MSC Semester I - Discrete Mathematics

Unit – I

Mathematical Logic: propositional logic, propositional equivalences, predicates & quantifiers, rule

of inference, direct proofs, proof by contraposition, proof by contradiction.

Boolean Algebra: Boolean functions and its representation, logic gates, minimizations of circuits

by using Boolean identities and K-map.

Unit – II

Basic Structures: Sets representations, set operations, functions, sequences and summations.

Division algorithm, modular arithmetic, solving congruences, applications of congruences.

Recursion: Proofs by mathematical induction, recursive definitions, structural induction,

generalized induction, recursive algorithms.

Unit – III

Counting: Basic counting principle, inclusion-exclusion for two-sets, pigeonhole principle,

permutations and combinations, Binomial coefficient and identities, generalized permutations and

combinations.

Recurrence Relations: introduction, solving linear recurrence relations, generating functions,

principle of inclusion-exclusion, applications of inclusion-exclusion.

Relations: relations and their properties, representing relations, closures of relations, equivalence

relations, partial orderings.

Unit – IV

Graphs: Graphs definitions, graph terminology, types of graphs, representing graphs, graph

isomorphism, connectivity of graphs, Euler and Hamilton paths and circuits, Dijkstra’s algorithm to

find shortest path, planar graphs–Euler’s formula and its applications, graph coloring and its

applications

Trees: Trees definitions–properties of trees, applications of trees –BST, Haffman Coding, tree

traversals: pre-order, in-order, post-order, prefix, infix, postfix notations, spanning tress–DFS, BFS,

Prim’s, Kruskal’s algorithms.