Helmut Koch

Introduction to Classical Mathematics I (eBook, PDF)

From the Quadratic Reciprocity Law to the Uniformization Theorem

• Format: PDF

Produktbeschreibung

Zur Zeit liegt uns keine Inhaltsangabe vor.

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 453
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9789401132183
• Artikelnr.: 44183540

Inhaltsangabe

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.

Rezensionen

` Recommended for all libraries, this single volume may fill many gaps in smaller collections. '
Science & Technology

`The book is well-written, the presentation of the material is clear. ... This very valuable, excellent book is recommended to researchers, students and historians of mathematics interested in the classical development of mathematics. '
Acta Scientiarum Mathematicarum, 56:3-4

` Recommended for all libraries, this single volume may fill many gaps in smaller collections. '
Science & Technology

`The book is well-written, the presentation of the material is clear. ... This very valuable, excellent book is recommended to researchers, students and historians of mathematics interested in the classical development of mathematics. '
Acta Scientiarum Mathematicarum, 56:3-4