David Wells

Games and Mathematics (eBook, PDF)

Subtle Connections

• Format: PDF

Produktbeschreibung

The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 18. Oktober 2012
• Englisch
• ISBN-13: 9781139558624
• Artikelnr.: 38276486

Autorenporträt

David Wells is the author of more than a dozen books on popular mathematics, puzzles and recreations. He has written many articles on mathematics teaching and a secondary mathematics course based on problem-solving. A former British under-21 chess champion, he has also worked as a game inventor and puzzle editor.

Inhaltsangabe

Introduction
Part I. Mathematical recreations and abstract games: 1. Recreations from Euler to Lucas
2. Four abstract games
3. Mathematics and games: mysterious connections
4. Why chess is not mathematics
5. Proving versus checking
Part II. Mathematics: game-like, scientific and perceptual: 6. Game-like mathematics
7. Euclid and the rules of his geometrical game
8. New concepts and new objects
9. Convergent and divergent series
10. Mathematics becomes game-like
11. Maths as science
12. Numbers and sequences
13. Computers and mathematics
14. Mathematics and the sciences
15. Minimum paths from Heron to Feynmann
16. The foundations: perception, imagination and insight
17. Structure
18. Hidden structure, common structure
19. Mathematics and beauty
20. Origins: formality in the everyday world
Bibliography
Index.

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Introduction; Part I. Mathematical recreations and abstract games: 1. Recreations from Euler to Lucas; 2. Four abstract games; 3. Mathematics and games: mysterious connections; 4. Why chess is not mathematics; 5. Proving versus checking; Part II. Mathematics: game-like, scientific and perceptual: 6. Game-like mathematics; 7. Euclid and the rules of his geometrical game; 8. New concepts and new objects; 9. Convergent and divergent series; 10. Mathematics becomes game-like; 11. Maths as science; 12. Numbers and sequences; 13. Computers and mathematics; 14. Mathematics and the sciences; 15. Minimum paths from Heron to Feynmann; 16. The foundations: perception, imagination and insight; 17. Structure; 18. Hidden structure, common structure; 19. Mathematics and beauty; 20. Origins: formality in the everyday world; Bibliography; Index.

Rezensionen

'One of the wellsprings out of which the discipline of mathematics has developed is human delight in intellectual play, manifest in the ubiquity of abstract games across millennia and cultures. The author of this fascinating book is expert in both domains, and in the art of clearly explaining significant aspects of mathematics in ways both accessible to non-experts and illuminating to experts. Through a delightfully rich variety of historical and multicultural examples, he unveils the intimate relationship between abstract games and mathematics as the study of structures, and, in so doing, illuminates much more about mathematical behaviour and cognition. At a time when too much of mathematics education in school seems designed to squeeze out every last drop of playfulness, we are reminded that mathematics can, and should, be an intellectual playground.' Brian Greer, Portland State University