Semester:

2021 Autumn/Monsoon (Aug  Dec)
 Set theory
 axioms (at the level of Halmos's Naive Set Theory), functions, permutations, equivalence relations, partitions, orders, partial orders, preorders, quasiorders, induction, cardinality, lattices, monotone functions, fixed points;
 Combinatorial structures
 set systems, graphs, hypergraphs;
 Algebraic structures
 groups, rings, fields, polynomials, matrices, vector spaces, Markov chains, codes;
 Convexity
 polytopes, duality, volumes; Counting: permutation, partitions, functions, inclusionexclusion, Mobius inversion, Polya's counting theory;
 Extremal combinatorics of the Boolean cube
 chains, covers, intersecting families, covers, isoperimetric inequalities, correlation inequalities, designs;
 Extremal graph theory
 girth versus density, Ramseylike theorems, TuranLike theorems, Knesser graph;
 Methods
 the probabilistic, method, the linear algebra/polynomial method, the entropy method;