Concepts of Modern MathematicsPaperback Dover Books on Mathematics
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- Publisher: Dover Publications Inc.
- Format: Paperback | 352 pages
- Dimensions: 137mm x 213mm x 20mm | 386g
- Publication date: 1 February 1995
- Publication City/Country: New York
- ISBN 10: 0486284247
- ISBN 13: 9780486284248
- Edition: Revised
- Edition statement: Revised edition
- Illustrations note: 200ill.
- Sales rank: 56,394
Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of "pure "mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more. By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.
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Table of contents
Preface to the Dover Edition Preface to the First Edition 1. Mathematics in General 2. Motion without Movement 3. Short Cuts in the Higher Arithmetic 4. The Language of Sets 5. What is a Function? 6. The Beginnings of Abstract Algebra 7. Symmetry: The Group Concept 8. Axiomatics 9. Counting: Finite and Infinite 10. Topology 11. The Power of Indirect Thinking 12. Topological Invariants 13. Algebraic Topology 14. Into Hyperspace 15. Linear Algebra 16. Real Analysis 17. The Theory of Probability 18. Computers and Their Uses 19. Applications of Modern Mathematics 20. Foundations Appendix Notes Glossary of Symbols Index