Combinatorics. Instructor: Prof. Sunil Chandran, Department of Computer Science and Automation, IISc Bangalore.
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September 25, 2023
English
English [CC]
Description
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
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- 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
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- 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 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
About the instructor
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