Combinatorial Mathematics - MATH F421

Elective Course: Semester I 2025- 2026

Instructor: Dr. Yasmeen Akhtar

Audience: 3rd & 4th-year B.E. students and Mathematics Graduate students  at BITS Pilani K K Birla Goa Campus

                        Schedule: Tuesday, Thursday, 11:00-11:50 AM at A604

                                                Wednesday 8:00-8:50 AM at A604

Course Handout: Available on Quantaaws.

Evaluation: Quizzes-20%, Project-20%, Midsemester Exam-25%, Comprehensive Exam-35%

Lecture:

12/08/25 - Instructions related to the course, Basic Counting Principles, Permutation and Combination, Problems

13/08/25 - Permutations and Combinations of Multiset, Problems

14/08/25 - More Problems on Permutations and Combinations of Multiset, The Pigeonhole Principle, Problems

19/08/25 - The Pigeonhole Principle-Strong Form, Examples

20/08/25 - The Ramsey Number and problems 

21/08/25 - Generalization of Ramsey Number and problems 

22/08/25 - Last date for submitting Project Proposal

26/08/25 - Generalized Principle of Inclusion-Exclusion (GPIE), Combinations of Multiset with finite repetitions

27/08/25 - Holiday

28/08/25 - Derangement and Problems based on it

30/08/25 - (Wednesday's Schedule): Permutations with Absolute Forbidden Positions (Disjoint sub-boards), Rook polynomial

02/09/25 - Permutations with Absolute Forbidden Positions (Non-disjoint sub-boards), Problems

 03/09/25 - Permutations with Relative Forbidden Positions, Generating Permutations, Inversion Sequence 

04/09/25 - Generating combinations and r-sets, Problems

09/09/25 - Relation and its Properties, Poset

10/09/25 - Cover relation, Totally ordered set, linear extension of  poset

11/09/25 - Equivalence relation, counting equivalence relation, Some special real-valued functions on a finite poset

13/09/25 - (Tuesday's Schedule): Möbius Function, Möbius Inversion

16/09/25 - GPIE from Möbius Inversion, Counting the number of ways of placing n non-attacking rooks on an n by n board with forbidden positions using the Mobius Inversion 

17/09/25 - Classical Mobius Inversion, Catalan Numbers 

18/09/25 - Quiz 1

23/09/25 - Catalan Numbers, Problems

24/09/25 - Stirling Numbers of the second kind, Bell Numbers

25/09/25 - Stirling Numbers of the first kind, Partition Numbers

27/09/25 - (Thursday's Schedule):  Different types of partition numbers, Euler's Pentagonal Number Theorem

30/09/25 - 

01/10/25 - 

02/10/25 - Holiday

07/10/25 - Midsem Exam

14/10/25 - 

15/10/25 - 

16/10/25 - 

21/10/25 - 

22/10/25 - 

23/10/25 - 

28/10/25 - 

29/10/25 - 

30/10/25 - 

04/11/25 - 

05/11/25 - Holiday

06/11/25 - 

11/11/25 - 

12/11/25 - 

13/11/25 - 

18/11/25 - 

19/11/25 - 

20/11/25 - 

25/11/25 - 

26/11/25 - 

27/11/25 - 

10/12/25 - Comprehensive Exam