Logic, Mathematical reasoning, Sets, Basics of counting, Relations.
Graph Theory: Euler graphs, Hamiltonian paths and circuits, planar graphs, trees, rooted and binary trees, distance and centres in a tree, fundamental circuits and cut sets, graph coloringsand applications, chromatic number, chromatic partitioning, chromatic polynomial, matching, vector spaces of a graph.
Analytic Number Theory: Euclid’s lemma, Euclidean algorithm, basic properties of congruences, residue classes and complete residue systems, Euler-Fermat theorem, Lagrange’s theorem and its applications, Chinese remainder theorem, primitive roots. Algebra: groups, cyclic groups, rings, fields, finite fields and their applications to cryptography.
Linear Algebra: vector spaces and subspaces, linear independence, basis and dimensions, linear transformations and applications.
Probability and Statistics: introduction to probability concepts, random variables, probability distributions (continuous and discrete), Bayesian approach to distributions, mean and variance of a distribution, joint probability distributions, theory of estimation,
Bayesian methods of estimation. Random Processes: general concepts, power spectrum, discrete-time processes, random walks and other applications, Markov chains, transition probabilities.