Discrete Mathematics - MATH F213

Mathematics Core Course: Semester I 2022- 2023

Instructor: Dr. Yasmeen Akhtar

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

Tutors: Pronoma Banerjee, Jishnu Warrier, Tanishq Joshi

Lectures: Monday, Wednesday, and Friday 10-10:50 AM at A604

Tutorial: Thursday 8-8:50 AM at A604

Course Handout: Here

Schedule:

01/09/22 - Tutorial 1: Introduction, Propositional Logic, and Operators

02/09/22 - Tautology, Contradiction, Logical equivalences, Laws of logic, Logical Dual

05/09/22 -Satisfiability, Normal Forms: DNF, CNF, PDNF, and PCNF

07/09/22 - Quantifiers: Universal, Existential, Uniqueness

08/09/22 - Tutorial 2

09/09/22 - Valid argument, Fallacy, Rules of Inference

12/09/22 - Institute Holiday

14/09/22 - Introduction to Proof, Vacuous, Trivial, Direct, and Indirect proofs

15/09/22 - Tutorial 3

16/09/22 - Proof of Equivalence, Proof by Cases, Existence Proof

17/09/22 - Extra Class: Proof of Uniqueness, Counterexample, Mathematical Induction, Strong Induction, Addition and Multiplication Rules for Counting

19/09/22 - rescheduled

21/09/22 - rescheduled

22/09/22 - Tutorial 4

23/09/22 - rescheduled

26/09/22 - rescheduled

28/09/22 - rescheduled

29/09/22 - Tutorial 5

30/09/22 - rescheduled

03/10/22 - Subtraction Rule and Division Rules for Counting, Generalized Principle of Inclusion-Exclusion, Generalized Pigeonhole Principle, Permutation and Combination, Binomial Theorem

05/10/22 - Holiday

06/10/22 - Tutorial 6-Quiz 1

07/10/22 - Multinomial Theorem, Pascal's Identity, Vandermonde's Identity, Examples

10/10/22 - Example, Permutations and Combinations with Repetition, Permutations with Constrained Repetition, The signless Stirling Number of first kid, Stirling Number of second kind

12/10/22 - Distribution of Objects into Boxes (4 cases)

13/10/22 - Tutorial 7

14/10/22 - Bell Numbers, Derangement, Catalan Numbers (Recurrence Formula)

17/10/22 - Quiz 2

19/10/22 - Catalan Numbers (Explicit Formula), Recurrence relation Examples

20/10/22 - Tutorial 8

21/10/22 - Solving Linear Homogeneous Recurrence Relation with Constant Coefficients (degree 2)

24/10/22 - Holiday

26/10/22 - Solving Linear Homogeneous Recurrence Relation with Constant Coefficients (degree k)

27/10/22 - Solving Linear Nonhomogeneous Recurrence Relation with Constant Coefficients

28/10/22 - Solving Recurrence Relation using Generating Function

01/11/22 - Midterm Exam

07/11/22 - Method of Telescoping Sums, Divide and Conquer Algorithm

09/11/22 - Solving Nonlinear Recurrence Relations

10/11/22 - Tutorial 9

11/11/22 - Relations, Properties

14/11/22 - Equivalence relation, representing the relation

16/11/22 - Operations on binary relations

17/11/22 - Tutorial 10

18/11/22 - Waves (No class)

21/11/22 - Non-Instructional Day (No class)

23/11/22 - Partial Ordering, Hasse Diagram

24/11/22 - Tutorial 11

25/11/22 - Lattice, Complete Lattice

26/11/22 - Extra Class: Lattice as algebra, Sub-lattice, bounded lattice, Dual Poset

28/11/22 - Dual lattice, Distributive Lattice and characterization

30/11/22 - Complemented Lattice

01/12/22 - Tutorial 12

02/12/22 - Topological Sorting, Boolean Algebra

05/12/22 - Boolean function, Laws of Boolean Algebra, Boolean Operators, Dual of Boolean expression

07/12/22 - minterms, maxterms, Sum-of-products expansion, product-of-sum expansion, Functionally complete

set of operators, NAND and NOR operators

08/12/22 - Tutorial 13

09/12/22 - Logic gates, Combinatorial Circuit Design

15/12/22 - Tutorial 14

23/12/22 - Comprehensive Exam