What's a representation? An intro to modern math's magical machinery |

This video is an introduction to the representation theory of finite groups. It is pretty dense, but I did my best not to include much heavy mathematics. I'll leave some links below for some more background on several of the topics in the video. None of these are necessary to understand the video, but they're definitely helpful and a good place to branch out.

3B1B's intro to group theory:    • Group theory, abstraction, and the 19...  
3B1B's Intro to linear algebra:    • Vectors | Chapter 1, Essence of linea...  
Borcherds' representation theory (advanced):    • Representation theory: Introduction  
Quanta vid on Langlands:    • The Biggest Project in Modern Mathema...  

This video was made in large part for 3Blue1Brown's Summer of Math Exposition 2 #some2. Thanks to Grant Sanderson, James Schloss, and everyone else who helped organize it. See the main video for more information here:    • Summer of Math Exposition 2 Invitation  

Timestamps:
0:00 - Introduction
2:27 - Groups
4:54 - GL(V)
5:54 - bird
6:01 - Linear algebra crash course
8:48 - Cyclic group representation
12:20 - Symmetric group cycles
14:15 - A5 representation
18:25 - Summary

Credits:
Thumbnail has pics from nature and thewalrus (illustrator Jonathan Dyck)
Images of cubes and dodecahedron come from robertlovespi, who has an amazing site about tons of polyhedra
bird:    • Crow searching for a nut I'd hidden a...  
end credits bird gif from user arashigul on gifer