Discrete Mathematics

Syllabus 

UNIT- I

MATHEMATICAL LOGIC & BOOLEAN ALGEBRA: 1. Basic concept of mathematical logic, Statements, Connectives, Conditional and bi-conditional statements, 2. Logical equivalence, Logical implication & quantifiers, 3. Basic concept of Boolean Algebra, Properties of Boolean Algebra, 4. Boolean functions, Disjunctive & conjunctive normal forms of Boolean functions,5.  Applications of Boolean Algebra in switching circuits & logic circuits.

UNIT-II

SET THEORY, RELATIONS, FUNCTIONS: 1. Basic concept of set theory, Relations, Properties of relation in a set, 2. Equivalence relation, 3. Composition of relations, Partial order & total order relations, 4. Lattices & Hasse diagram, 5. Introduction to function, Inverse, Identity, Injective, Surjective & Bijective functions, 6. Composition of functions and some special functions.

UNIT-III

ALGEBRAIC STRUCTURES: 1. Groups, Subgroups, Cosets, 2. Lagrange’s theorem, Isomorphism, Automorphism, Homomorphism, Rings, Integral domains and Fields.

UNIT-IV

GRAPH THEORY:1.  Introduction to graph theory, 2. Walks, Paths & Circuits, 3. Types of graphs, Shortest path problems, Eulerian and Hamiltonian graphs, 4. Basic concept of tree: spanning tree, minimum spanning tree, search tree, rooted binary tree, 5. Cut sets, 6. Network flow, 7. Matrix representation of graphs.

UNIT-V

COMBINATORICS: 1. Permutation and combination, 2. Pigeon-hole principle, 3. Mathematical induction, 4. Principle of Inclusion and Exclusion, Generating function, Recurrence relation.