The Mathematical Experience,9780395929681

The Mathematical Experience

by
Edition: Reprint
ISBN13: 9780395929681
ISBN10: 0395929687
Format: Paperback
Pub. Date: 1999-01-14
Publisher(s): Lightning Source Inc
List Price: $26.70

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Summary

This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

Author Biography

Philip J. Davis is a professor of applied mathematics at Brown University. Reuben Hersh is a professor of mathematics at the University of New Mexico in Albuquerque.

Table of Contents

Preface xi(2)
Acknowledgements xiii(4)
Introduction xvii
Overture 1(5)
1. The Mathematical Landscape
6(26)
What is Mathematics?
6(2)
Where is Mathematics?
8(1)
The Mathematical Community
9(4)
The Tools of the Trade
13(4)
How Much Mathematics is Now Known?
17(3)
Ulam's Dilemma
20(4)
How Much Mathematics Can There Be?
24(2)
Appendix A -- Brief Chronological Table to 1910
26(3)
Appendix B -- The Classification of Mathematics, 1868 and 1979 Compared
29(3)
2. Varieties of Mathematical Experience
32(36)
The Current Individual and Collective Consciousness
32(2)
The Ideal Mathematician
34(10)
A Physicist Looks at Mathematics
44(8)
I. R. Shafarevitch and the New Neoplatonism
52(3)
Unorthodoxies
55(5)
The Individual and the Culture
60(8)
3. Outer Issues
68(54)
Why Mathematics Works: A Conventionalist Answer
68(9)
Mathematical Models
77(2)
Utility
79(10)
1. Varieties of Mathematical Uses
79(1)
2. On the Utility of Mathematics to Mathematics
80(3)
3. On the Utility of Mathematics to Other Scientific or Technological Fields
83(2)
4. Pure vs. Applied Mathematics
85(2)
5. From Hardyism to Mathematical Maoism
87(2)
Underneath the Fig Leaf
89(24)
1. Mathematics in the Marketplace
89(4)
2. Mathematics and War
93(3)
3. Number Mysticism
96(4)
4. Hermetic Geometry
100(1)
5. Astrology
101(7)
6. Religion
108(5)
Abstraction and Scholastic Theology
113(9)
4. Inner Issues
122(81)
Symbols
122(4)
Abstraction
126(8)
Generalization
134(2)
Formalization
136(4)
Mathematical Objects and Structures; Existence
140(7)
Proof
147(5)
Infinity, or the Miraculous Jar of Mathematics
152(6)
The Stretched String
158(5)
The Coin of Tyche
163(5)
The Aesthetic Component
168(4)
Pattern, Order, and Chaos
172(8)
Algorithmic vs. Dialectic Mathematics
180(7)
The Drive to Generality and Abstraction The Chinese Remainder Theorem: A Case Study
187(9)
Mathematics as Enigma
196(2)
Unity within Diversity
198(5)
5. Selected Topics in Mathematics
203(69)
Group Theory and the Classification of Finite Simple Groups
203(6)
The Prime Number Theorem
209(8)
Non-Euclidean Geometry
217(6)
Non-Cantorian Set Theory
223(14)
Appendix A
237(1)
Nonstandard Analysis
237(18)
Fourier Analysis
255(17)
6. Teaching and Learning
272(46)
Confessions of a Prep School Math Teacher
272(2)
The Classic Classroom Crisis of Understanding and Pedagogy
274(11)
Polya's Craft of Discovery
285(6)
The Creation of New Mathematics: An Application of the Lakatos Heuristic
291(7)
Comparative Aesthetics
298(3)
Nonanalytic Aspects of Mathematics
301(17)
7. From Certainty to Fallibility
318(45)
Platonism, Formalism, Constructivism
318(3)
The Philosophical Plight of the Working Mathematician
321(1)
The Euclid Myth
322(8)
Foundations, Found and Lost
330(9)
The Formalist Philosophy of Mathematics
339(6)
Lakatos and the Philosophy of Dubitability
345(18)
8. Mathematical Reality
363(49)
The Riemann Hypothesis
363(6)
Pie and Pie
369(6)
Mathematical Models, Computers, and Platonism
375(5)
Why Should I Believe a Computer?
380(7)
Classification of Finite Simple Groups
387(4)
Intuition
391(9)
Four-Dimensional Intuition
400(6)
True Facts About Imaginary Objects
406(6)
Glossary 412(5)
Bibliography 417(18)
Index 435

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