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Last updated:

September 25, 2023

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FREE

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Description

Combinatorics. Instructor: Prof. Sunil Chandran, Department of Computer Science and Automation, IISc Bangalore.

This course covers the topics typically covered in a first level combinatorics course. It introduces the elementary notions in combinatorics and presents the most elementary techniques in combinatorics - pigeonhole principle, inclusion-exclusion principle, recurrence relations and generating functions. (from nptel.ac.in)

Course Curriculum

    • Lecture 01 – Pigeon Hole Principle, Part 1 Unlimited
    • Lecture 02 – Pigeonhole Principle, Part 2 Unlimited
    • Lecture 03 – Pigeonhole Principle, Part 3 Unlimited
    • Lecture 04 – Pigeonhole Principle, Part 4 Unlimited
    • Lecture 05 – Elementary Concepts and Basic Counting Principles Unlimited
    • Lecture 06 – Elementary Concepts; Binomial Theorem; Bijective Proofs Part 1 Unlimited
    • Lecture 07 – Bijective Proofs Part 2 Unlimited
    • Lecture 08 – Bijective Proofs Part 3; Properties of Binomial Coefficients; Combinatorial Identities Unlimited
    • Lecture 09 – Combinatorial Identities Part 2; Permutations of Multisets Part 1 Unlimited
    • Lecture 10 – Permutations of Multisets Part 2 Unlimited
    • Lecture 11 – Multinomial Theorem, Combinations of Multisets Part 1 Unlimited
    • Lecture 12 – Combinations of Multisets Part 2 Unlimited
    • Lecture 13 – Combinations of Multisets Part 3, Bounds for Binomial Coefficients Unlimited
    • Lecture 14 – Stirling’s Formula, Generalization of Binomial Coefficients Part 1 Unlimited
    • Lecture 15 – Generalization of Binomial Coefficients Part 2 Unlimited
    • Lecture 16 – Generalization of Binomial Coefficients Part 3, Double Counting Part 1 Unlimited
    • Lecture 17 – Double Counting Part 1 Unlimited
    • Lecture 18 – Hall’s Theorem for Regular Bipartite Graphs; Inclusion-Exclusion Principle Part 1 Unlimited
    • Lecture 19 – Inclusion-Exclusion Principle Part 2 Unlimited
    • Lecture 20 – Inclusion-Exclusion Principle Part 3 Unlimited
    • Lecture 21 – Inclusion-Exclusion Principle Part 4 Unlimited
    • Lecture 22 – Inclusion-Exclusion Principle Part 5 Unlimited
    • Lecture 23 – Recurrence Relations Part 1 Unlimited
    • Lecture 24 – Recurrence Relations Part 2 Unlimited
    • Lecture 25 – Recurrence Relations Part 3 Unlimited
    • Lecture 26 – Recurrence Relations Part 4 Unlimited
    • Lecture 27 – Recurrence Relations Part 5 Unlimited
    • Lecture 28 – Generating Functions Part 1 Unlimited
    • Lecture 29 – Generating Functions Part 2 Unlimited
    • Lecture 30 – Solving Recurrence Relations using Generating Functions Part 1 Unlimited
    • Lecture 31 – Solving Recurrence Relations using Generating Functions Part 2 Unlimited
    • Lecture 32 – Exponential Generating Functions Part 1 Unlimited
    • Lecture 33 – Exponential Generating Functions Part 2, Partition Number Part 1 Unlimited
    • Lecture 34 – Partition Number Part 2 Unlimited
    • Lecture 35 – Partition Number Part 3 Unlimited
    • Lecture 35 – Partition Number Part 3 Unlimited
    • Lecture 36 – Partition Number Part 4, Catalan Numbers Part 1 Unlimited
    • Lecture 37 – Catalan Numbers Part 2 Unlimited
    • Lecture 38 – Catalan Numbers Part 3, Stirling Numbers of the Second Kind Unlimited
    • Lecture 39 – Difference Sequences Unlimited
    • Lecture 40 – Stirling Numbers Unlimited
    • Lecture 41 – Summary Unlimited

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