M. Sc. Mathematics


  • Knowledge skill: Get advanced knowledge of principles, methods and clear perception of innumerous power of mathematical ideas and
  • Critical Thinking: Inculcate critical thinking to carry out scientific investigation objectively without being biased with preconceived
  • Analytical & Logical Reasoning: Equip statements with skills to analyse problems, formulate hypotheses, evaluate and validate results and draw reasonable conclusions
  • Scientific Communication Skills: Imbibe effective scientific or technical communication skill.
  • Professional & Ethical Skills: Continue to acquire relevant knowledge and skills appropriate to professional activities and demonstrate high standards when dealing with ethical issues in Mathematical
  • Research Skills: Prepare students for pursuing research or careers in industry in concerned subject and allied
  • Enlightened Citizenship: Create awareness to become an enlightened citizen with commitment to deliver one’s responsibilities within the scope of bestowed rights and privileges.
  • Lifelong Learning: Inculcate the habit of self-learning throughout life, through self-paced and self-directed learning aimed at personal development, and adapting to changing academic demands of work place through knowledge/ skill development/



  • Strong Foundation in Knowledge: Have strong foundation in core areas of Mathematics, and able to communicate and apply this knowledge in all the fields of learning including higher research and
  • Abstract Skills: Develop abstract mathematical thinking and thereby enable them to evaluate hypothesis, theories, methods and evidence within their proper
  • Problem Solving: Solve complex problems by critical understanding, analysis and
  • Application & Research Efficiency: Provide a systematic understanding of the concepts and theories of mathematics and their application in the real world, to an advanced level, motivate and prepare students for research studies in Mathematics & related fields and enhance career prospects in a huge array of
  • Lifelong Practical Knowledge: Recognize the need to engage in lifelong learning through continuous education and research leading to higher



