Basic Connectives and Truth Tables, Logic Equivalence :The laws of Logic,Logical Implications: Rules of Inference, The use of Quantifiers, Quantifier Definitions,Proofs of Theorems.
Sets and Subsets, Set Operations and the Laws of Set Theory, Counting and VennDiagrams, Principles of Inclusion and Exclusion, The rules of sum and product,Permutations and Combinations with repetition
Mathematical Induction, Recursive definitions, The Greatest Common DivisorEuclidian Algorithms, The first order Linear recurrence relation.
Cartesian products and Relations, Functions-Plain and One-to-One, Onto Functions,Stirling Numbers and the Second Kind, Special functions, The Pigeon-hole principle,Function composition and inverse functions. Properties of Relations, Computer recognition-Zero One Matrices and Directed graphs, Posets and Hasse Diagrams, Equivalence relationand Partitions, lattices.
Terminology, Definitions, Properties and Examples, Connectivity and Adjacency, Eulerand Hamilton, Representation and Isomorphism, Planarity and Chromatic Number, DirectedGraphs and Weighted Graphs, Rooted Trees, Trees and Sorting