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The Combinatorics Roadmap (How to Get Started in Combinatorics)

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Tags: combinatoricsset-theorypigeonhole-principlecombinationspermutationspascals-triangleproblem-solvingdiscrete-mathematicsfactorialshigh-school-mathintroduction-to-combinatoricsbinomial-theoremmultinomial-theoremprinciple-of-inclusion-exclusionderangementsvariationsmath-olympiadring-permutation

The Combinatorics Roadmap is a collection of mini-classes covering the most basic of to the more complex combinatorics. Learning the basics of the exciting field of combinatorics. I'll walk you through the basics you need to understand in order to master combinatorics in this video. I'll give you a clear and concise road map to help you navigate this challenging and interesting field, from the fundamentals of combinatorial reasoning to diving into more complex subjects. This video is intended to give you a good foundation in combinatorics and encourage you to explore its many wonders further, regardless of whether you're a student or just an avid maths enthusiast. Contents: 0:32 Level 0 - Sets 3:08 Level 1 - Sum & Product Rules 4:40 Level 2 - Permutations 7:14 Level 3 - Variations 9:50 Level 4 - Ring Permutations 12:35 Level 5 - Generalized Permutations 14:37 Level 6 - Combinations 20:05 Level 7 - Pascal's Triangle 22:30 Level 8 - The Binomial Theorem 27:42 Level 9 - Generalized Combinations 31:05 Level 10 - The Multinomial Theorem. 32:52 Level 11 - Repeatable Permutation and Variation 34:14 Level 12 - Repeatable Combinations (Balls and Urns) 37:22 Level 13 - The Pigeonhole Principle 40:37 Level 14 - The Principle of Inclusion-Exclusion (PIE) 44:29 Level 15 - Derangements Big thanks to my dear friend @Awyyn for providing the awesome music in this video! Please check out her other works. Her tunes made the Combinatorics Roadmap even more enjoyable. 🙌

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5.1 Overall score*

113 Rank

9 Votes

4 Comments

Comments

This obviously is a long video, but it covers a lot of really cool topics and I thought it was done really well. I really like how you build in intuition about probability a very abstract idea and made it very intuitive to understand. These topics are very important. Using Pascal‘s triangle was a wonderful idea of building that intuition.Nice work.

7.5

Very good video! A good selection of core counting principles starting from the basics, tied together with a compelling organization. The concrete examples and animation flowing throughout makes this very engaging and accessible.

I might have liked a definition of “combinatorics” at the start or something to define what unites the rest of the video.

Tiny nitpick: at 16:35 the displayed “p [2] [3] [4] = p!” was confusing to parse.

Even-Tinier nitpick: some manim text animations like at 43:21 could have better made matching parts just move a little instead of completely transforming everything (manim has decent ways to fix this).

5.1

It addresses a lot of important concepts and terminologies but didn’t really connect them in an innate logical way (or not well explained), only in a semantic way. However, it for sure is very informative, just a little dry.

Audio quality is rather poor.