Dive into a comprehensive 3-hour 42-minute video tutorial on the fundamentals of discrete mathematics. Explore essential concepts including set theory, relations, functions, counting principles, and propositional logic. Begin with an introduction to discrete mathematics and set theory, covering various types of sets, operations, and algebraic laws. Progress through relations, their types, and closure properties, before delving into functions and their classifications. Learn about counting principles, including the sum and product rule, pigeon-hole principle, and permutations and combinations. Conclude with an exploration of propositional logic, connectives, tautologies, contradictions, and propositional equivalence. Gain a solid foundation in discrete mathematics, crucial for understanding compiler programming, machine learning, and artificial intelligence.
Overview
Syllabus
Basics of Discrete Mathematics Part 1.
Introduction to Discrete mathematics.
Introduction to Set Theory.
Types of Sets.
Operations on Sets.
Laws of Set Algebra.
Sums on Algebra of Sets.
Relations.
Types of relations.
Closure properties in relations.
Equivalence relation.
Partial ordered Relation.
Functions.
Types of Functions.
Identity Functions.
Composite Functions.
Mathematical Functions.
Summary of Basics of Discrete Mathematics Part 1.
Basics of Discrete Mathematics Part 2.
Introduction to Counting Principle.
Sum and Product Rule.
Pigeon-hole principle.
Permutation and combination.
Propositional logic.
Connectives.
Tautology.
Contradiction.
Contingency.
Propositional equivalence.
Inverse, Converse and contrapositive.
Summary of Basics of Discrete Mathematics Part 2.
Taught by
Great Learning
