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

 
9783031116155: Algebraic Curves and Riemann Surfaces for Undergraduates: The Theory of the Donut
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  • PublisherSpringer
  • Publication date2023
  • ISBN 10 3031116151
  • ISBN 13 9783031116155
  • BindingPaperback
  • Edition number1
  • Number of pages464

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Anil Nerode, Noam Greenberg
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Book Description Paperback. Condition: new. Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9783031116155

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Book Description Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 464 pp. Englisch. Seller Inventory # 9783031116155

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Book Description Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783031116155

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