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M.C.A, , Computer Applications, , Regulations 2019, , SEMESTER I, MAD 6188, , MATHEMATICAL FOUNDATION FOR, , L, , T, , P C, , 3, , 1, , 0, , COMPUTER APPLICATIONS, 4, , OBJECTIVES:, The objective of this course is to, , , Provide mathematical background on Number System and Combinatorics, , , , Give Sufficient exposure to Propositions and Logical operations, , , , Deal and solve problems on Matrices, , , , Familiarize the concepts in Set Theory, , , , Explain the concepts in Graph Theory, , MODULE I, , NUMBER SYSTEMS, COMBINATORICS, , 12, , Decimal Number System - Binary Number System - Hexadecimal Number, System - Octal Number System - Permutations and Combinations Mathematical Induction - Pigeonhole principle, MODULE II, , PROPOSITIONS AND LOGICAL OPERATIONS, , 12, , Notation - Connections - Normal forms - Truth Tables - Equivalence and, Implications - Theory of inference for statement calculus, Predicate calculus Rules of Logic Mathematical Induction and Quantifiers, MODULE III, , MATRICES, , 12, , Matrices: Definition and Classification - Algebra of Matrices - Special Matrices Elementary Operations of a Matrix. Determinants : Definitions & Properties Minors and Cofactors -Operations on Determinants -Determinants: System of, Linear Equations-Characteristic Equation- Eigen values and Eigenvectors., MODULE IV, , SETS AND RELATIONS, , 12, , Basic concepts of Sets - Set Operations and Venn Diagrams - Set Identities, Cartesian products - Power sets - Representation and Properties of Relations., , B.S. Abdur Rahman Crescent Institute of Science and Technology, , 29

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M.C.A, , Computer Applications, , MODULE V, , Regulations 2019, , GRAPH THEORY, , 12, , Simple Graph, Multigraph, Weighted Graph, Paths and Circuits, Shortest Paths in, Weighted Graphs, Eulerian Paths and Circuits, Hamiltonian Paths and Circuits,, Trees and Rooted Trees, Prefix Codes, Tree Traversals, Spanning Trees and, Cut- Sets., , Total Hours: 60, TEXT BOOKS :, Judith L. Gersting, “Mathematical Structures for Computer Science”, 5th, , 1., , Edition, W.H. Freeman and Company, New York, 2003., Grimaldi R.P. and Ramana B.V., “Discrete and Combinatorial Mathematics”,, , 2., , Pearson Education, 5th Edition, Harlow, 2006., Veerarajan.T., “Engineering Mathematics” (5th edition) Tata Mc Graw Hill, , 3., , Publishing Co. New Delhi, 2012., , REFERENCE BOOKS :, Grimaldi R.P. and Ramana B.V., “Discrete and Combinatorial Mathematics”,, , 1., , Pearson Education, 5th Edition, Harlow, 2006., Trembley.J.P and Manohar R., “Discrete Mathematical Structures with, , 2., , Applications to Computer Science”, Tata McGraw – Hill Publishing Company, Limited, Reprint, New, Delhi, 2008., OUTCOMES:, On completion of this course, students will be able to:, , , Explain the concepts in Mathematical Induction, Set Theory, Graph theory, , , , Demonstrate the use of Matrices in solving linear equations, , , , Apply, , the, , Combinatorics,, , Proposition,, , Logical, , Operators, , involving, , combinatorics problems, , , Solve logical proofs in Mathematical Logics derived from truth tables., , , , Apply set operations and functions in solving in Set Problem., , B.S. Abdur Rahman Crescent Institute of Science and Technology, , 30