Induction And Analogy In Mathematics Pdf

induction and analogy in mathematics pdf

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A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity.

Induction and Analogy in Mathematics

Analogical Reasoning pp Cite as. Analogical reasoning is a traditional mode of argument which has been applied in a variety of contexts — such as rhetorics, ethics, politics, mythology, metaphysics, theology, mathematics, logic, physics, biology, medicine, psychology, jurisprudence, engineering, and artificial intelligence. Within its everyday and scientific applications, analogy has been employed for different purposes — such as heuristics, justification, and problem solving. Unable to display preview. Download preview PDF. Skip to main content. This service is more advanced with JavaScript available.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs and how to get involved. Authors: Ryan Zielinski. Comments: 73 pages.

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Analogy and Similarity in Scientific Reasoning

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper We will take the unorthodox approach of presenting the material from the point of view of someone who is trying to solve the problem himself. Keywords: analogy, Johann Faulhaber, finite sums, heuristics, inductive reasoning, number theory, George Polya, problem solving, teaching of mathematics.

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. 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 material in both volumes is fresh and highly original; the presentation is stimulating, informal, and occasionally humorous; examples from science, legal reasoning, and daily life make the arguments clear even to a nonspecialist.


I. INDUCTION AND ANALOGY IN MATHEMATICS. VOL. II. numbers" appeared previously in the American Mathematical Monthly; I wish to express my thanks.


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Halmos reviewing the book summarised the central thesis of the book thus: ". Polya begins Volume I with a discussion on induction , not mathematical induction , but as a way of guessing new results. This is the well known Goldbach's conjecture. The first problem in the first chapter is to guess the rule according to which the successive terms of the following sequence are chosen: 11, 31, 41, 61, 71, , ,.

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Analogy and Analogical Reasoning

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I. INDUCTION AND ANALOGY IN MATHEMATICS. VOL. II. We secure our mathematical knowledge by demonstrative reasoning, but we support our.

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