Syllabus
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Course Code: MS-20-14 Course Name: Discrete Mathematical Structures |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Set Theory: Basic Set Theory, Operations on Sets, Algebra of sets, Venn Diagrams. Relations: Binary Relations, Complement of relations, Inverse of relations, Composite relations, Properties, Equivalence, Partial Order and Total order relations. Functions: Functions on Set, Domain, Co-domain, Representation of Functions, Types, Identity and Inverse Functions, Composition of Functions. |
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| 2 | Propositional Calculus: Propositional logic, Equivalences, Predicates, Quantifiers, Nested Quantifiers, Rules of Inference, Normal Forms, Proofs: Methods, Strategy. Counting: Pigeonhole Principle, Inclusion-Exclusion Principle, Permutations and Combinations, Binomial Coefficients, Counting Principles. |
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| 3 | Advanced Counting Techniques: Recurrence Relations, Solving Recurrence Relations Lattices and Boolean algebra: Lattices, Hasse Diagram, Principle of Duality, Types of Lattices, Special Lattices, Boolean Expression, Equivalent circuits, Dual, Normal Forms. |
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| 4 | Graphs: Introduction, Terminology, Types of Graphs, Representation of Graphs, Paths and Circuits, Cut-set and Cut - Vertices, Graph Isomorphism, Homomorphism, Connectivity, Bipartite Graphs, Subgraphs, Operations on Graphs, Euler and Hamiltonian Graphs, Shortest Path Problem, Planar & Dual Graphs, Coloring. Tree: Tree Notations, Properties of tree, Types of Tree, Operations, Minimum Spanning Tree (MST). |
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