#monoids #grouptheory #computerscience #abstractalgebra

What are monoids, why are they so abstract, and how do you calculate an empty product? In this video, we explain the exact purpose for each of the rules of monoids, with specific focus on the neutral element. We show many examples such as string concatenation and computer programs. And we already foreshadow the videos about group theory by looking at inverses.

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This is the very first video we ever made, for the 2021 Summer of Math Exposition. It explains monoids by stacking books on top of each other, which is really just a fancy way of concatenating strings vertically instead of horizontally ;-)

0:00 Introduction
1:30 What is a monoid?
3:36 Example: blocks
4:58 Homomorphisms
6:30 Elements are active
7:42 Example: Computer programs
11:09 Associativity
12:36 Commutativity
13:51 Why these specific rules?
16:13 The neutral element
18:30 Abstraction = power
19:30 Inverses

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