Concepts of Modern Mathematics
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Concepts of Modern Mathematics

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Description

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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Product details

  • Paperback | 352 pages
  • 137.16 x 213.36 x 20.32mm | 385.55g
  • New York, United States
  • English
  • Revised
  • Revised edition
  • Illustrations, unspecified
  • 0486284247
  • 9780486284248
  • 47,151

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
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Rating details

389 ratings
4.04 out of 5 stars
5 37% (143)
4 37% (144)
3 21% (83)
2 4% (14)
1 1% (5)
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