Mathematical Experience

ISBN-10: 0395929687
ISBN-13: 9780395929681
Edition: 1998
List price: $24.95 Buy it from $3.00
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Description: This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

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Book details

List price: $24.95
Copyright year: 1998
Publisher: Houghton Mifflin Harcourt Publishing Company
Publication date: 1/14/1999
Binding: Paperback
Pages: 464
Size: 6.25" wide x 9.50" long x 1.25" tall
Weight: 1.782
Language: English

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

Phillip J. Davis is professor of applied mathematics at Brown University.

Preface
Acknowledgements
Introduction
Overture
The Mathematical Landscape
What is Mathematics?
Where is Mathematics?
The Mathematical Community
The Tools of the Trade
How Much Mathematics is Now Known?
Ulam's Dilemma
How Much Mathematics Can There Be?
Brief Chronological Table to 1910
The Classification of Mathematics. 1868 and 1979 Compared
Varieties of Mathematical Experience
The Current Individual and Collective Consciousness
The Ideal Mathematician
A Physicist Looks at Mathematics
I. R. Shafarevitch and the New Neoplatonism
Unorthodoxies
The Individual and the Culture
Outer Issues
Why Mathematics Works: A Conventionalist Answer
Mathematical Models
Utility
Varieties of Mathematical Uses
On the Utility of Mathematics to Mathematics
On the Utility of Mathematics to Other Scientific or Technological Fields
Pure vs. Applied Mathematics
From Hardyism to Mathematical Maoism
Underneath the Fig Leaf
Mathematics in the Marketplace
Mathematics and War
Number Mysticism
Hermetic Geometry
Astrology
Religion
Abstraction and Scholastic Theology
Inner Issues
Symbols
Abstraction
Generalization
Formalization
Mathematical Objects and Structures; Existence
Proof
Infinity, or the Miraculous Jar of Mathematics
The Stretched String
The Coin of Tyche
The Aesthetic Component
Pattern, Order, and Chaos
Algorithmic vs. Dialectic Mathematics
The Drive to Generality and Abstraction The Chinese Remainder Theorem: A Case Study
Mathematics as Enigma
Unity within Diversity
Selected Topics in Mathematics
Group Theory and the Classification of Finite Simple Groups
The Prime Number Theorem
Non-Euclidean Geometry
Non-Cantorian Set Theory
Appendix A
Nonstandard Analysis
Fourier Analysis
Teaching and Learning
Confessions of a Prep School Math Teacher
The Classic Classroom Crisis of Understanding and Pedagogy
Polya's Craft of Discovery
The Creation of New Mathematics: An Application of the Lakatos Heuristic
Comparative Aesthetics
Nonanalytic Aspects of Mathematics
From Certainty to Fallibility
Platonism, Formalism, Constructivism
The Philosophical Plight of the Working Mathematician
The Euclid Myth
Foundations, Found and Lost
The Formalist Philosophy of Mathematics
Lakatos and the Philosophy of Dubitability
Mathematical Reality
The Riemann Hypothesis
[pi] and [characters not reproducible]
Mathematical Models, Computers, and Platonism
Why Should I Believe a Computer?
Classification of Finite Simple Groups
Intuition
Four-Dimensional Intuition
True Facts About Imaginary Objects
Glossary
Bibliography
Index

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