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＜電子ブック＞
Introduction to Classical Mathematics I : From the Quadratic Reciprocity Law to the Uniformization Theorem / by Helmut Koch
(Mathematics and Its Applications ; 70)

版	1st ed. 1991.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1991
大きさ	XVII, 453 p : online resource
著者標目	*Koch, Helmut author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Mathematics LCSH:History FREE:Number Theory FREE:History of Mathematical Sciences FREE:Mathematics
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-94-011-3218-3

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