A.Y. 2019-20

M. Phil. and Ph. D. Course

 M Phil/ Ph D Course

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

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

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.

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.

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. 

In this course, we study Commutative Algebra from M. F. Atiyah and I. G. Macdonald's Introduction to commutative algebra.

Created as an exercise.

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.

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)