Discrete Mathematics
24CST401 · S4 · 4 credits
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Module 01Mathematical Logic (8 hours)expand
Statements and Notation-Connectives-Negation-Conjunction-Disjunction-Statement Formulas and Truth tables, Conditional and Biconditional-Tautologies-Equivalence of Formulas-Duality Law-Tautological implications- Normal Forms-Theory of inference for statement Calculus-Rules of inference, Predicate Calculus.
Module 02Algebraic Structures (6 hours)expand
Semigroups and Monoids, Homomorphism of semigroups and monoids, Sub semigroups and sub monoids, Groups, Subgroups and homomorphisms, Cosets and Lagrange’s theorem.
Module 03Sets, Relations, Posets and Lattice (8 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- Dual Lattice – Sub lattice –Properties of glb and lub – Properties of Lattice - Special Lattice : Complete Lattice – Bounded Lattice – Completed Lattice – Distributive Lattice.
Module 04Counting Theory (7 hours)expand
The Rule of Sum – Extension of Sum Rule - The Rule of Product - Extension of Product Rule – Permutations, Combinations, The Binomial Theorem, Combination with Repetition. The Pigeonhole Principle, The principle of Inclusion and Exclusion Theorem Generalisation of the principle, Derangements.
Module 05Fundamentals of Graphs (7 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. Planar Graphs, Bipartite graphs, Chromatic Number, Matchings, Coverings, Four color problem.
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