Visual Thinking in Mathematics
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31 153 Ft
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Product details:
- Publisher OUP Oxford
- Date of Publication 5 July 2007
- ISBN 9780199285945
- Binding Hardback
- No. of pages298 pages
- Size 241x162x23 mm
- Weight 605 g
- Language English
- Illustrations numerous line figures 0
Categories
Short description:
Marcus Giaquinto presents an investigation into the different kinds of visual thinking involved in mathematical thought, with chapters on basic geometry, arithmetic, algebra, and more advanced mathematics. He argues that the use of mental images and physical diagrams is rarely just a superfluous aid: it is often a means of discovery, understanding, and even proof. Drawing on work in cognitive psychology, philosophy, and mathematics, this book will appeal to anyone with an interest in mathematical thinking.
MoreLong 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.
Table of Contents:
Introduction
Simple Shapes: Vision and Concepts
Basic Geometrical Knowledge
Geometrical Discovery by Visualizing
Diagrams in Geometric Proofs
Mental Number Lines
Visual Aspects of Calculation
General Theorems from Specific Images
Visual Thinking in Basic Analysis
Symbol Manipulation
Cognition of Structure
Mathematical Thinking: Algebraic v. Geometric?
