Visual Thinking in Mathematics by Marcus Giaquinto (English) Hardcover Book

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The Nile on eBay Visual Thinking in Mathematics by Marcus Giaquinto Marcus Giaquinto presents an investigation into the different kinds of visual thinking involved in mathematical thought, drawing on work in cognitive psychology, philosophy, and mathematics. He argues that mental images and physical diagrams are rarely just superfluous aids: they are often a means of discovery, understanding, and even proof. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used,Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on thenature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures. Visual Thinking in Mathematicsreopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitivesciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking. Author Biography Marcus Giaquinto is a Reader in Philosophy at University College London. Table of Contents 1: Introduction2: Simple Shapes: Vision and Concepts3: Basic Geometrical Knowledge4: Geometrical Discovery by Visualizing5: Diagrams in Geometric Proofs6: Mental Number Lines7: Visual Aspects of Calculation8: General Theorems from Specific Images9: Visual Thinking in Basic Analysis10: Symbol Manipulation11: Cognition of Structure12: Mathematical Thinking: Algebraic v. Geometric? Review "The author provides a lot of signposting, making all the arguments easy to follow and the monograph a pleasure to read."--Mathematical Reviews "I recommend this book highly. It is rich with insight, stimulating and worth careful thought. Furthermore, its concise presentation of recent psychological work is invaluable."--Andrew Arana, Analysis Reviews Promotional Multi-disciplinary approach; draws on the latest research in cognitive science, psychology, mathematics education, and philosophy Long Description Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used,Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numericalcognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures. Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking. Review Quote "The author provides a lot of signposting, making all the arguments easy to follow and the monograph a pleasure to read."--Mathematical Reviews "I recommend this book highly. It is rich with insight, stimulating and worth careful thought. Furthermore, its concise presentation of recent psychological work is invaluable."--Andrew Arana,Analysis Reviews Feature Original work on a fascinating topicMulti-disciplinary approach; draws on the latest research in cognitive science, psychology, mathematics education, and philosophyWide range of mathematical examples from geometry, algebra, arithmetic, and real analysisOffers solutions to long-standing philosophical problems Details ISBN 0199285942 Author Marcus Giaquinto Short Title VISUAL THINKING IN MATHEMATICS Language English ISBN-10 0199285942 ISBN-13 9780199285945 Media Book Format Hardcover Year 2007 Place of Publication Oxford Country of Publication United Kingdom Affiliation University College London DOI 10.1604/9780199285945 UK Release Date 2007-07-05 AU Release Date 2007-07-05 NZ Release Date 2007-07-05 Pages 298 Publisher Oxford University Press Publication Date 2007-07-05 Alternative 9780199575534 DEWEY 510.1 Illustrations numerous line figures Audience Further / Higher Education Imprint Oxford University Press We've got this At The Nile, if you're looking for it, we've got it. 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