Latest posts tagged with #VisualAlgebra on Bluesky
#MathCoffeeSelfie from Starbucks
Working from a coffee shop due to a mysterious power outage on campus. If all goes well, I should have Chapter 6 (group extensions) of #VisualAlgebra completely finalized by the end of today.
Three actions of D₄: on itself by multiplication, on itself by conjugation, and on its subgroups by conjugation. Action graphs of each are shown.
This week, I recorded 4 new #VisualAlgebra YouTube videos on group actions. I heavily use the following concepts:
1. G-sets
2. Action graphs
3. Group switchboards
4. Fixed point tables.
Interested? I'll give you a preview here. Please share!
#MathSky 🧵👇1/16
Subgroup lattice of the symmetric group S_4 and five Cayley graphs: four on Archimedean solids and one of the Nauru graph.
Subgroup lattices of all five group of order 12, with their "towers of p-groups" colored, to illustrate the Sylow theorems.
Subgroup lattices and Cayley graphs of both semidirect products of C_5 and C_4. On the left, the lattice of D_5 appears at the bottom (it's a subgroup), but it appears at the top of the one on the right (it's a quotient).
The subgroup lattices of D_6 four times, highlighting three semidirect product decompositions, and one direct product decomposition.
New #VisualAlgebra video!
Lecture 3.2: Subgroup lattices
youtu.be/zDIsbKs16es
There are LOTS of fun pictures in here. I'm obviously biased, but I really think that this will be greatly beneficial to anyone taking or teaching abstract algebra. Check it out!
1/2 👇
Cayley graph of Aut(C7) with nodes labeled by rewirings of C7.
Cayley graphs of both nonabelian semidirect products of C5 with C4, each laid out two different ways: by rewiring edges, vs. relabeling nodes.
Cayley graphs of the four semidirect products of C8 and C2.
Cayley graph construction of the smallest nonabelian group of odd order: the semidirect product of C7 with C3.
I made two new #VisualAlgebra videos about semidirect products, that are done even before I introduce the concept of a normal subgroup. Check them out! #MathSky
Lecture 2.9: Semidirect products, intuitively
youtu.be/H_XFikkqrgg
Lecture 2.10: Examples of semidirect products
youtu.be/c2DL2Sk4-XY
Cayley graphs of the quaternion group Q_8, the dihedral group D_8, the dicyclic group Dic_8 (i.e., the generalized quatenrion group Q_{16}), and the diquaternion group DQ_8.
Cayley graph of the diquaternion group DQ_{16}, and a Cayley graph of a mystery group that's slightly different.
Two Cayley graphs (?) of mysterious group of order 32, that resemble the Cayley graph of a generalized quaternion group.
Two Cayley graphs (???) on 32 nodes, that resemble the Cayley graphs of the semidihedral and semiabelian groups.
Hey #MathSky! I just made two new #VisualAlgebra videos, and each of them has some fun group theory puzzles.
Lecture 2.7: Dicyclic and diquaternion groups
Lecture 2.8: Semidihedral and semiabelian groups
Come learn about these fun relatively unknown groups!
URL in the replies. 👇
Screenshot of my YouTube Visual Algebra playlist.
🚨🚨 #MathSky Announcement! 🚨🚨
As I'm going through and finalizing chapters in my #VisualAlgebra book, I'm recording a new set of YouTube videos in tandem. This will be more than twice as long as my existing #VisualGroupTheory playlist, with MUCH more content. I just released the first 14.
1/3 👇
I didn’t realize ChatGPT is already that good. I should use it with my ~800 page #VisualAlgebra book draft. Occasionally I find an oversight, like forgetting to say the G has to be finite. And I’m sure there are others.
Btw, any video you post that throws shade on analysis gets shown in my #VisualAlgebra classes. The students (and I) love ‘em.
It’s been a bit harder ever since Nikki Haley (on our BoD) got TikTok banned on campus as a stunt while she ran for president. 🙄
I used to post long #VisualAlgebra threads on #MathTwitter before realizing that I was actually in #TheBadPlace. I'm going to make my debut #MathSky thread today, with visuals that I've never publicly shared. (Can you guess the topic?) I'm excited to show you, and I hope you enjoy!
1/19 🧵👇
