MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY, JAIPUR.
DEPARTMENT OF MATHEMATICS
SYLLABUS
MAT-627: Discrete Mathematical Structures
4 Credits ( 3L+1T+0P)
Formal Logic-Statements, Symbolic Representation and Tautologies, Quantifiers, Predicates
and Validity, Propositional Logic, Lattices: Partially ordered sets and Lattices, Hasse
Diagrams, lattices as algebraic systems sub-lattices, direct product and Homomorphisms,
Complete lattices, Modular lattices, distributed lattices, the complemented lattices, convex
sub lattices, Congruence relations in lattices.
Graphs: Complete graphs, regular graphs, bipartite graphs, Vertex degree, subgraphs, paths
and cycles, the matrix representation of graphs, fusion, trees and connectivity, bridges,
spanning trees, chromatic number, connector problems, shortest path problems, cut vertices
and connectivity. Polya’s theory of enumeration and its application.
Books Recommended:
1. Elements of Discrete Mathematics by C. L. Liu, McGraw-Hill Book Co.
2. Discrete mathematical structures by Kolman, Busby and Ross, 4th edition. PHI, 2002.
3. Discrete Mathematics with Graph Theory by Goodaire and Parmenter, Pearson
edition.2nd edition.
4. Graph Theory with Applications to Engineering and Computer Sciences by N. Deo,
PHI learning, 2009.