MSC Mathematics Syllabus Kerala University

This year I have completed B.SC Mathematics Course. After It I will take admission at Kerala University for Master Degree Program. So I need syllabus of M.Sc Mathematics Course offering by Kerala University. So will you please provide detailed syllabus to see once before taking admission?

[Rajkumar Agarwal]

As you want to download syllabus of M.Sc Mathematics Course offering by Kerala University, so here I am giving complete syllabus:

Kerala University M.SC Mathematics Syllabus

SEM I
MM 211 Linear Algebra
MM 212 Real Analysis - I
MM 213 Diff. Equation
MM 214 Topology - I

SEM II
MM 221 Algebra
MM 222 Real Analysis-II
MM 223 Topology-II
MM 224 Computer Programm- ing in C++

SEM III
MM 231 Complex Analysis - I
MM 232 Functional Analysis -I
MM 233 Elective - I
MM 234 Elective – II

SEM IV
MM 241 Complex Analysis - II
MM 242 Functional Analysis-II
MM 243 Elective - III
MM 244 Elective - IV
MM 245 Dissertation / Project
Comprehensive Viva

MM 211 LINEAR ALGEBRA
UNIT 1
Vector spaces: Definition, Examples and properties, Subspaces, Sum and Direct sum of subspaces, Span
and linear independence of vectors, Definition of finite dimensional vector spaces, Bases: Definition and
existence, Dimension Theorems.
[Chapters 1,2 of Text]
UNIT II
Linear maps, their null spaces and ranges, Operations on linear maps in the set of all linear maps from one
space to another , Rank-Nullity Theorem , Matrix of linear map, its invetibilty.
[Chapter 3 of Text]
UNIT III
Invariant subspaces, Definition of eigen values and vectors, Polynomials of operators, Upper triangular
matrices of linear operators, Equivalent condition for a set of vectors to give an upper triangular operator,
Diagonal matrices, Invariant subspaces on real vector spaces.
[Chapter 5 of Text]
UNIT IV
Concept of generalized eigen vectors, Nilpotent operators characteristic polynomial of an operator,
Cayley-Hamilton theorem, Condition for an operator to have a basis consisting of generalized eigen
vectors, Minimal polynomial. Jordan form of an operator (General case of Cayley-Hamilton Theorem
may be briefly sketched from the reference text)
[Chapter 8 of Text]
UNIT V
Change of basis, trace of an operator, Showing that trace of an operator is equal to the trace if its matrix,
determinant of an operator, invertibilty of an operator and its determinant, relation between characteristic
polynomial and determinant, determinant of matrices of an operator w.r.t. two base are the same.
Determinant of a matrix (The section volumes may be omitted)

Kerala University M.SC Mathematics Syllabus