Logic, Propositional Equivalences, Predicates and Quantifiers Sets, Proof Techniques,Mathematical Induction, Contradiction, Counting Techniques, Pigeon Hole Principle.
Set Theory, Relation, Composition of Relation, Matrix Representation, Equivalence Relation, Partial order relation (Posets), Hasse diagram, Topological Sorting, Lattice, Functions, Permutation Functions.
Definition and examples of simple graphs, Isomorphism, Connectedness, Adjacency, Subgraph, Matrix Representation. Eulerian and Hamiltonian graphs, Trees, Bipartite Graph, Simple Graph, Hall’s Marriage Theorem.
Groups, Subgroups, Cosets, Lagrange's Theorem, Permutation Groups, Isomorphism, Ring, Field.
Multinomial coefficients, Recurrence Relations, Generating functions, Combinations with repetitions, Linear algebraic equations with unit coefficients. Principles of inclusion, exclusion