MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE MCA 1st Year 1st Semester E-Book
E-Book PDF Download File Syllabus
Contents
UNIT– I Fundamentals of Logic: Basic Connectives and Truth Tables, Logical Equivalence, Logical Implication, UseofQuantifiers,DefinitionsandtheProofofTheorems. Set Theory: Diagrams. Set and Subsets, Set Operations, and the Laws of Set theory, Counting and Venn Properties of the Integers: The well– ordering principle, Recursive Definitions, Division Algorithms,FundamentaltheoremofArithmetic.
UNIT– II Relations and Functions: Relations: Principle of Inclusion and Exclusion: Cartesian Product, Functions onto Functions, Special Functions, PigeonholePrinciple,CompositionandInverseFunctions. PartialOrders,EquivalenceRelationsandPartitions. Principles of Inclusion and Exclusion, Generalization of Principle.
UNIT– III GeneratingFunctions: IntroductoryExamples,DefinitionAndExamples,PartitionsofIntegers. Recurrence Relations: First– order linear recurrence relation, second– order linear homogenousrecurrencerelationwithconstantcoefficients.
UNIT– IV Algebraic Structures: Algebraic System– General Properties, Semi Groups, Monoids, Homomorphism,Groups,ResidueArithmetic.
UNIT– V Graph Theory: Definitions and examples, sub graphs, complements and graph Isomorphism, Vertexdegree,Planargraphs,HamiltonianpathsandCycles. Trees: Definitions, properties and Examples, Rooted Trees, Spanning Trees and Minimum SpanningTrees.
