MSc Mathematics is a two-year postgraduate program which is being divided into four semesters. This degree has been awarded to those who complete the program. In this degree, candidates get a deeper knowledge of advanced mathematics through a vast preference of subjects such as geometry, calculus, algebra, number theory, dynamical systems, differential equations, etc. The students become more skilled and specialized in a particular subject after the master degree program. In this course, students learn to collect big data and analyse them with the help of different tools and methods.
Courses in Mathematics;-
MSc Mathematics have two types of courses. One is the postgraduate course in Mathematics and another one is combined with the Computer Science Applications. In the MSc Mathematics, students get a deep insight into pure and applied mathematics. Students learn about the problem-solving skills and reasoning skills which helps them to solve them the real-life problems. In other types of postgraduate, the students learn about modelling and solving real-world problems with the help of computer applications. Computational Mathematics is one of the prominent subjects through which candidate learn to solve mathematical problems with the help of computer simulation which is opposite to the analytic methods of applied mathematics.
The minimum eligibility criteria for the M.Sc Mathematics course is student should have passed B.Sc. (Mathematics) or B.Sc. (Mathematics with Computer Science Applications) or any other relevant degree with Mathematics and English as main subjects with a minimum of 60% marks. The minimum percentage varies from University to University. Some institutes also consider the B.Tech and B.E candidates. Few universities take admission in the postgraduate course through the merit basis and some institutes through the merit basis.
Course Duration and Fees;-
MSc Mathematics is a postgraduate which is being offered by various colleges and institutes. It is a two-year program and several institutes offer distance mode of learning. The duration of the distance program is a minimum of 2 years and a maximum of 4 years. Syllabus
The coursework of the MSc Mathematics includes assignments and projects which helps the students in getting the deep knowledge of the subjects which they can implement in real-life problems. The degree courses consist of main subjects which are compulsory to study and there are some elective subjects also. The final marks of the students depend on the internal and external assessment which includes the presentations, tests, assignments, thesis, and attendance.
The subjects of the MSc Mathematics which are being offered in almost all the institutions or colleges are:
1. Advanced Abstract Algebra Field Theory, Galois Theory, Isomorphism Theorems, Refinement Theorem, Extension Fields, Algebraic and Transcendental Extension, Refinement Theorem and Jordan Holder Theorem for infinite groups.
2. Real Analysis Algebras and sets of algebras, Summable functions, Borel Sets, Realization of nonnegative measurable functions, Structure of measurable functions, Weiersttrass’s theorem on the approximation of a continuous function by a polynomial.
3. Advanced Differential Equations Non-Linear ordinary differential equations of particular forms, Riccati’s equation, Total differential equation, Partial differential equation of first order, Lagrange’s linear equation, Linear Partial differential equations with the constant equation, Linear homogeneous boundary value problems
4. Differential Geometry Theory of curves, tangent, Osculating plane and Osculating sphere, Ruled Surface, Metric of a surface, Orthogonal trajectories, Normal curvature, Meunier’s Theorem, Gaussian curvature
5. Dynamics of a Rigid Body D ’Alembert’s Principle, Principle of Conservation of Energy, Centre of percussion, Motion of a rigid body in two dimensions, Lagrange’s Equations for holonomic dynamical system, Hamilton’s equations of motion
6. Linear Algebra Linear Transformations, Orthogonal and Unitary Transformations, Linear functionals – Dual space and Bidual space, Matrix, Eigen-values, eigen vectors, Annihilators, Determinants, Cayley Hamilton theorem and Diagonalization, Canonical and Bilinear form, Principal axis theorem, Orthogonality
7. Topology Topological Spaces, Adhere Points and derived sets, Closure of a set, subspace, Continuity and Homeomorphism, Separation axioms, Product space, General Product Space, Harsdorf Space, Compact and Locally Compact Spaces
8. Special Functions Calculus of Variations, Euler’s Equation, Functionals, Gauss Hypergeometric Functions, Integration Representational, Linear Transformation Formulas, Contiguous Function Relation, Kummer’s Confluent Hypergeometric Functions and its properties, Kummer’s First Transformation, Legendre’s Polynomial and functions, Christoffel’s Summation Formula, Bessel Function, Hermite Polynomial, Laguerre polynomials – Recurrence Relations
9. Differential Geometry and Tensors Geodesics, Gauss’s Formula, Geodesic Curvature and Torsion, Gauss-Bonnet Theorem, Weingarten Equations, Mainardi – Codazzi Equations, Bonnet’s Theorem on parallel surface, Tensor Analysis, Kronecker Delta, Contravariant and Covariant Tensors, Quotient Law of Tensor, Riemannian Space, Metric Tensor, Permutations Symbols and Permutations Tensors, Riemann Christoffel Tensor, Bianchi’s Identity, Schur’s Theorem
10. Hydrodynamics Kinematics of an ideal fluid, Euler’s Hydrodynamics Equations, Irrotational motion in two dimensions, Cauchy’s Integral, Kelvin’s minimum energy theorem, Blasius Theorem
The post-graduate in Mathematics have a deep knowledge of pure and applied mathematics subjects. They have developed problem-solving and reasoning skills over time so these things help in considerably improve the chances of being hired in the research field. Students can get a chance in the financial sector and the government sector. They will be the best for the work profile of analytic science consultant, actuarial analyst, database manager, external auditor, data analyst, customer coordinator, credit analyst, and quantitative risk analyst. Students can choose the teaching field and become a professor in government and private colleges. Secondary school teacher, technical subject matter experts, academic coordinator, middle school teachers, and science teachers are also earning good amount after their post-graduate degree.
After completing a postgraduate degree in mathematics, students can opt for higher studies. They can go in the research field and pursue M. Phil. or PhD in mathematics. There are a large number of colleges and institute which offers this course. The eligibility criteria for admission in this course, students have to qualify for the Council of Scientific & Industrial Research – National Eligibility Test (CSIR – NET), University Grant Commission – National Eligibility Test (UGC – NET). Some college considers Gate Aptitude Test Engineering (GATE) and National Board for Higher Mathematics (NBHM).