Algebraic Curves and Riemann Surfaces for Undergraduates : The Theory of the Donut
1st ed. 2022
Book Details
Format
Paperback / Softback
ISBN-10
3031116151
ISBN-13
9783031116155
Edition
1st ed. 2022
Publisher
Springer International Publishing AG
Imprint
Springer International Publishing AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jan 17th, 2023
Print length
450 Pages
Weight
778 grams
Dimensions
15.50 x 23.50 x 2.50 cms
Product Classification:
Calculus & mathematical analysisComplex analysis, complex variablesAlgebraic geometry
Ksh 7,200.00
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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.
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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