discrete structure1
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28DISCRETESTRUCTURECT551Lecture : 3 Year : IITutorial : 0 Part : IIPractical : 0CourseObjectives:to gain knowledge in discrete mathematics and finite state automata inanalgorithmicapproach.to gain fundamental and conceptual clarity in the area of Logic,Reasoning, Algorithms, Recurrence Relation, Graph Theory, and TheoryofAutomata.1.Logic,InductionandReasoning (12hours)1.1.PropositionandTruthfunction1.2.PropositionalLogic1.3.ExpressingstatementsinLogicPropositionalLogic1.4.ThepredicateLogic1.5.Validity1.6.InformalDeductioninPredicateLogic1.7.RulesofInferenceandProofs1.8.InformalProofsandFormalProofs1.9.ElementaryInductionandCompleteInduction1.10.MethodsofTableaux1.11.ConsistencyandCompletenessoftheSystem2.FiniteStateAutomata (10hours)2.1.SequentialCircuitsandFinitestateMachine2.2.FiniteStateAutomata2.3.LanguageandGrammars2.4.NondeterministicFiniteStateAutomata2.5.LanguageandAutomata2.6.RegularExpressionanditscharacteristics3.RecurrenceRelation (8hours)3.1.RecursiveDefinitionofSequences3.2.SolutionofLinearrecurrencerelations3.3.SolutiontoNonlinearRecurrenceRelations3.4.ApplicationtoAlgorithmAnalysis4.GraphTheory (15hours)4.1.UndirectedandDirectedGraphs4.2.WalkPaths,Circuits,Components4.3.ConnectednessAlgorithm4.4.ShortestPathAlgorithm4.5.BipartiteGraphs,PlanarGraphs,RegularGraphs4.6.PlanarityTestingAlgorithms4.7.EulerianGraph4.8.HamiltonianGraph4.9.TreeasaDirectedGraph4.10.BinaryTree,SpanningTree4.11.CutsetsandCutvertices4.12.NetworkFlows,MaxflowandMincutTheorem4.13.DataStructuresRepresentingTreesandGraphsinComputer4.14.NetworkApplicationofTreesandGraphs4.15.ConceptofGraphColoringReferences:1.Kenth Rosen, Discrete Mathematical Structures with Applications toComputerScience,WCB/McGrawHill2.G.Birkhoff,T.C.Bartee,ModernAppliedAlgebra,CBSPublishers.3.R.Johnsonbaugh,DiscreteMathematics,PrenticeHallInc.4.G.Chartand, B.R.Oller Mann, Applied and Algorithmic Graph Theory,McGrawHill5.Joe L. Mott, Abrahan Kandel, and Theodore P. Baker, DiscreteMathematics for Computer Scientists and Mathematicians, PrenticeHallofIndiaEvaluationScheme:Thequestionswillcoverallthechaptersofthesyllabus.TheevaluationschemewillbeasindicatedinthetablebelowChapters Hours Marksdistribution*1 12 242 10 163 8 84 15 32Total 45 80*TherecouldbeaminordeviationinMarksdistribution