CS- 302 Discrete Structures

Unit-I

Set Theory, Relation, Function, Theorem Proving Techniques : Set Theory: Definition of sets,

countable and uncountable sets, Venn Diagrams, proofs of some general identities on sets Relation:

Definition, types of relation, composition of relations, Pictorial representation of relation, Equivalence

relation, Partial ordering relation, Job-Scheduling problem Function: Definition, type of functions, one

to one, into and onto function, inverse function, composition of functions, recursively defined

functions, pigeonhole principle. Theorem proving Techniques: Mathematical induction, Proof by

contradiction.

Unit-II

Algebraic Structures: Definition, Properties, types: Semi Groups, Monoid, Groups, Abelian

group, properties of groups, Subgroup, cyclic groups, Cosets, factor group, Permutation groups,

Normal subgroup, Homomorphism and isomorphism of Groups, example and standard results,

Rings and Fields: definition and standard results.

Unit-III

Propositional Logic: Proposition, First order logic, Basic logical operation, truth tables,

tautologies, Contradictions, Algebra of Proposition, logical implications, logical equivalence,

predicates, Normal Forms, Universal and existential quantifiers. Introduction to finite state machine

Finite state machines as models of physical system equivalence machines, Finite state machines as

language recognizers

Unit-IV

Graph Theory: Introduction and basic terminology of graphs, Planer graphs, Multigraphs and

weighted graphs, Isomorphic graphs, Paths, Cycles and connectivity, Shortest path in weighted

graph, Introduction to Eulerian paths and circuits, Hamiltonian paths and circuits, Graph coloring,

chromatic number, Isomorphism and Homomorphism of graphs.

Unit V

Posets, Hasse Diagram and Lattices: Introduction, ordered set, Hasse diagram of partially,

ordered set, isomorphic ordered set, well ordered set, properties of Lattices, bounded and

complemented lattices. Combinatorics: Introduction, Permutation and combination, Binomial

Theorem, Multimonial Coefficients Recurrence Relation and Generating Function: Introduction to

Recurrence Relation and Recursive algorithms , Linear recurrence relations with constant

coefficients, Homogeneous solutions, Particular solutions, Total solutions , Generating functions ,

Solution by method of generating functions,

Refereences:

1. C.L.Liu, “Elements of Discrete Mathematics” Tata Mc Graw-Hill Edition.

2. Trembley, J.P & Manohar; “Discrete Mathematical Structure with Application CS”, McGraw Hill.

3. Kenneth H. Rosen, “Discrete Mathematics and its applications”, McGraw Hill.

4. Lipschutz; Discrete mathematics (Schaum); TMH

5. Deo, Narsingh, “Graph Theory With application to Engineering and Computer.Science.”, PHI.

6. Krishnamurthy V; “Combinatorics Theory & Application”, East-West Press Pvt. Ltd., New Delhi.

7. S k Sarkar “ Discrete Mathematics”, S. Chand Pub