Goldstein, Catherine
The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae
Part I. A Book’s History
1. A Book in Search of a Discipline (1801–1860)
Catherine Goldstein, Norbert Schappacher
2. Several Disciplines and a Book (1860–1901)
Catherine Goldstein, Norbert Schappacher
Part II. Algebraic Equations, Quadratic Forms, Higher Congruences: Key Mathematical Techniques of the
3. The
Olaf Neumann
4. Composition of Binary Quadratic Forms and the Foundations of Mathematics
Harold M. Edwards
5. Composition of Quadratic Forms: An Algebraic Perspective
Della D. Fenster, Joachim Schwermer
6. The Unpublished Section Eight: On the Way to Function Fields over a Finite Field
Günther Frei
Part III. The German Reception of the
7. A Network of Scientific Philanthropy: Humboldt’s Relations with Number Theorists
Herbert Pieper
8. ‘O T?ò?’ A???µ??í???: The Rise of Pure Mathematics as Arithmetic with Gauss
José Ferreirós
Part IV. Complex Numbers and Complex Functions in Arithmetic
9. From Reciprocity Laws to Ideal Numbers: An (Un)Known Manuscript by E.E. Kummer
Reinhard Bölling
10. Elliptic Functions and Arithmetic
Christian Houzel
Part V. Numbers as Model Objects of Mathematics
11. The Concept of Number from Gauss to Kronecker
Jacqueline Boniface
12. On Arithmetization
Birgit Petri, Norbert Schappacher
Part VI. Number Theory and the
13. The Hermitian Form of Reading the
Catherine Goldstein
14. Number Theory at the
Anne-Marie Décaillot
Part VII. Spotlighting Some Later Reactions
15. An Overview on Italian Arithmetic after the
Aldo Brigaglia
16. Zolotarev’s Theory of Algebraic Numbers
Paola Piazza
17. Gauss Goes West: The Reception of the
Della Fenster
Part VIII. Gauss’s Theorems in the Long Run: Three Case Studies
18. Reduction Theory of Quadratic Forms: Towards
Joachim Schwermer
19. Gauss Sums
Samuel James Patterson
20. The Development of the Principal Genus Theorem
Franz Lemmermeyer
DRM-restrictions
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Avainsanat: MATHEMATICS / General MAT000000
- Tekijä(t)
- Goldstein, Catherine
- Schappacher, Norbert
- Schwermer, Joachim
- Julkaisija
- Springer
- Julkaisuvuosi
- 2007
- Kieli
- en
- Painos
- 1
- Kategoria
- Eksaktit luonnontieteet
- Tiedostomuoto
- E-kirja
- eISBN (PDF)
- 9783540347200