Week 1:Logic: Proposition and Predicate Logic, introduction to proof techniques
Week 2:Advanced proof techniques, resolution, induction
Week 3: Set theory and relations
Week 4:Various types of relations and functions
Week 5:Combinatorics Part I: permutations, combinations, sum rule, product rule, pigeon-hole principle, Ramsey numbers
Week 6:Combinatorics Part II: Combinatorial proofs, Catalan numbers, counting using recursion, principal of inclusion-exclusion, advanced counting techniques
Week 7: Recurrence equations and various methods of solving recurrence equations
Week 8:Cardinality theory, countable and uncountable sets, Cantor’s diagonalization, uncomputable functions
Week 9:Graph theory Part I: basic definitions, Euler’s theorem, bipartite graphs and matching, Hall’s marriage theorem, various operations on graphs
Week 10:Graph theory part II: isomorphism, vertex-connectivity, edge-connectivity, Euler graphs and Hamiltonian graphs, various characterizations, vertex and edge coloring
Week 11: Abstract algebra: groups, rings, fields
Week 12:Basic number theory: modular arithmetic, prime numbers and properties, GCD, Chinese remainder theorem, Fermat’s little theorem, RSA cryptosystem
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