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

Author:   Anil Nerode ,  Noam Greenberg
Publisher:   Springer International Publishing AG
Edition:   1st ed. 2022
ISBN:  

9783031116155


Pages:   450
Publication Date:   17 January 2023
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Algebraic Curves and Riemann Surfaces for Undergraduates: The Theory of the Donut


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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.

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Author:   Anil Nerode ,  Noam Greenberg
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2022
Weight:   0.837kg
ISBN:  

9783031116155


ISBN 10:   3031116151
Pages:   450
Publication Date:   17 January 2023
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

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Anil Nerode, Distinguished Professor of Mathematics at Cornell University, has, over a period of 66 years, made significant contributions to mathematical logic, automata theory, computability theory, and hybrid systems engineering, publishing around 100 papers and 5 books. He first learned elliptic function theory as a graduate student from André Weil in the early 1950s and has taught it over the years, resulting in the present book. ​Noam Greenberg is Professor of Mathematics at Victoria University of Wellington, New Zealand. His main research interests are computability theory, algorithmic randomness, reverse mathematics, higher recursion theory, computable model theory, and set theory. He was a Royal Society of New Zealand Rutherford Discovery Fellow and is a Fellow of the Royal Society of New Zealand.

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