Students in this programme will be expected to complete the following courses, normally over a period of eight semesters (4 years):
MATH F111 Mathematics I
Functions and graphs; limit and continuity; applications of derivative and integral. Conics; polar coordinates; convergence of sequences and series. Maclaurin and Taylor series. Partial derivatives. Vector calculus in Rn; vector analysis; theorems of Green, Gauss and Stokes
MATH F112 Mathematics II
Complex numbers, analytic functions, Cauchy's theorems; elementary functions; series expansions; calculus of residues and applications. Vector space; basis and dimension; linear transformation; range and kernel of a linear transformation; row reduction method and its application to linear system of equations.
MATH F113 Probability & Statistics
Probability spaces; conditional probability and independence; random variables and probability distributions;marginal and conditional distributions; independent random variables; mathematical expectation; mean and variance; binomial, Poisson and normal distributions; sum of independent random variables; law of large numbers; central limit theorem (without proof);sampling distribution and test for mean using normal and student's t distribution; test of hypothesis; correlation and linear regression.
MATH F211 Mathematics III
Eigen-values and eigen-vectors. Inner product space and orthonormal bases. Elementary differential equations, Hypergeometric equations, Lengendre polynomials, Bessel functions; Fourier series; Sturm-Liouville problem, series solution for differential equation, systems of first order equations; Laplace transformation and application to differential equations; one dimensional wave equation, one dimensional heat equation & Laplace equation in rectangular form.
MATH F212 Optimization
Introduction to optimization; linear programming; simplex methods; duality and sensitivity analysis; transportation model and its variants; integer linear programming nonlinear programming; multi-objective optimization;evolutionary computation techniques.
MATH F213 Discrete Mathematics
Logic and methods of proof, Elementary Combinatorics, recurrence relations, Relations and digraphs, orderings, Boolean algebra and Boolean functions.
MATH F214 Elementary Real Analysis
Countability and uncountability of sets; real numbers; limits and continuity; compactness and connectedness in a metric space;
Riemann integration; uniform convergence.
MATH F215 Algebra-I
Groups, subgroups, a counting principle, normal subgroups and quotient groups, Cayley’s theorem, automorphisms, permutation groups, and Sylow’s theorems. Rings, ring of real quaternions, ideals and quotient rings, homorphisms, Eculidean rings, polynomial rings, and polynomials over the rational field.
MATH F241 Mathematical Methods
Integral Transforms: Fourier, Fourier sine/cosine and their inverse transforms (properties, convolution theorem and application to solve differential equation), Discrete Fourier Series, Fast Fourier transform, Calculus of Variation: Introduction, Variational problem with functionals containing first order derivatives and Euler equations, Variational problem with moving boundaries. Integral equations: Classification of integral equations, Voltera equations, Fredholm equations, Greens functions.
MATH F242 Operations Research
Introduction to Data Processing; Files and File Structures; Indexing Techniques; Sorting, Searching and Merging Techniques; Introduction to Database Management Systems; Design of Information Systems; Emerging trends in Data Processing.
MATH F243 Graphs and Networks
Basic concepts of graphs and digraphs behind electrical communication and other networks behind social, economic and empirical structures; connectivity, reachability and vulnerability; trees, tournaments and matroids; planarity; routing and matching problems; representations; various algorithms; applications.
MATH F244 Measure and Integration
Lebesgue measure and integration in real numbers, Convergence and Convergence theorems, absolutely continuous functions, differentiability and integrability, theory of square integrable functions, and abstract spaces.
MATH F311 Introduction to Topology
Metric Spaces; Topological Spaces - subspaces, Continuity and homoeomorphism, Quotient spaces and product spaces; separation Axioms; Urysohn’s Lemma and Tietze extension Theorem; Connectedness; Compactness, Tychonoff’s Theorem, Locally Compact Spaces; Homohtopy and the fundamental group.
MATH F341 Introduction to Functional Analysis
Banach spaces; fundamental theorems of functional analysis; Hilbert space; elementary operator theory; spectral theory for self-adjoint operators.
MATH F342 Differential Geometry
Curve in the plane and 3D-space; Curvature of curves; Surfaces in 3D-space; First Fundamental form; Curvature of Surfaces; Gaussian and mean Curvatures; Theorema Egreguim; Geodesics; Gauss-Bonnet Theorem.
MATH F343 Partial Differential Equations
Nonlinear equations of first order, Charpits Method, Method of Characteristics; Elliptic, parabolic and hyperbolic partial differential equations of order 2, maximum principle, Duhamel’s principle, Greens function, Laplace transform & Fourier transform technique, solutions satisfying given conditions, partial differential equations in engineering & science.
MATH F312 Ordinary Differential Equations
Existence and uniqueness theorems; properties of linear systems; behaviour of solutions of nth order equations; asymptotic behaviour of linear systems; stability of linear and weakly nonlinear systems; conditions for boundedness and the number of zeros of the nontrivial solutions of second order equations; stability by Liapunov's direct method; autonomous and non-autonomous systems.
MATH F313 Numerical Analysis
Solution of non-linear algebraic equation; interpolation and approximation; numerical differentiation and quadrature; solution of ordinary differential equations; systems of linear equations; matrix inversion; eigenvalue and eigenvector problems; round off and conditioning.