This page is dedicated to notes and assignments in Discrete Mathematics, as a part of the Pre-PhD course "Critical Approaches to Liberal Arts" in UPES. This is a joint course with Dr. Sakshi Chanana. The focus will be primarily on logic and graph theory.
Books:
Discrete Mathematics - Elementary and Beyond. L. Lovasz, J. Pelikan, K. Vestergombi. Publisher: Springer
Discrete and Combinatorial Mathematics. Ralph Grimaldi. Publisher: Pearson
What is discrete mathematics, why is it important.
Revised basic concepts like the fundamentals of counting, permutations, and combinations.
Exercise Set for Week 1: Exercise Set 1
Introduced multisets.
Discussed permutations and combinations of multisets.
With focus on some key results and formulae.
Discussed Pigeonhole Principle and Strong Pigeonhole Principle.
Introduced Logic, with a focus on what constitutes a statement that can have a truth value (True or False.)
Exercise Set for Week 2: Exercise Set 2
Discussed the basics of logic: Primitive statements, introduced the logical connectives.
Discussed Negation of statements and DeMorgan's law.
Introduced truth tables, and defined logical equivalence.
Discussed the distributive laws, and simplified compound statements using logical equivalence, distributive laws and deMorgan's law.
Defined tautologies, contradictions.
Defined validity of an argument with an example.
Exercise Set for Week 3: Exercise Set 3
Discussed Rules of inference: Rule of detachment, Law of Syllogism, Rule of denying.
Discussed further the rules of inference: Rule of Conjunction, Law of Disjunctive Syllogism, Rule of Contradiction and Law of Constructive Dilemma.
Exercise Set for Week 4: Exercise Set 4