The Department of Mathematics started its PhD programme in July 2013. A wide range of the following research areas are offered in which the enrolled students can pursue their PhD work:
Numerical Analysis
Differential Equations and Boundary Value Problems
Fourier Analysis
Analysis, Function Spaces
Integral Operators and weighted Norm Inequalities
Graph Theory, Discrete Mathematics
Finite Elements Methods
Parallel Computations
Statistical Approximation, Stochastic Processes
Mathematical Biology, Non-linear Dynamical Systems
Optimization, Swarm Intelligence
Candidates must have completed a minimum of 17 years of formal education, i.e. 12 years of regular schooling, followed by either a 3-year Bachelor’s degree and a 2-year Master’s degree, or a 4-year Bachelor’s degree and a 1-year Master’s degree in Mathematics, Computer Science, Statistics, Operations Research, Physics, or an equivalent field, with a minimum aggregate of 55% marks or an equivalent grade.
Candidates with 4-year Bachelor degree in the subject are also eligible for admission to PhD programme provided they have secured a minimum of 80% marks or equivalent grade.
The number of seats through the Entrance Test mode is 6, while the number of seats through the Direct mode shall be based on availability.
The questions may be asked in the Entrance Test in the following areas:
Analysis: Real functions; limit, continuity, differentiability; sequences; series; uniform convergence; functions of complex variables; analytic functions, complex integration; singularities, power and Laurent series; metric spaces; stereographic projection; topology, compactness, connectedness; normed linear spaces, inner product spaces; dual spaces, linear operators; Lebesgue measure and integration; convergence theorems.
Algebra: Basic theory of matrices and determinants; eigenvalues and eigenvectors; Groups and their elementary properties; subgroups, normal subgroups, cyclic groups, permutation groups; Lagrange's theorem; quotient groups, homomorphism of groups; Cauchy Theorem and p-groups; the structure of groups; Sylow's theorems and their applications; rings, integral domains and fields; ring homomorphism and ideals; polynomial rings and irreducibility criteria; vector space, vector subspace, linear independence of vectors, basis and dimensions of a vector space, inner product spaces, orthonormal basis; Gram-Schmidt process, linear transformations.
Differential Equations: First order ordinary differential equations (ODEs); solution of first order initial value problems; singular solution of first order ODEs; system of linear first order ODEs; method of solution of dx/P=dy/Q=dz/R; orthogonal trajectory; solution of Pfaffian differential equations in three variables; linear second order ODEs; Sturm-Liouville problems; Laplace transformation of ODEs; series solutions; Cauchy problem for first order partial differential equations (PDEs); method of characteristics; second order linear PDEs in two variables and their classification; separation of variables; solution of Laplace, wave and diffusion equations; Fourier transform and Laplace transform of PDEs.
Numerical Analysis: Numerical solution of algebraic and transcendental equations; direct and iterative methods for system of linear equations; matrix eigenvalue problems; interpolation and approximations; numerical differentiation and integration; composite numerical integration; double numerical integration; numerical solution for initial value problems; finite difference and finite element methods for boundary value problems.
Probability and Statistics: Axiomatic approach of probability; 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.
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