# An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves

IIT Madras, , Prof. T.E. Venkata Balaji

Updated On 02 Feb, 19

IIT Madras, , Prof. T.E. Venkata Balaji

Updated On 02 Feb, 19

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An Introduction to Riemann Surfaces and Algebraic Curves Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit httpwww.nptel.iitm.ac.insyllabus111106044Goals of the LectureTo develop a suitable definition of a structure of a RiemannSurface on a 2-dimensional surface that will allow us to carry outComplex Analysis (i.e., study of holomorphic (or) analytic functions)on the given surface.KeywordsComplex plane, open set, analytic (or) holomorphic function, Cauchy-Riemannequations, complex differentiable, convergent power series, Taylor expansion,Taylor coefficients, open map, biholomorphic map (or) holomorphic isomorphism,homeomorphism (or) topological isomorphism, complex coordinate chart,compatibility of charts, transition functions, Riemann surface structure

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.