000			02011nam a2200301Ia 4500
003			OSt
005			20240201181209.0
008			231229s9999 xx 000 0 und d
020			_a9783031116155
040			_cIISER BPR
041			_aEng
082			_a516.352 _bNER _223rd
100			_aNerode, Anil
245		0	_aAlgebraic curves and riemann surfaces for undergraduates : _bThe theory of the donut
250			_a1st ed.
260			_aSwitzerland: _bSpringer Nature, _cc2022
300			_axiv, 450p. : _bill (pbk). ; _c22cm.
520			_aThe 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. Includes bibliography and index.
650			_aMathematics
650			_aGeometry
650			_aAlgebric Curves
650			_aRiemann Surfaces
700			_aGreenberg, Noam
942			_cBK _2ddc
942			_2ddc
947			_a4823.552331
948			_a0.22
999			_c3203 _d3203