Mathematics-- the music of reason /
Guardat en:
| Autor principal: | |
|---|---|
| Format: | Llibre |
| Idioma: | English |
| Publicat: |
Berlin ; :
New York : Springer-Verlag,
1992.
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| Matèries: | |
| Accés en línia: | Table of contents only |
Taula de continguts:
- I. Mathematics and Mathematicians. 1. The Concept of Mathematics. 2. A Mathematician's Life. 3. The Work of Mathematicians and the Mathematical Community. 4. Masters and Schools
- II. The Nature of Mathematical Problems. 1. "Pure" Mathematics and "Applied" Mathematics. 2. Theoretical Physics and Mathematics. 3. Applications of Mathematics in the Classical Era. 4. The Utilitarian Attacks. 5. Fashionable Dogmas. 6. Conclusions
- III. Objects and Methods in Classical Mathematics. 1. The Birth of Pre-Mathematical Ideas. 2. The Idea of Proof. 3. Axioms and Definitions. 4. Geometry, from Euclid to Hilbert. 5. Numbers and Magnitudes. 6. The Idea of Approximation. 7. The Evolution of Algebra. 8. The Method of Coordinates. 9. The Concept of Limit and the Infinitesimal Calculus
- App. 1. Calculation of Ratios in Euclid's Book V
- App. 2. The Axiomatic Theory of Real Numbers
- App. 3. Approximation of the Real Roots of a Polynomial
- App. 4. Arguments by "Exhaustion"
- App. 5. Applications of Elementary Algorithms of the Integral Calculus
- IV. Some Problems of Classical Mathematics. 1. Intractable Problems and Sterile Problems. 2. Prolific Problems
- App. 1. Prime Numbers of the Form 4k-1 or 6k-1
- App. 2. The Decomposition of [actual symbol not reproducible](s) as a Eulerian Product
- App. 3. Lagrange's Method for the Solution of ax[superscript 2] + bxy + cy[superscript 2] = n in Integers
- App. 4. Bernoulli Numbers and the Zeta Function
- V. New Objects and New Methods. 1. New Calculations. 2. The First Structures. 3. The Language of Sets and General Structures. 4. Isomorphisms and Classifications. 5. Mathematics of Our Day. 6. Intuition and Structures
- App. 1 The Resolution of Quartic Equations
- App. 2 Additional Remarks on Groups and on the Resolution of Algebraic Equations
- App. 3 Additional Remarks on Rings and Fields
- App. 4. Examples of Distances
- App. 5. Fourier Series.