Introduction to Classical Mathematics I From the Quadratic Reciprocity Law to the Uniformization Theorem
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1991, 1991
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| Edition: | 1st ed. 1991 |
| Series: | Mathematics and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Congruences
- 2. Quadratic forms
- 3. Division of the circle (cyclotomy)
- 4. Theory of surfaces
- 5. Harmonic analysis
- 6. Prime numbers in arithmetic progressions
- 7. Theory of algebraic equations
- 8. The beginnings of complex function theory
- 9. Entire functions
- 10. Riemann surfaces
- 11. Meromorphic differentials on closed Riemann surfaces
- 12. The theorems of Abel and Jacobi
- 13. Elliptic functions
- 14. Riemannian geometry
- 15. On the number of primes less than a given magnitude
- 16. The origins of algebraic number theory
- 17. Field theory
- 18. Dedekind’s theory of ideals
- 19. The ideal class group and the group of units
- 20. The Dedekind ?-function
- 21. Quadratic forms and quadratic fields
- 22. The different and the discriminant
- 23. Theory of algebraic functions of one variable
- 24. The geometry of numbers
- 25. Normal extensions of algebraic number- and function fields
- 26. Entire functions with growth of finite order
- 27. Proof of the prime number theorem
- 28. Combinatorial topology
- 29. The idea of a Riemann surface
- 30. Uniformisation
- Appendix 1. Rings
- A1.1 Basic ring concepts
- A1.2 Euclidean rings
- A1.3 The characteristic of a ring
- A1.4 Modules over euclidean rings
- Al.5 Construction of fields
- A1.6 Polynomials over fields
- Appendix 2. Set theoretic topology
- A2.1 Definition of a topological space
- A2.2 Compact spaces
- Appendix 3. Green’s theorem
- Appendix 4. Euclidean vector and point spaces
- Appendix 5. Projective spaces
- Name index
- General index