Explore the foundations of discrete mathematics through a comprehensive course covering first-order logic, mathematical induction, probability theory, graph theory, set theory, and combinatorics. Learn about logical inferences, quantified proportions, sample spaces, conditional probability, Bayes' theorem, information theory, graph isomorphism, Euler and Hamiltonian circuits, planar graphs, relations, partial orders, lattices, Boolean algebra, permutations and combinations, and the principle of inclusion and exclusion. Develop problem-solving skills and gain a solid understanding of mathematical proofs and logical reasoning essential for computer science and advanced 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
