By Prof. Narayanan N   |   IIT Madras
Learners enrolled: 837
We start with the finite and infinite avatars of the Pigeonhole Principle, Basic counting tools and the twelvefold way followed by compositions and partitions of integers and Stirling numbers. We then look at Inclusion exclusion and Mobius inversion followed by generating functions. We then look at Polya's theorem, graphs and conclude with a short introduction to species of structures.


PRE-REQUISITES    : Basic Mathematical Maturity expected from a Mathematics student at the level of 10+2. Familiarity with group theory will be added
advantage (not necessary).

INDUSTRY SUPPORT : TCS, Infosys, Microsoft Research, Any companies developing discrete mathematics related areas or algorithms.
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Mathematics
  • Algebra
Credit Points : 3
Level : Undergraduate
Start Date : 25 Jul 2022
End Date : 14 Oct 2022
Enrollment Ends : 08 Aug 2022
Exam Date : 30 Oct 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1 : Pigeonhole Principle

Week 2 : Basic and Bijective counting.

Week 3 : Compositions and Partitions.

Week 4 : Advanced Counting.

Week 5 : Inclusion Exclusion, Mobius Inversion.

Week 6 : Generating Functions

Week 7 : Graph theory, introduction, trees, connectivity.

Week 8 : Menger, Hall, Konig - equivalence and System of Distinct Representatives.

Week 9 : Planar graphs.

Week 10: Groups and Polya theory.

Week 11: Species of structures.

Week 12: An overview, scope and further directions.

Books and references


  1. Introductory Combinatorics 5th Edition, Richard Brualdi, Pearson.


  1. Bijective Combinatorics. Nicholas Loehr. CRC press.
  2. Enumerative combinatorics. Richard Stanley. Cambridge university press.

Instructor bio

Prof. Narayanan N

IIT Madras
My research interests are related to combinatorics, graph theory and combinatorial algebra.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 30 October 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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