Mathematical reasoning; propositions; negation disjunction and conjuction; implication and equivalence; truth tables; predicates; quantifiers; natural deduction; rules of Inference; methods of proofs; use in program proving; resolution principle; application to PROLOG. (10 lectures)

Set theory; Paradoxes in set theory; inductive definition of sets and proof by induction;

Peono postulates; Relations; representation of relations by graphs; properties of relations;equivalence relations and partitions; Partial orderings; Posets; Linear and well-ordered sets; (10 lectures)

Graph Theory; elements of graph theory, Euler graph, Hamiltonian path, trees, tree

traversals, spanning trees; (4 lectures)

Functions; mappings; injection and surjections; composition of functions; inverse functions;special functions; Peono postulates; pigeonhole principle; recursive function theory; (6 lectures)

Definition and elementary properties of groups, semigroups, monoids, rings, fields, vector

spaces and lattices; (4 lectures)

Elementary combinatorics; counting techniques; recurrence relation; generating functions; (6 lectures)

*Text Books*

*1. C.L.Liu, Elements of Discrete Mathematics, second edition 1985, McGraw-Hill Book*

Company. Reprinted 2000.

2. K.H.Rosen, Discrete Mathematics and applications, fifth edition 2003, TataMcGraw Hill

publishing Company.

Reference Books

1. J .L.Mott, A.Kandel, T.P .Baker, Discrete Mathematics for Computer Scientists and

Mathematicians, second edition 1986, Prentice Hall of India.

2. W.K.Grassmann and J.P.Trembnlay, Logic and Discrete Mathematics, A Computer Science