Department Of Mathematics/A.Y. 2019-20 #### Number Theory

This is an introductory course on Number Theory at PG Level. #### Complex Analysis

This is a basic course on Complex Analysis designed for students of M.Sc. I, Department of Mathematics, SPPU.  In this course we study mainly Analytic functions, Complex Integration, Singularities, Maximum modulus theorem. Reference books: (i) Functions of one complex variable by J. B, Conway (ii) Complex Variables with Applications by Ponnusamy and Silverman. #### Spectral Graph Theory

One of the aims of this course to study applications of linear algebraic methods in graph theory. Spectral values associated to adjacency operators on graphs will be studied in detail. #### MT 17-Banach Algebra

This is an introduction to Banach Algebra.

Topics to be discussed are Banach Algebra: Definition and examples, Homeomorphism, Isometries, Ideals, Invertibility, Resolvent and Spectrum, Gelfand Theorem for commutative Banach algebra, Semisimple Banach algebra, Spectral Radius formula, Topological divisors of zero, Gelfand-Naimark theorem, C*-algebra. #### Algebraic Geometry

Groebner bases form a basis of wide range of  computational techniques in Commutative Algebra and Algebraic Geometry. In the second part of the curse we study Invariant Theory of Finite Groups and its connections to Geometry. #### Commutative Algebra

In this course, we study Commutative Algebra from M. F. Atiyah and I. G. Macdonald's Introduction to commutative algebra. #### MT-201 Functional Analysis

This is an introduction to Functional Analysis.

Topics to be discussed are Normed linear spaces and continuity of linear maps, linear functionals and Hahn Banach theorems, Banach spaces, Uniform boundedness principle, Closed graph and Open mapping theorems, Bounded Inverse theorem, Hilbert spaces, Orthonormal sets, projections and Riesz representation theorem.