Descrizione

Gutes Exemplar; (der OUmschlag fehlt); Einband stw. minimal berieben; Schnitt stw. gering fleckig. - Englisch. - INHALT : 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? ----- Appendix A-Brief Chronological Table to 1910 ----- Appendix B-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 Neo-platonism ----- Unorthodoxies ----- The Individual and the Culture ----- Outer Issues ----- Why Mathematics Works: A Conventionalist Answer ----- Mathematical Models Utility ----- 1. Varieties of Mathematical Uses ----- 2. On the Utility of Mathematics to Mathematics ----- 3. On the Utility of Mathematics to Other Scientific or Technological Fields ----- 4. Pure vs. Applied Mathematics ----- 5. From Hardyism to Mathematical Maoism Underneath the Fig Leaf ----- 1. Mathematics in the Marketplace ----- 2. Mathematics and War ----- 3. Number Mysticism ----- 4. Hermetic Geometry ----- 5. Astrology ----- 6. 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 Dubita-bility ----- Mathematical Reality The Riemann Hypothesis ----- 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. ISBN 376433018X