Algebraic Curves and Riemann Surfaces for Undergraduates is popular PDF and ePub book, written by Anil Nerode in 2023-01-16, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Algebraic Curves and Riemann Surfaces for Undergraduates can be Read Online from any device for your convenience.
Algebraic Curves and Riemann Surfaces for Undergraduates Book PDF Summary
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.
Detail Book of Algebraic Curves and Riemann Surfaces for Undergraduates PDF
- Author : Anil Nerode
- Release : 16 January 2023
- Publisher : Springer Nature
- ISBN : 9783031116162
- Genre : Mathematics
- Total Page : 453 pages
- Language : English
- PDF File Size : 8,5 Mb
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