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Introduction to Classical Mathematics I

From the Quadratic Reciprocity Law to the Uniformization Theorem

  • Book
  • © 1991

Overview

Authors:
  1. Helmut Koch

    1. Karl-Weierstrass-Institut für Mathematik, Berlin, Germany

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Part of the book series: Mathematics and Its Applications (MAIA, volume 70)

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Table of contents (30 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Congruences

    • Helmut Koch
    Pages 1-10

  3. Quadratic forms

    • Helmut Koch
    Pages 11-22

  4. Division of the circle (Cyclotomy)

    • Helmut Koch
    Pages 23-34

  5. Theory of surfaces

    • Helmut Koch
    Pages 35-43

  6. Harmonic analysis

    • Helmut Koch
    Pages 44-58

  7. Prime numbers in arithmetic progressions

    • Helmut Koch
    Pages 59-66

  8. Theory of algebraic equations

    • Helmut Koch
    Pages 67-89

  9. The beginnings of complex function theory

    • Helmut Koch
    Pages 90-107

  10. Entire functions

    • Helmut Koch
    Pages 108-117

  11. Riemann surfaces

    • Helmut Koch
    Pages 118-136

  12. Meromorphic differentials and functions on closed Riemann surfaces

    • Helmut Koch
    Pages 137-153

  13. The theorems of Abel and Jacobi

    • Helmut Koch
    Pages 154-164

  14. Elliptic functions

    • Helmut Koch
    Pages 165-181

  15. Riemannian geometry

    • Helmut Koch
    Pages 182-209

  16. On the number of primes less than a given magnitude

    • Helmut Koch
    Pages 210-218

  17. The origins of algebraic number theory

    • Helmut Koch
    Pages 219-222

  18. Field theory

    • Helmut Koch
    Pages 223-231

  19. Dedekind’s theory of ideals

    • Helmut Koch
    Pages 232-250

  20. The ideal class group and the group of units

    • Helmut Koch
    Pages 251-261
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Reviews

` 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

Authors and Affiliations

  • Karl-Weierstrass-Institut für Mathematik, Berlin, Germany

    Helmut Koch

Bibliographic Information

  • Book Title: Introduction to Classical Mathematics I

  • Book Subtitle: From the Quadratic Reciprocity Law to the Uniformization Theorem

  • Authors: Helmut Koch

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-011-3218-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Kluwer Academic Publishers 1991

  • Hardcover ISBN: 978-0-7923-1231-4Published: 31 May 1991

  • Softcover ISBN: 978-0-7923-1238-3Published: 31 May 1991

  • eBook ISBN: 978-94-011-3218-3Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XVII, 453

  • Additional Information: Originally published in German

  • Topics: Number Theory, History of Mathematical Sciences, Mathematics, general

  • Industry Sectors: IT & Software

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