DISCRETE STRUCTURE IT- 402
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META TAGS:-RGPV IT 4TH SEM DISCRETE STRUCTURE SYLLABUS I IT-402 DISCRETE STRUCTURE SYLLABUS I RGTU IT 4TH SEM SYLLABUS I IT 4TH SEM DISCRETE STRUCTURE SYLLABUS I DOWNLOAD RGPV 4TH SEM SYLLABUS IN PDF I RGTU DISCRETE STRUCTURE SYLLABUS I DISCRETE STRUCTURE PAPERS I RGPV DISCRETE STRUCTURE I RGPV IT 4TH SEM SYLLABUS I RGTU IT 4TH SEM SYLLABUS
RGPV / RGTU DISCRETE STRUCTURE IT- 402 SYLLABUS
Branch : Information Technology, IV Semester
Course :Discrete Structure
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 Group,Abelian group, properties of groups,Subgroup,cyclic groups, Co-sets ,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,Multi-graphs 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 CoefficientsRecurrence 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,

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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