The Mathematical Experience. With an Introduction by Gian-Carlo Rota.

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xix, 439 p., Ill. Mit Zeitungsausschnitten. Der Einband ist leicht bestoßen, ansonsten ein sehr gutes und sauberes Exemplar ohne Anstreichungen. With newspaper clippings. The binding is slightly bumped, otherwise a very good and clean copy without markings. - Contents -- Preface -- Acknowledgements -- Introduction -- Overture -- 1. 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 Mathe-matics. 1868 and 1979 Compared -- 2. 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 -- 3. 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 -- 4. Inner Issues -- Symbols -- Abstraction -- Generalization -- Formalization -- Mathematical Objects and Structures; Exis- -- tence -- 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 -- 5. 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 -- 6. Teaching and Learning -- Confessions of a Prep School Math -- Teacher -- The Classic Classroom Crisis of Understand-ing and Pedagogy -- Pólya's Craft of Discovery -- The Creation of New Mathematics: An Application of the Lakatos Heuristic -- Comparative Aesthetics -- Nonanalytic Aspects of Mathematics -- 7. 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 Mathe-matics -- Lakatos and the Philosophy of Dubita-bility -- 8. Mathematical Reality -- The Riemann Hypothesis ? and -- 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 9780140134742 Sprache: Englisch Gewicht in Gramm: 800. Bestandsnummer des Verkäufers 1253791

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