R.G.P.V. BHOPAL,M.P.
INFORMATION TECHNOLOGY 3RD SEMESTER
IT-302 DISCRETE STRUCTURE
UNIT-I
Set Theory, Relation,Function,Theorem Proving Techniques:Set Theory: Definition of sets, countable & 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.
Set Theory, Relation,Function,Theorem Proving Techniques:Set Theory: Definition of sets, countable & 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 & 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,Multi-graphs & 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 & combination, Binomial Theorem, Multimonial Coefficients Recurrence Relation & Generating Function: Introduction to Recurrence Relation & Recursive algorithms, Linear recurrence relations with constant coefficients, Homogeneous solutions, Particular solutions, Total solutions ,Generating functions , Solution by method of generating functions,
REFERENCE BOOKS:-
- C.L.Liu, “Elements of Discrete Mathematics” Tata Mc Graw-Hill Edition.
- Trembley, J.P & Manohar; “Discrete Mathematical Structure with Application CS”, McGraw Hill.
- Kenneth H. Rosen, “Discrete Mathematics and its applications”, McGraw Hill.
- Lipschutz; Discrete mathematics (Schaum); TMH
- Deo, Narsingh, “Graph Theory With application to Engineering and Computer.Science.”, PHI.
- Krishnamurthy V; “Combinatorics Theory & Application”, East-West Press Pvt. Ltd., New Delhi.
- S k Sarkar “ Discrete Mathematics”, S. Chand Pub
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