Propositional Logic, , Applications of Propositional Logic, Propositional Equivalences, Predicated and Quantifiers, Nested Quantifiers , Rules of Inference , Introduction to Proofs .

Sets, Set Operations, Functions, Sequences and Summations, Cardinality of Sets, variable Relations and their properties, n-ary relations and their applications, representing relations, closures of relations and equivalence relations, partial orderings.

Mathematical Induction , Strong Induction and Well-ordering, Recursive Definitions and Structural Induction, Recursive Algorithms, Program Correctness.

The Basics of Counting, The Pigeonhole Principle, Permutations and Combinations, Binomial Coefficients and Identities, Generalized Permutations and Combinations, Generating Permutations and Combinations.
Advanced Counting Techniques : Applications of Recurrence Relations, Solving Recurrence Relations, Divide and Conquer Algorithms and Recurrence Relations, Generating Functions, Inclusion-Exclusion.

Semi groups and Monoids - Definition and Examples, Sub semi groups and Sub monoids, Homomorphism of Semigroups , Monoids , Groups and Subgroups, Group Homomorphism, Cosets and Lagrange's Theorem, Normal Subgroups, Quotient Groups, Permutation Groups, Algebraic Systems with Two Binary Operations, Rings, Subrings and Homomorphisms.