Algebraic Curves and Riemann Surfaces for Undergraduates: The Theory of the Donut

Anil Nerode,Noam Greenberg

Format
Paperback
Publisher
Springer International Publishing AG
Country
Switzerland
Published
2 December 2022
Pages
418
ISBN
9783031116155

Algebraic Curves and Riemann Surfaces for Undergraduates: The Theory of the Donut

Anil Nerode,Noam Greenberg

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 subject is the theory of elliptic functions and elliptic curves. A complex torus (or donut ) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric chord-and-tangent method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.

This item is not currently in-stock. It can be ordered online and is expected to ship in approx 2 weeks

Our stock data is updated periodically, and availability may change throughout the day for in-demand items. Please call the relevant shop for the most current stock information. Prices are subject to change without notice.

Sign in or become a Readings Member to add this title to a wishlist.