This course in Discrete Mathematics aims to teach students the fundamentals of mathematical logic, probability, graph theory, relations, sets, and Boolean algebra. By the end of the course, students will be able to apply mathematical induction, analyze graphs, understand relations, and solve problems using Boolean algebra. The teaching method includes lectures, examples, and problem-solving exercises. This course is intended for learners interested in computer science, mathematics, or related fields who want to strengthen their foundational knowledge in discrete mathematics.
Overview
Syllabus
First Order Logic (1).
First Order Logic (2).
Rules of Influence for Quantified proportions.
Mathematical Induction.
Mathematical Induction.
Sample Space ,Events.
Probability, Conditional probability.
Independent Events, Bayes Theorem.
Information and mutual information.
Basic definition.
Isomorphism and sub graphs.
Walks,paths and circuits, operations on graphs.
Euler graphs, Hamiltonian circuits.
Shortest path problem.
Planar graphs.
Basic definitions.
Properties of relations.
Graph of Relations.
Matrix of a Relation.
Closure of a Relation (1).
Closure of a Relation (2).
Partial Ordered Relation.
Partially ordered sets.
Lattices.
Boolean algebra.
Permutations and Combinations (Continued).
The principle of Inclusion and Exclusion.
Methods of Proof of an Implication.
Mathematical Induction.
Logical Inferences.
Introduction to the theory of sets.
Fundamentals of Logic.
Application of the principle of Inclusion and Exclusion.
Taught by
Ch 30 NIOS: Gyanamrit
