Hey as per my idea doing MSC f5rom VMOU is good option as it will give you good job opportunity

Eligibility
Candidate should have BSC degree from recognised university

Selection criteria
Admission is done directly on the basis of merit

VMOU MSC syllabus

Direct products of groups (external and internal).
lsomorphism theorems: Conjugacy and the class equation ofa group.
C ommutators. Derived subgroups. Solvable groups. Subnormal series and
Refinement theorem. Composition series and .lordan-l-lolder Theorem.
Euclidean rings : Division in commutative rings. Units. Associates and
Prime elements. Unique factorization domain.
Modules. Submodules. Quotient modules. Direct
homomorphisms._Generation of modules. Cyclic modules.
sums. Module
Linear transformation ot‘ vector spaces. Dual spaces. Dual basis and their
properties. Dual maps.
Basic theory of field extensions. Simple field extension. Algebraic and
Transcendental extensions.
Splitting fields. Normal extension. Separable and lnscparable extensions.
Automorphism of extensions.
Galois thoery : Galois extension and Galois group. Fundamental theorem
of Galois theory. Extensions by radicals and solvability. Insolvability of
the quintic.
Matrices of linear maps ot'eomposite maps and ot‘dual maps.
Rank and Nullity of linear maps and matrices. lnvertible matrices. liiigen
values and Eigen vectors. Change of basis and similar matrices.
Determinants of matrices and their properties. Existence and Uniqueness
of determinants, Characteristic polynomial and Eigen values.
Real Inner product space. Schwartz‘s inequality.
Pythagoras theorem, Gram-Schmidt orthogonalization.
Orthogonality. '
Bessel’s inequality. Parseval‘s identity. Direct Sum. Adjoint ot‘ a linear
map. Self-adjoint linear maps and matrices.
Orthogonal linear transformation and matrices. Principal axis theorem

Algebra and algebras of sets. Algebras generated by a class ofsubsets. Borel sets.
Lebesgue measure of sets of real numbers. Measurability and Measure of a set.
Existence of Non-measurable sets.
Measurable functions. Realization of non-negative measurable function as limit of
an increasing sequence of simple functions. Structure of measurable functions.
Convergence in measure. Egoroft‘s theorem.
Weierstrass‘s theorem on the approximation of continuous function by
polynomials. Lebesgue integral of bounded measurable functions, Lebesgue
theorem on the passage to the limit under the integral sign for bounded measurable
functions. '
Summable functions. Space of square summable functions.
Fourier series and coefficients. Parseval‘s identity, Riesz-Fisher Theorem.
Lp-spaces. Holder-Minkowski inequalities. Completeness of L"-spaces.
Topological spaces. Subspaces. Open sets. Closed sets. Neighbourhood system.
Bases and sub-bases, Continuous mapping and Homeomorphism.
Separation axioms (To. Ti. T3. T3. T4).
Compact and locally compact spaces.
Tychonoffs one point compactification.
Connected and Locally connected spaces.
Product and Quotient spaces.
Nets. Filters

Address:
Vardhaman Mahaveer Open University
Rawatbhata Rd,
Kota,
Rajasthan 324021
Phone: 0744 279 7000

Here I am attaching PDF for VMOU MSC syllabus;

Attached Files

VMOU MSC syllabus.pdf (450.5 KB, 98 views)