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Course Outcomes

After the completion of the course, the students will be able:
1 Abstract Algebra
  • To demonstrate the knowledge of finitely generated abelian groups and fundamental theorem.
  • To apply the concept of group homomorphisms, inner automorphism and fundamental homomorphism theorems.
  • To analyse group action on a set and G-sets to counting.
  • To apply isomorphism theorems and Sylow theorems.
  • To describe the structure and construction of field of quotients of an integral domain.
  • To demonstrate knowledge of polynomial rings, the evaluation homomorphisms and factorization of polynomials over a field.
  • To explain group rings, ring homomorphism, quotient rings, prime and maximal ideals.
2 Linear Algebra
  • To illustrate the concepts of vector spaces, basis and dimension, coordinates and summary of row equivalence through examples.
  • To differentiate different linear transformations, their algebra and representation of transformations by matrices.
  • To apply properties of determinants while solving problems on matrices or linear transformations.
  • To implement the ideas of canonical forms, characteristic values and annihilating polynomials.
  • To develop concepts of triangulation, diagonalization and direct sum decomposition.
3 Basic Topology
  • To analyse the concept of topological spaces, base and subbase.
  • To apply the concept of continuity and quotient spaces on different topology.
  • To explain the concept of local connectedness and path connectedness.
  • To differentiate levels of spaces based on axioms.
4 Real Analysis
  • To explain theorems associated with bounded variation and rectifiable curves.
  • To acquire the idea about Riemann-Stieltjes integral.
  • To explain uniform convergence
  • To describe theorems associated with uniform convergence.
  • To acquire the idea about special functions.
5 Graph Theory
  • To recall basic concepts of graph theory.
  • To draw line graphs and graph products.
  • To discuss connectivity of a graph.
  • To use the application of trees in everyday problems.
  • To solve problems on Eulerian and Hamiltonian graphs.
  • To practice problems of graph colouring using Brook’s theorem and Vizing’s theorem.
  • To discuss about planarity of graphs.
6 Advanced Abstract Algebra
  • To explain field extensions.
  • To construct finite fields.
  • To analyse the concepts of UFD and ED.
  • To acquire knowledge of field automorphisms and isomorphism extension theorem.
  • To describe Galois group and Galois theory.
  • To explain separable extensions and cyclotomic extensions.
7 Advanced Topology
  • To explain Urysohn characterization of normality, Tietze characterization of normality, products and co- products.
  • To analyse embedding lemma, Tychonoff embedding and metrization theorem.
  • To develop idea of convergence and related properties of nets and filters.
  • To describe compactness and variations  of compactness.
8 Numerical analysis with Python 3
  • To implement basics of python for programming.
  • To develop basic programming involving symbolic operations.
  • To apply programming techniques for finding limits and derivatives using Sympy.
  • To interpret the concepts of Gaussian elimination, interpolation, curve fitting and finding roots of equations using python programme.
  • To illustrate the concept of numerical integration using python.
9 Complex Analysis
  • To explain spherical representation of complex plane and elementary properties of analytic functions.
  • To analyse power series representation of analytic functions.
  • To examine the concept of singularities and residues.
  • To describe Cauchy’s theorem and residue theorem.
10 Measure Theory andIntegration
  • To explain Lebesgue measure.
  • To describe theorems associated with Lebesgue measure.
  • To define Lebesgue measurable functions and Lebesgue integration.
  • To explain theorems associated with Lebesgue measurable functions.
  • To describe general measurable space and measurable functions.
  • To acquire knowledge about integration over general measurable space and product measure
11 Advanced Complex Analysis
  • To apply the concept of harmonic and subharmonic functions.
  • To explain Weierstrass’s theorem, Gamma function and Hadamard’s theorem.
  • To examine the idea of Riemann zeta function and normal families.
  • To illustrate Riemann mapping theorem and Weierstrass’s theory.
12 Partial Differential Equations
  • To explain PDEs of first order, second and higher orders.
  • To apply various analytic methods for computing solutions of various PDEs.
  • To determine integral surfaces passing through a curve, characteristic curves of second order PDE and compatible systems.
  • To analyse behavior of solutions of PDEs using technique of separation of variables.
13 Multivariate Calculus and Integral Transforms
  • To explain integral transforms and convolutions.
  • To discuss multivariable differential calculus.
  • To describe sufficient conditions for equality of mixed partial derivatives.
  • To compute extrema of real valued functions of several variables.
  • To explain integration of differential forms.
14 Functional Analysis
  • To acquire the concepts of normed spaces and their properties.
  • To discuss linear operators on finite dimensional spaces and dual space.
  • To illustrate inner product spaces and properties of orthonormal sequences using examples and theorems.
  • To demonstrate different forms of Hahn-Banach Theorems.
15 Optimization Techniques
  • To determine solutions to linear programming problems using simplex method, two-phase method, big-M method revised simplex method or dual simplex method.
  • To apply the cutting plane method and branch and bound method for solving integer programming problems.
  • To analyse the concepts of flow and potential in networks and goal programming.
  • To discuss different methods for solving non-linear programming problems.
16 Spectral Theory
  • To distinguish different forms of convergence of operators and open mapping theorem.
  • To apply the concept of Banach fixed point theorem and properties of resolvent and spectrum.
  • To describe compact linear operators and their properties.
  • To discuss properties of bounded self adjoint linear operators, positive operators and properties of projections.
17 Analytic Number Theory
  • To apply the properties of arithmetical functions for solving problems.
  • To acquire the knowledge about the theory of prime numbers.
  • To utilize the concepts of congruences, Chines remainder theorem and Legendre symbol.
  • To implement Euler’s theorem, Wilson’s theorem and Mobius inversion formula.
18 Differential Geometry
  • To interpret the ideas of graphs and level sets, vector fields, the tangent space and vector field on surfaces and orientation.
  • To summarize the fundamentals of Gauss map, geodesics and parallel transport.
  • To describe the ideas of Weingarten map, curvature of plane curves and line integrals.
  • To discuss curvature of surfaces and parametrized surfaces.
19 Algorithmic Graph Theory
  • To explain basic concepts of graphs and elementary algorithms.
  • To implement the concept of trees, paths and distances using algorithms.
  • To establish the max-flow min-cut algorithm and Mengers theorem for finding connectivity.
  • To examine algorithm for finding maximum matching in bipartite graphs, factorizations and block designs.
20 Combinatorics
  • To solve permutation and combinations problems.
  • To apply pigeon hole principle and Ramsey numbers.
  • To use principles of inclusion and exclusion for solving problems.
  • To compute generating functions and recurrence relations.
21 Dissertation and Viva-voce
  • To deduce their arguments in comprehensible and scholarly manner.
  • To develop the spirit of research in their mind.