Uploads from Mathematical Visual Proofs

Currently Playing: Building the S3 Cayley Table

In this video, we fill out the Cayley table of the symmetric group on three letters, called S3. This set is the collection of all permutations of the set {1,2,3}, and it forms a group under permutation multiplication, which is composition. We use permutation diagrams to perform all 36 binary computations in the group and end by looking at the table using cycle decompositions of the 6 permutations. All of this is done to some driving synthwave music. This video was created for a class I am teaching on abstract algebra, but I thought it might be helpful to others learning about abstract algebra, or permutation groups. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. or join my Patreon: https://www.patreon.com/c/MathVisualProofs To see a longer, wide, high definition version of this video, check out https://youtu.be/0sMj_l32u44 If you want to see other videos combining synthwave and mathematical ideas, check out my Synthwave and Math playlist: https://youtube.com/playlist?list=PLZh9gzIvXQUsNIO0jVHE6kTkH0Q6IFJ1R&si=-QSLCX2Gfa4OsbFD If you want a good textbook for studying abstract algebra, check out this one by Tom Judson: http://abstract.ups.edu/aata/aata.html #permutations #abstractalgebra #cayleytable​ #math​​ #manim​ To learn more about animating with manim, check out: https://manim.community