Concepts of Modern Mathematics

Front Cover
Courier Dover Publications, Feb 1, 1995 - Mathematics - 339 pages
15 Reviews

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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Review: Concepts of Modern Mathematics

User Review  - Daniel - Goodreads

Good general introduction to give you a feel for some diverse areas of modern mathematics. However, the explanations are glossed over too quickly and I found it very difficult to follow some of the ... Read full review

Review: Concepts of Modern Mathematics

User Review  - Leemaslibros - Goodreads

Wonderful reading, disastrous (kindle) edition. Read full review

Contents

Mathematics in General
1
Motion without Movement
8
Short Cuts in the Higher Arithmetic
27
The Language of Sets
43
What is a Function?
63
The Beginnings of Abstract Algebra
76
The Group Concept
95
Axiomatics
113
Into Hyperspace
200
Linear Algebra
215
Real Analysis
229
The Theory of Probability
244
Computers and Their Uses
255
Applications of Modern Mathematics
269
Foundations
286
Appendix
299

Finite and Infinite
127
Topology
144
The Power of Indirect Thinking
159
Topological Invariants
174
Algebraic Topology
189
Notes
322
Glossary of Symbols
335
Index
337
Copyright

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Page 337 - N the set of natural numbers Z the set of integers Q the set of rational numbers R the set of real numbers C the set of complex numbers

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About the author (1995)

Ian Stewart is Professor of Mathematics at Warwick University in England. His many books include Does God Play Dice?, The collapse of Chaos (with Jack Cohen), Game, Set and Math, and Fearful Symmetry: Is God a Geometer? (with Martin Golubitsky). He contributed to a wide range of newspapers and
magazines, and writes the "Mathematical Recreations" column of Scientific American.

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