Department of Mathematics at Pune University offers MSC Mathematics course.

MSC Mathematics:
Eligibility :
Candidate must have BSC Mathematics graduation degree or equivalent degree with good academic record .

Course structure:
Semester 1 :

Real Analysis
Advanced Calculus
Linear Algebra
Number Theory
Ordinary Differential Equations

Semester 2 :
General Topology
Differential Geometry
Groups and Rings
Complex Analysis
Partial Differential Equations OR
Object Oriented Programming using C++

MT-501: Real Analysis

1. Metric Spaces, Normed Spaces, Inner Product Spaces:
Definitions and examples, Sequence Spaces, Function Spaces, Dimension.

2. Topology of Metric Spaces:
Open, Closed and Compact Sets, the Heine-Borel and Ascoli-Arzela’ Theorems,
Separability, Banach and Hilbert Spaces.

3. Measure and Integration :
Lebesgue Measure on Euclidean Space, Measurable and Lebesgue Integrable Functions, The
Convergence Theorems, Comparison of Lebesgue Integral with Riemann Integral, General
Measures and the Lebesgue LP-Space.

4. Fourier Analysis in Hilbert Space :
Orthonormal Sequences, Bessel’s Inequality, Parseval’s Theorem, Riesz-Fischer Theorem,
Classical Fourier Analysis.

5. Weierstrass Approximation Theorem, Generalised Stone-Weierstrass Theorem, Baire
Category Theorem and its Applications, Contraction Mapping.

Here is the attachment .


Contact :
Savitribai Phule Pune University
Ganeshkhind, Pune,
Maharashtra 411007
020 2569 6064

Attached Files

M.Sc. Maths Syllabus.pdf (59.0 KB, 69 views)