Algebraic Curves and Riemann Surfaces for Undergraduates: The Theory of the Donut by Anil Nerode, Noam Greenberg

Author(s): Anil Nerode, Noam Greenberg

Publisher: Springer, Year: 2023

ISBN: 3031116151,9783031116155,9783031116162

Size:9 MB (8937235 bytes)

Extension:pdf

"Algebraic Curves and Riemann Surfaces for Undergraduates: The Theory of the Donut" is a book co-authored by Anil Nerode and Noam Greenberg, which provides an accessible introduction to the theory of algebraic curves and Riemann surfaces, with a focus on undergraduate students. The book combines geometric and algebraic approaches to explore the properties and applications of these mathematical objects.

The book begins with an introduction to the basic concepts of complex analysis, including complex numbers, functions, and integrals, and then progresses to the study of algebraic curves, which are geometric objects defined by polynomial equations. The authors cover topics such as the topology and geometry of curves, the Riemann-Roch theorem, and the classification of algebraic curves. They also introduce Riemann surfaces, which are two-dimensional manifolds that can be viewed as the "natural" setting for studying algebraic curves.

The book emphasizes the intuitive geometric aspects of algebraic curves and Riemann surfaces, while also providing a solid foundation in the algebraic theory underlying these objects. It includes numerous examples, exercises, and illustrations to help readers develop their understanding of the material. The book also includes historical notes, which highlight the contributions of mathematicians to the development of the theory of algebraic curves and Riemann surfaces.

"Algebraic Curves and Riemann Surfaces for Undergraduates: The Theory of the Donut" is a valuable resource for undergraduate students interested in complex analysis, algebraic geometry, and related fields. It provides a gentle introduction to the theory of algebraic curves and Riemann surfaces, making it accessible to students with a basic background in complex analysis and algebra, and it offers insights into the beauty and richness of these mathematical objects, which have applications in various areas of mathematics, physics, and engineering.