Discrete Mathematics
24EST382 · S3 · 4 credits
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Module 01Mathematical Logic (4 hours)expand
Statements and Notation-Connectives, Negation, Conjunction, Disjunction. Statement Formulas and Truth tables, Conditional and Biconditional, Tautologies, Equivalence of Formulas, Duality Law.
Module 02Sets, Relations, Posets and Lattice (5 hours)expand
Sets and Relations, Partial Order relations, Equivalence Relation- irreflexive relations. Partially ordered Set – Hasse Diagram, Maximal-Minimal Element, Least upper bound (lub), Greatest lower bound(glb). Equivalence Relations and Partitions - Equivalence Class. Lattice, Sub lattice
Module 03Counting Theory (4 hours)expand
The Rule of Sum, Extension of Sum Rule, The Rule of Product, Extension of Product Rule. Permutations, Combinations, The Binomial Theorem (without proof), Combination with Repetition. Pigeonhole Principle.
Module 04Algebraic Structures (5 hours)expand
Semigroups and Monoids, Homomorphism of semigroups and monoids, Sub semigroups and sub monoids, Groups, Subgroups
Module 05Fundamentals of Graphs (4 hours)expand
Basic Concepts of Graph Theory: Definition, Finite and infinite Graphs, Incidence and Degree, Isolated vertex, pendant vertex and null graph. Graph Isomorphism –Subgraphs, Walk, Path and Circuits, Euler Graphs, Hamiltonian paths and circuits (Concepts only). Cut sets, Connectivity- Edge connectivity, vertex connectivity.
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