The Nature and Growth of Modern Mathematics

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Princeton University Press, 1982 - Mathematics - 758 pages
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The book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story - ultimately linked to modern digital computers - the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; erogodic theorems; epsilon-delta arithmetization; integral equations.
  

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Contents

From Babylonian Beginnings to Digital Computers
1
Mathematical Method and Main Streams Are Launched
18
Mathematical Reasoning from Eudoxus to Lobachevsky
41
Algebra from Hypatia to Hamilton
61
Equations Human and Inhuman
83
A Universal Language
100
Forefathers of Modern Mathematics and Their Legacy
134
A Calculus for Heaven and Earth
167
A Special Group and Its Application
434
Geometry for UniverseBuilders
449
PostRelativity Geometry
478
East Meets West in the Higher Arithmetic
497
The Reformation of Analysis
528
Royal Roads to Functional Analysis
550
Infinite Hierarchy
577
Angelic Geometry
598

Determinism and Its Creators
204
The Elements of Strategy in War and Peace
246
Probabilistic Models Great Expectations and Randomized Strategies
258
General Games and Statistical Decision Theory
275
From Dice to Quantum Theory and Quality Control
291
Realm of Random Variables
316
Demons Energy Maxwell and Gibbs
344
Sweet Manuscript of Youth
368
The Unification of Geometry
401
The Leonardos of Modern Mathematics
625
TwentiethCentury VistasAnalysis
639
TwentiethCentury VistasAlgebra
656
TwentiethCentury VistasLogic and Foundations
684
Retrospect and Prospect
698
Suggestions for Further Reading
719
Index
723
Copyright

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