Monoids | Group theory episode 1
#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. Please support our channel on Patreon, and get early access to new videos: https://www.patreon.com/user?u=86649007 We only have a single link for you today, and it may look familiar: [AA1] • What is a monoid? | #SoME1 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 This video is published under a CC Attribution license ( https://creativecommons.org/licenses/... )
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