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Now that my #VisualAlgebra class is in the books, I want to post a long "meta thread" of all 16 weekly threads, with daily summaries. Here's my entire class, including lectures, HW, & exams, in one convenient place.
And stayed tuned for some surprise announcements below!👇🧵
And stayed tuned for some surprise announcements below!👇🧵
We started #Week1 of #VisualAlgebra with a few quotes from "A Mathematician's Apology" on the beauty of mathematics, and then saw Cayley diagrams for the symmetries of the rectangle and triangle.
In #Week2 of #VisualAlgebra, we explored the Rubik's cube, more Cayley diagrams, group presentations, the impossibility of the word & halting problems, and we classified all frieze groups.
We started #Week11 of #VisualAlgebra with a new diagram of one of the isomorphism theorems. I made this over spring break. The concept is due to Douglas Hofstadter (author of "Gödel, Escher, Bach"), who calls this a "pizza diagram".
1/14 Mon 🧵👇
1/14 Mon 🧵👇
Though we constructed semidirect products visually last week, we haven't yet seen the algebraic definition. On Friday, we saw inner automorphisms, which was the last step we needed.
Recall the analogy for Aâ‹ŠB:
A = automorphism, B = "balloon".
2/14 M
Recall the analogy for Aâ‹ŠB:
A = automorphism, B = "balloon".
2/14 M
Next, we asked when a group G is isomorphic to a direct product or semidirect product of its subgroups, N & H.
Here are two examples of groups that we are very familiar with.
3/14 M
Here are two examples of groups that we are very familiar with.
3/14 M
