Discrete Mathematics - MATH F213
Mathematics Core Course: Semester I 2021- 2022
Instructors: Dr. Yasmeen Akhtar, Dr. Tarkeshwar Singh
Audience: 2nd-, 3rd-year B.E. and 2nd-year M.Sc. students at BITS Pilani K K Birla Goa Campus
Tutors: Aneesha Jain, Shruti Rastogi, Sarthak Krishna
Schedule: Online via Google Classroom on Meet
Lectures: Monday, Wednesday, Friday 4 PM-4:50 PM
Tutorial: Thursday 2 PM-2:50 PM
Chamber Consultation Hour: Tuesday 4 PM - 5 PM
Course Handout: Here.
Weekly schedule:
23/08/21 - Introduction, Propositional Logic, Operators: Negation, Conjunction, Disjunction, Conditional, Biconditional
25/08/21 - Tautology, Contradiction, Logical equivalences, Laws of logic
26/08/21 - Satisfiability, Normal Forms: PDNF, PCNF
27/08/21 - Predicate Logic: Quantifiers
Lecture 1 Lecture 2 Lecture 3 Lecture 4
30/08/21 - Holiday
01/09/21 - Argument, Rules of Inference
02/09/21 - Tutorial
03/09/21 - Rules of inference for quantified statements
Assignment 1 Lecture 5 Lecture 6
06/09/21 - Introduction to Proof: Vacuous, Trivial, Direct
08/09/21 - Indirect Proof: Contraposition, Contradiction
09/09/21 - Tutorial
10/09/21 - Holiday
Assignment 2 Lecture 7 Lecture 8
13/09/21 - Proof of equivalence, Proof by cases, Existence and Uniqueness proof, Counterexample
15/09/21 - Mathematical Induction, Strong Induction, Structural Induction
16/09/21 - Tutorial
17/09/21 - Counting: Sum Rule, Product Rule, The Pigeonhole Principle
Assignment 3 Lecture 9 Lecture 10 Lecture 11
20/09/21 - The Principle of Inclusion-Exclusion (GPIE)
22/09/21 - Permutations and Combinations
23/09/21 - Tutorial
24/09/21 - Permutations and Combinations with Repetition Quiz I (Postponed)
Assignment 4 Lecture 12 Lecture 13 Lecture 14
27/09/21 - Constrained Repetitions, Partitions, Binomial Theorem
29/09/21 - Vandermonde's Identity, Pascal's Identity, Newton's Binomial Theorem
30/09/21 - Tutorial
01/10/21 - Multinomial Theorem, Derangement
Assignment 5 Lecture 15 Lecture 16 Lecture 17
04/10/21 - Catalan Numbers
06/10/21 - The signless Stirling number of the first kind (Stirling cycle number)
07/10/21 - Tutorial
08/10/21 - The Stirling number of the second kind
Assignment 6 Lecture 18 Lecture 19 Lecture 20
11/10/21- Quiz I
13/10/2021 onwards - Dr. Tarkeshwar Singh