Sets.  Sequences and functions, Elementary logic.  Propositional calculus, Methods of Proof,  Mathematical induction, recurrence relation,  loop invariants.  Relations.  Equivalence of Relations and Partitions.  Partially ordered sets.  Properties of General Relations, Introduction to combinatorics.  Basic counting techniques.  Elementary Probability, Inclusion-exclusion principle and binomial methods.  Counting and partitions.  Pigeon hole principle.  Algebraic structures;  groups and semi-groups.