Algebraic Curves and Riemann Surfaces for Undergraduates The Theory of the Donut
The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subjec...
Main Authors: | , |
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Format: | eBook |
Language: | English |
Published: |
Cham
Springer International Publishing
2022, 2022
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Edition: | 1st ed. 2022 |
Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 1 Introduction
- Part I Algebraic curves
- 2 Algebra
- 3 Affine space
- 4 Projective space
- 5 Tangents
- 6 Bézout’s theorem
- 7 The elliptic group
- Part II Riemann Surfaces
- 8 Quasi-Euclidean spaces
- 9 Connectedness, smooth and simple
- 10 Path integrals
- 11 Complex differentiation
- 12 Riemann surfaces
- Part III Curves and surfaces
- 13 Curves are surfaces
- 14 Elliptic functions and the isomorphism theorem
- 15 Puiseux theory
- 16 A brief history of elliptic functions