# Master of Arts [MA] (Mathematics)

The course MA Mathematics is divided into 4 semesters i.e., 2 semesters per year. The process of examination is odd-even and twice a year exams are held. There are theoretical as well as practical/internal examinations of the subject. There is separate weightage given to theoretical and internal examinations.

Paper Marks
Theoretical 70%
Internal 30%

The marks of the internal examination are based upon practical files, tests, and assignments. There is also a period of internship or training which certain universities count in their curriculum.

### MA Mathematics: Syllabus

The topics covered in MA Mathematics curriculum are similar in the outlook for all universities. An overview of the syllabus is given below.

Paper Topic Objective
Field Theory Splitting fields, separability, automorphism of field extensions, primitive elements, Galois theory of equations, the solution of equations by radicals The objective here is to teach students the physical theory of field and classical approach to solving equations.
Complex Analysis Branch of logarithms, conformal mappings, homotopy, open mapping theorem, residue, contour integration In this paper, students learn the theory of functions and are trained in modern techniques of solving the problems related to complex numbers.
Measure and Integration Measurable sets, measurable functions, regularity, Borel and Lebesgue Measurability, nonmeasurable sets The objective of this paper is to define the learning in prospects of integrals and measurements of numbers and integrals. Students also learn integrals from various theories and theorems which can be applied to practical fields also.
Topology Boundary and limit points of subsets, basis, and sub-basis of a topology, homeomorphism, product topology, path connected spaces, convergence In this course, students learn the properties of mathematical studies that are preserved through twisting, deformation, and stretchings of an object.
Functional Analysis Normed spaces, Banach spaces, finite-dimensional normed spaces and subspaces, compactness and finite dimensions In this course, students learn the core of vector spaces. The whole idea is to provide them the skill of analyzing.
Commutative Algebra Prime spectrums of rings, Jacobson radical of ring, Prime avoidance lemma, rings of formal power series, restriction and extension of scalars Idea is to promote commutative algebra as a field and provide students with the geometrical and dimensional approach on algebra.
Elective 1 Any foreign Language like German, Spanish, French To provide with inter-disciplinary courses and make students enjoy their learning in a more fun and creative way.