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...

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Bibliographic Details
Main Authors: Nerode, Anil, Greenberg, Noam (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2022, 2022
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