## MSc in Applied Mathematics

The Department of Mathematics offers a 2-year M. Sc. in Applied Mathematics as well as a PhD in Mathematics and Applied Mathematics. In M.Sc. Applied Mathematics students have to study core topics in Algebra and Analysis. We reinforce them in applications by concentrating on Analytical and Computational methods for differential and Integral equations, Numerical Analysis, Graph Theory and Networks, Optimization, Probability and Statistics, Topology, Computational Fluid Dynamics, Financial Derivatives and Modelling. The Department has its own state of the art Computational Laboratory that ensures high quality of research work. The laboratory based courses train students in application oriented practical subjects. Students are exposed to advanced research topics through electives and a mandatory one year project. Regular visits by academicians from India and abroad to the Department ensures a collaborative research environment.

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**Minimum Eligibility**

12 years of schooling + a 3-year Bachelor’s degree (with Mathematics as a subject for at least two years) from an institution recognized by the government of any of the SAARC countries, with a minimum of 55% marks in aggregate or an equivalent grade. Candidates who have a 4-year Bachelor’s degree or 2-year Bachelor’s degree and have cleared the first year of the Master’s programme are also eligible.

** Format of the Entrance Test Paper **

The duration of the Entrance Test will be 2 hours and the question paper will consist of 100 multiple choice questions in two parts.

**PART A:** will have 40 questions on Basic Mathematics.

**PART B:** will have 60 questions on undergraduate level Mathematics.

Calculators will not be allowed. However, Log Tables may be used.

** The combined syllabus for both Part A and Part B is as follows: **

**Calculus and Analysis: ** Limit, continuity, uniform continuity and differentiability; Bolzano Weierstrass theorem; mean value theorems; tangents and normal; maxima and minima; theorems of integral calculus; sequences and series of functions; uniform convergence; power series; Riemann sums; Riemann integration; definite and improper integrals; partial derivatives and Leibnitz theorem; total derivatives; Fourier series; functions of several variables; multiple integrals; line; surface and volume integrals; theorems of Green; Stokes and Gauss; curl; divergence and gradient of vectors.

**Algebra:** Basic theory of matrices and determinants; groups and their elementary properties; subgroups, normal subgroups, cyclic groups, permutation groups; Lagrange's theorem; quotient groups; homomorphism of groups; isomorphism and correspondence theorems; rings; integral domains and fields; ring homomorphism and ideals; vector space, vector subspace, linear independence of vectors, basis and dimension of a vector space.

**Differential equations: ** General and particular solutions of ordinary differential equations (ODEs); formation of ODE; order, degree and classification of ODEs; integrating factor and linear equations; first order and higher degree linear differential equations with constant coefficients; variation of parameter; equation reducible to linear form; linear and quasi-linear first order partial differential equations (PDEs); Lagrange and Charpits methods for first order PDE; general solutions of higher order PDEs with constant coefficients.

**Numerical Analysis:** Computer arithmetic; machine computation; bisection, secant; Newton-Raphson and fixed point iteration methods for algebraic and transcendental equations; systems of linear equations: Gauss elimination, LU decomposition, Gauss Jacobi and Gauss Siedal methods, condition number; Finite difference operators; Newton and Lagrange interpolation; least square approximation; numerical differentiation; Trapezoidal and Simpsons integration methods.

**Probability and Statistics: ** Mean, median, mode and standard deviation; conditional probability; independent events; total probability and Baye’s theorem; random variables; expectation, moments generating functions; density and distribution functions, conditional expectation.

**Linear Programming:** Linear programming problem and its formulation; graphical method, simplex method, artificial starting solution, sensitivity analysis, duality and post-optimality analysis.

**Negative Marks for Wrong Answers: ** If the answer given to any of the Multiple Choice Questions is wrong, ¼ of the marks assigned to that question will be deducted.