#VisualAlgebra
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visualalgebra.bsky.social
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
Three actions of D₄: on itself by multiplication, on itself by conjugation, and on its subgroups by conjugation. Action graphs of each are shown.
March 22, 2025 at 9:24 PM
livewildly.bsky.social
"Can I show you what I'm proudest of?"

~ Dolly right now, probably
Matt Macauley @VisualAlgebra My 7-year-old daughter heard me say that Dolly Parton died, and got visibly very sad. I was surprised she even knew that name. "You know Dolly Parton?" In the sweetest timid voice, she replied: "Well, I don't _know_ know her. But she sent me books."
August 27, 2026 at 10:06 PM
visualalgebra.bsky.social
🚨🚨 #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 👇
Screenshot of my YouTube Visual Algebra playlist.
December 29, 2024 at 6:45 PM
visualalgebra.bsky.social
My 7-year-old made her first Cayley graph and Cayley table today! And she LOVED it! At 9pm, she was too excited to go to sleep…”but I just want to do more algebra!” 🥰 #MathSky #VisualAlgebra
Bird’s eye view of my 7-year-old daughter drawing a Cayley graph of the Klein 4-group on an iPad. Cayley graph and Cayley table of the Klein 4-group on an iPad, with some of it in a 7-year-old’s handwriting
June 3, 2026 at 3:29 AM
visualalgebra.bsky.social
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.
#MathCoffeeSelfie from Starbucks
June 15, 2025 at 6:02 PM
visualalgebra.bsky.social
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 🧵👇
a woman is sitting on a couch in front of a wall that says `` welcome ! everything is fine . ''
Alt: "Everything is Fine" opening scene from NBC's "The Good Place", with Kristen Bell.
media.tenor.com
November 23, 2024 at 5:08 PM
tienchihmath.bsky.social
Courtesy of @visualalgebra who sadly hasn’t joined us yet.
Kefir grains in water in jar with coffee filter lid.
April 6, 2024 at 11:50 PM
visualalgebra.bsky.social
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 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.
January 18, 2025 at 7:57 PM
visualalgebra.bsky.social
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. 👇
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.
December 31, 2024 at 7:43 PM
visualalgebra.bsky.social
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 👇
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.
February 1, 2025 at 5:44 PM
visualalgebra.bsky.social
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.
November 29, 2024 at 3:03 PM
visualalgebra.bsky.social
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. 🙄
November 28, 2024 at 2:06 AM
othesharon.bsky.social
This guy seems to have lots of series on algebraic topics from a visual perspective, which might be good for your needs: www.youtube.com/@ProfessorMa...
I haven't watched the lectures but liked the original visual group theory notes from a while ago.
Professor Macauley
Coming in 2026: new book on Visual Algebra! I am recording on a new set of videos to go along with it. For more details, see: https://www.math.clemson.edu/~macaule/visualalgebra/
www.youtube.com
October 24, 2025 at 2:42 AM