Top Tweets for #VisualAlgebra
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!
π§΅π1/16
New #VisualAlgebra video!
Lecture 3.2: Subgroup lattices
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, and please share!
1/2 π(URL below)
I made two new #VisualAlgebra videos about semidirect products, that are done even before I introduce the concept of a normal subgroup.
Lecture 2.9: Semidirect products, intuitively
https://t.co/QQ3GnA4tN5
Lecture 2.10: Examples of semidirect products
https://t.co/Ym049Yp0JR
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. π
π¨π¨ #MathTwitter Announcement! π¨π¨
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.
1/3 π
I haven't posted a #VisualAlgebra thread in a while. I've made a bunch of never-before-seen visuals on algebraic number theory, and I'm really excited to share them with you!
1/nπ§΅π
If you want to learn more, and explore hundreds of other colorful visuals of algebraic concepts, check out my #VisualAlgebra website:
https://t.co/WhG6aVkdaC
Feel free to share, to show others the beauty of actions & G-sets, which many people, sadly, never get to see.
22/22
If you want to see the entire exam, you can find it here:
https://t.co/bJYBjPNJGw
If you want to see my course materials, such as slides, HW, and all 18 #VisualAlgebra exams I've given, they're all here:
https://t.co/WhG6aVkdaC
Enjoy!
10/10
And many of these are deeply insightful for holistically understanding groups, rings, and fields.
#VisualAlgebra isn't "instead" of the classic material, it's IN ADDITION to.
Here's one last question from my exam; I like this style and have hundreds just like this.
9/10
There are a few more parts of this question; see below. This problem CANNOT be done purely algebraically.
In other words, #VisualAlgebra isn't just a pleasing way to see things. There are TONS of questions I can ask that are INACCESSIBLE from the standard curriculum.
8/10
I want to share some fun unique problems from my Graduate #VisualAlgebra Final Exam yesterday.
This first one involves quotients of the Gaussian integers. Note how one quotient has order 10, and the other has order 13.
What does this tell us about irreducibility?
1/10
I really like how this #VisualAlgebra exam turned out. Here's my favorite problem, which shows the subgroup lattice of a finite simple group of order 2,588,772, and its 1,058,074 subgroups.
The full exam is here:
https://t.co/w3ZUdz4Ysf
Just finished Chapter 7 of #VisualAlgebra this evening (or a very rough draft of it). Imported it back into the main doc, and hit compile...553 pages!
I debating stopping here, but I think I'll write one more chapter, on Galois Theory. Too much rich material to pass up!
Next up: ring theory! Even #VisualAlgebra enthusiasts have said that rings aren't an inherently visual subject.
I disagree!
You'll see visual approaches that I've literally never shown anyone before.
6/7 W
At this point, I got a phone call and had to abruptly end class. Which brings me to the Ξ΅>0 that I promised would make an appearance this week.
I cashed in a hoard of male privilege points to make it to my in-person undergraduate #VisualAlgebra class just 8 hours later.
5/10 W
And that's all for today, so now it's time for our poll!
Which one of these British #VisualAlgebra terms is the bloody worst?
6/6 M
We began Wed. with a Cayley diagram of A_5=<(12345),(12)(34)> on a truncated icosahedron. Which reminds me: be on the lookout for some nearly 20-year-old never-before-seen artistic visuals of A_5 in the Forward to my #VisualAlgebra book...
1/18 Wed π§΅βοΈπ
Here's the Klein 4-group, our first example. I'm going *a lot* faster than I do in undergrad #VisualAlgebra, b/c everyone in this class has already taken at least one full semester of algebra. The 1st week is just getting up to speed w/ Cayley graphs & lots of examples.
2/8 W
#Week1 of #GraduateVisualAlgebra in the books! As promised in my ugrad #VisualAlgebra meta-thread (https://t.co/ymz8DObloI), I'll post summaries for each day -- LOTS of never-before-seen materials!
We'll return to Felix & his topological πΌ later in the class.
1/8 Wed π§΅π
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!ππ§΅
...is learning the Sylow theorems (!) and recently said:
"I wish there were a way to visualize what was going on..."
So, en route to Florida, is an (almost) camera-ready copy of the first 5 chapters of #VisualAlgebra -- 353 pages with 356 figures.
He's going to LOVE this.
2/2
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