#### Fractional Calculus and Fractional Differential Equations

** M Phil/ Ph D Course**

This course gives introduction to **Fractional Calculus and Fractional Differential Equations.**

#### 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

#### 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.

#### MT-403: Software Engineering

Each student wishes to do this course should complete the online course from the link below.

**https://in.udacity.com/course/writing-readmes--ud777**

Holidays for University Department Jan-2020 to Dec-2020 (Click Here)