Fundamentals of Logic: Basic Connectives and Truth Tables, Logic Equivalence – The Laws of
Logic, Logical Implication – Rules of Inference. Fundamentals of Logic contd.: The Use of
Quantifiers, Quantifiers, Definitions and the Proofs of Theorems,
Properties of the Integers: Mathematical Induction, The Well Ordering Principle – Mathematical
Induction, Recursive Definitions. Principles of Counting.
Fundamental Principles of Counting: The Rules of Sum and Product, Permutations, Combinations – The Binomial Theorem,
Combinations with Repetition,.
Relations and Functions: Cartesian Products and Relations, Functions – Plain and One-to-One,
Onto Functions. The Pigeon-hole Principle, Function Composition and Inverse Functions.
Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs, Partial
Orders – Hasse Diagrams, Equivalence Relations and Partitions.
The Principle of Inclusion and Exclusion: The Principle of Inclusion and Exclusion,
Generalizations of the Principle, Derangements – Nothing is in its Right Place, Rook Polynomials.
Recurrence Relations: First Order Linear Recurrence Relation, The Second Order Linear
Homogeneous Recurrence Relation with Constant Coefficients,
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 Prefix Codes