Fundamentals of Logic: Basic Connectives and Truth Tables, Logic Equivalence – TheLaws of Logic, Logical Implication – Rules of Inference. The Use of Quantifiers,Quantifiers, Definitions and the Proofs of Theorems,Textbook 1: Ch 2
Properties of the Integers: Mathematical Induction, The Well Ordering Principle –Mathematical Induction, Recursive Definitions. Fundamental Principles of Counting:The Rules of Sum and Product, Permutations, Combinations – The Binomial Theorem,Combinations with Repetition,Textbook 1: Ch 4: 4.1, 4.2 Ch 1.
Relations and Functions: Cartesian Products and Relations, Functions – Plain and One-to-One, Onto Functions. The Pigeon-hole Principle, Function Composition and InverseFunctions. Properties of Relations, Computer Recognition – Zero-One Matrices andDirected Graphs, Partial Orders – Hasse Diagrams, Equivalence Relations and Partitions.Textbook 1: Ch 5:5.1 to 5.3, 5.5, 5.6, Ch 7:7.1 to 7.4
The Principle of Inclusion and Exclusion: The Principle of Inclusion and Exclusion,Generalizations of the Principle, Derangements – Nothing is in its Right Place, RookPolynomials. Recurrence Relations: First Order Linear Recurrence Relation, The SecondOrder Linear Homogeneous Recurrence Relation with Constant Coefficients.Textbook 1: Ch 8: 8.1 to 8.4, Ch 10:10.1 to 10.2
Introduction to Graph Theory: Definitions and Examples, Sub graphs, Complements,and Graph Isomorphism, Vertex Degree, Euler Trails and Circuits , Trees: Definitions,Properties, and Examples, Routed Trees, Trees and Sorting, Weighted Trees and PrefixCodesTextbook 1: Ch 11: 11.1 to 11.3, Ch 12: 12.1 to 12.4