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