The goal of the course is to brush up and build basic concepts and background required for other theoretical courses, with an emphasis on writing clear, precise proofs of mathematical statements. There are four modules: Graph theory, Combinatorics, Algebra, Probability with some possible overlap of topics across modules.

From the offical course website

Graph Theory

Date Topics
August 10 Graph theory: Introduction, simple results related to connectivity,
characterization of bipartite graphs
August 17 Bipartite graphs continued, degree-sum formula, Mantel’s theorem, trees
August 24 Eulerian graphs: characterization, directed graphs, tournaments
August 29 Matchings: Definition, Maximum vs. maximal matching,
augmenting path, Berge’s theorem
August 31 Bipartite matching, Hall’s theorem
Sept 5 König-Egerváry theorem, planar graphs: definition,
Euler’s formula
Sept 7 Characterization of planar graphs, 6-coloring
Sept 7 (Extra Class) Tutte’s theorem for perfect matching

Combinatorics

Date Topics
Sept 12 Pigeonhole principle: applications including
Chinese remainder theorem and Erdös-Szekeres theorem, permutations and combinations, counting with and without repetitions