Visual Thinking in Mathematics
(Sprache: Englisch)
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...
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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.
Klappentext zu „Visual Thinking in Mathematics “
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.
Inhaltsverzeichnis zu „Visual Thinking in Mathematics “
- 1: Introduction
- 2: Simple Shapes: Vision and Concepts
- 3: Basic Geometrical Knowledge
- 4: Geometrical Discovery by Visualizing
- 5: Diagrams in Geometric Proofs
- 6: Mental Number Lines
- 7: Visual Aspects of Calculation
- 8: General Theorems from Specific Images
- 9: Visual Thinking in Basic Analysis
- 10: Symbol Manipulation
- 11: Cognition of Structure
- 12: Mathematical Thinking: Algebraic v. Geometric?
Autoren-Porträt von Marcus Giaquinto
Marcus Giaquinto is a Reader in Philosophy at University College London.
Bibliographische Angaben
- Autor: Marcus Giaquinto
- 2007, 298 Seiten, Maße: 16,7 x 25,1 cm, Gebunden, Englisch
- Verlag: Oxford University Press
- ISBN-10: 0199285942
- ISBN-13: 9780199285945
Sprache:
Englisch
Rezension zu „Visual Thinking in Mathematics “
"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
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