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TCS-301 Discrete Structures

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.
Function: Definition, type of functions, one to one, into and onto function, inverse function,
composition of functions, recursively defined functions.
Theorem proving Techniques: mathematical induction (simple and strong), pigeonhole
principle, prove by contradiction.

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.
Posets, Hasse Diagram and Lattices: Introduction, ordered set, Hasse diagram of partially,
ordered set, isomorphic ordered set, well ordered set, properties of Lattices, bounded I and
complemented lattices.
Propositional Logic: Proposition, First order logic, Basic logical operation, truth tables,
tautologies, Contradictions, Algebra of Proposition, logical implications, logical equivalence,
predicates, Universal and existential quantifiers.
Combinatorics & Graphs: Recurrence Relation, Generating function., Permutation &
Combination, Probabilistic Permutation & Combination

Text books: 

2. Trembley, J.P & R. Manohar, “Discrete Mathematical Structure with Application to
    Computer Science”, McGraw Hill, Reprint 2010
Reference Book:
1. Discrete Mathematics & its application with combinatory and graph theory,K.H.Rosen, TMH(6th edition).
2. C.L.Liu, ‘Discrete Mathematics’ TMH.


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