Discrete Mathematics - MATH F213

Elective Course: Semester II 2021- 2022

Instructors: Dr. Yasmeen Akhtar, Dr. Tarkeshwar Singh

Audience: 2nd- and 3rd-year B.E. students at BITS Pilani K K Birla Goa Campus

Tutors: Unaat Jain, Rohit Jain, Abhigyan Bajpai, Herambh Krishnaa Sundaresan

Schedule: Online via Google Meet

Lectures: Tuesday, Thursday 2-2:50 PM and Saturday 8-8:50 AM

Chamber Consultation Hour: TBA

Course Handout: Here.

Weekly schedule:

18/01/22 - Introduction, Propositional Logic, and Operators

20/01/22 - Tautology, Contradiction, Logical equivalences, Laws of logic

22/01/22 - Satisfiability, PDNF, PCNF

Lecture 1 Lecture 2 Lecture 3

25/01/22 - Quantifiers

27/01/22 - Rules of Inference

29/01/22 - Introduction to Proof, Vacuous and Trivial Proof

Lecture 4 Lecture 5 Lecture 6

01/02/22 - Direct and Indirect Proof

03/03/22 - Proof of Equivalence, Proof by Cases, Existence Proof, Counterexample

05/02/22 - Holiday

Lecture 7 Lecture 8

08/02/22 - Quiz 1

10/02/22 - Mathematical Induction

12/02/22 - Addition and Multiplication Rule for Counting

Lecture 9 Lecture 10

15/02/22 - Generalized Pigeonhole Principle, Principle of Inclusion-Exclusion (Sunstraction Rule for Counting) and Generalization

17/02/22 - Division Rule for Counting, Permutation, and Combination

19/02/22 - Binomial Theorem, Permutation, and Combination with Repetition

Lecture 11 Lecture 12 Lecture 13

22/02/22 - Constrained Repetition and Multinomial Theorem

24/02/22 - Distribution of objects into boxes (different cases)

26/02/22 - Pascal's Identity, Derangement

Lecture 14 Lecture 15 Lecture 16

01/03/22 - Sterling Numbers

03/03/22 - Quiz 2 (postponed) Catalan Numbers

05/03/22 - Linear Recurrence Relation with Constant Coefficients

Lecture 17 Lecture 18 Lecture 19

08/03/22 - Solving Linear Recurrence Relation with Constant Coefficients

12/03/22 - Midsemester exam

Lecture 20

22/03/22 onwards Prof. T. Singh will be teaching the second half.