzles of Great Mathematicians

Author: Miodrag Petkovi_
Publisher: American Mathematical Soc.
ISBN: 0821848143
Category : Mathematics
Languages : en
Pages : 346

Book Description
This entertaining book presents a collection of 180 famous mathematical puzzles and intriguing elementary problems that great mathematicians have posed, discussed, and/or solved. The selected problems do not require advanced mathematics, making this book accessible to a variety of readers. Mathematical recreations offer a rich playground for both amateur and professional mathematicians. Believing that creative stimuli and aesthetic considerations are closely related, great mathematicians from ancient times to the present have always taken an interest in puzzles and diversions. The goal of this book is to show that famous mathematicians have all communicated brilliant ideas, methodological approaches, and absolute genius in mathematical thoughts by using recreational mathematics as a framework. Concise biographies of many mathematicians mentioned in the text are also included. The majority of the mathematical problems presented in this book originated in number theory, graph theory, optimization, and probability. Others are based on combinatorial and chess problems, while still others are geometrical and arithmetical puzzles. This book is intended to be both entertaining as well as an introduction to various intriguing mathematical topics and ideas. Certainly, many stories and famous puzzles can be very useful to prepare classroom lectures, to inspire and amuse students, and to instill affection for mathematics.

Rethinking Economics as Social Theory

Author: Richard E. Wagner
Publisher: Edward Elgar Publishing
ISBN: 1802204768
Category : Political Science
Languages : en
Pages : 209

Book Description
Taking an innovative look at the origins of economics, this forward-thinking book relocates economics from a materialistic general theory of rational action into an idealistic theory of social organization and individual action. Adding new insightful analytical methods such as complexity theory, graph theory and computational modelling to the original insights of the Scottish Enlightenment, Richard E. Wagner explores economics in an ever-changing society, looking at the key civilizing processes and the important social questions.

A Century in Books

Author: Princeton University Press Staff
Publisher: Princeton University Press
ISBN: 0691238170
Category : Language Arts & Disciplines
Languages : en
Pages : 192

Book Description
It all began atop a drugstore in Princeton, New Jersey, in November 1905. From its modest beginnings, Princeton University Press was to become one of the world's most important scholarly publishers, embracing a wealth of disciplines that have enriched our cultural, academic, and scientific landscape. Both as a tribute to our authors and to celebrate our centenary, Princeton University Press here presents A Century in Books. This beautifully designed volume highlights 100 of the nearly 8,000 books we have published. Necessarily winnowed from a much larger list, these books best typify what has been most lasting, most defining, and most distinctive about our publishing history--from Einstein's The Meaning of Relativity (1922) to the numerous mathematical and other works that marked the Press's watershed decade of the 1940s, including von Neumann and Morgenstern's Theory of Games and Economic Behavior; from milestones of literary criticism by Erich Auerbach and Northop Frye to George Kennan's Pulitzer Prize-winning book on Soviet-American relations; from Milton Friedman and Anna Jacobson Schwartz's A Monetary History of the United States, 1867-1960 to more recent landmarks such as L. Luca Cavalli-Sforza, Paolo Menozzi, and Alberto Piazza's The History and Geography of Human Genes and Robert Shiller's Irrational Exuberance. In addition to succinct descriptions of the 100 titles and a short introduction on the history of the Press, the book features five essays by prominent scholars and writers: Michael Wood discusses the impact on Princeton University Press of intellectuals who fled Nazi Germany and authored many influential books. Anthony Grafton recounts our rich publishing tradition in history, politics, and culture. Sylvia Nasar traces our evolution into a leading voice in economics publishing. Daniel Kevles reflects on Einstein, a figure of special importance to Princeton. And Lord Robert May writes on our long-standing tradition of publishing in mathematics and science. A Century in Books is more than a celebration of 100 years of publishing at Princeton University Press--it is a treasure trove of 100 years of books that have added to the richness of twentieth-century intellectual life.

The SAGE Encyclopedia of Research Design

Author: Bruce B. Frey
Publisher: SAGE Publications
ISBN: 1071812106
Category : Social Science
Languages : en
Pages : 3889

Book Description
The SAGE Encyclopedia of Research Design maps out how one makes decisions about research design, interprets data, and draws valid inferences, undertakes research projects in an ethical manner, and evaluates experimental design strategies and results. From A-to-Z, this four-volume work covers the spectrum of research design strategies and topics including, among other things: fundamental research design principles, ethics in the research process, quantitative versus qualitative and mixed-method designs, completely randomized designs, multiple comparison tests, diagnosing agreement between data and models, fundamental assumptions in analysis of variance, factorial treatment designs, complete and incomplete block designs, Latin square and related designs, hierarchical designs, response surface designs, split-plot designs, repeated measures designs, crossover designs, analysis of covariance, statistical software packages, and much more. Research design, with its statistical underpinnings, can be especially daunting for students and novice researchers. At its heart, research design might be described simply as a formalized approach toward problem solving, thinking, and acquiring knowledge, the success of which depends upon clearly defined objectives and appropriate choice of statistical design and analysis to meet those objectives. The SAGE Encyclopedia of Research Design will assist students and researchers with their work while providing vital information on research strategies.

Foundations of Bayesianism

Author: D. Corfield
Publisher: Springer Science & Business Media
ISBN: 9401715866
Category : Science
Languages : en
Pages : 419

Book Description
This is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. The volume includes important criticisms of Bayesian reasoning and gives an insight into some of the points of disagreement amongst advocates of the Bayesian approach. It will be of interest to graduate students, researchers, those involved with the applications of Bayesian reasoning, and philosophers.

A Century of Advancing Mathematics

Author: Paul Zorn
Publisher: The Mathematical Association of America
ISBN: 0883855887
Category : Mathematics
Languages : en
Pages : 436

Book Description
The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott. This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.