Visual Thinking in Mathematics by Marcus Giaquinto (English) Paperback 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 Paperback 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 `Review from previous edition The author shows great ambition in tackling such an interesting topic with an interdisciplinary spirit.'Sun-Joo Shin, Notre Dame Philosophical 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 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 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 Text `Review from previous edition The author shows great ambition in tackling such an interesting topic with an interdisciplinary spirit.' Sun-Joo Shin, Notre Dame Philosophical Reviews Review Quote 'Review from previous edition The author shows great ambition in tackling such an interesting topic with an interdisciplinary spirit.' Sun-Joo Shin, Notre Dame Philosophical Reviews Feature Original work on a fascinating topic Multi-disciplinary approach; draws on the latest research in cognitive science, psychology, mathematics education, and philosophy Wide range of mathematical examples from geometry, algebra, arithmetic, and real analysis Offers solutions to long-standing philosophical problems Details ISBN 0199575533 Author Marcus Giaquinto Short Title VISUAL THINKING IN MATHEMATICS Language English ISBN-10 0199575533 ISBN-13 9780199575534 Media Book Format Paperback Year 2011 Imprint Oxford University Press Place of Publication Oxford Country of Publication United Kingdom Publication Date 2011-09-22 Illustrations Illustrations Affiliation University College London UK Release Date 2011-09-22 NZ Release Date 2011-09-22 Pages 298 Publisher Oxford University Press Alternative 9780199285945 DEWEY 510.1 Audience Further / Higher Education AU Release Date 2011-10-03 We've got this At The Nile, if you're looking for it, we've got it. 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