This week I posted a paper which I basically wrote during my first couple years of graduate school to the arXiv. You can find the preprint "A partition formula from idempotents" at https://arxiv.org/abs/2308.10177.

I feel a bit conflicted about this paper. Even after posting it I'm not sure how interesting it is. I showed the formula obtained therein to several people, including my advisor, while I was in grad school and people seemed generally unsure what to make of it.

Partition numbers are not something I ever studied much. My impression is that there is neither a known elementary formula nor a proof that one cannot exist. I'm not even sure if there is a rigorous, accepted definition of what would constitute a closed-form elementary formula in this context, since lots of fun can be had in summing over neat sets as in this paper.

#combinatorics #RepresentationTheory #AbstractAlgebra #algebra #NumberTheory

#Mechanical #Circuits

As an #EE, I take pride in the fact that, although #ME came before us and #CE before them, much of the #engineering formalism arose in the 19th Century in the electrical context. Much of engineering theories are shared between EE, ME, and CE, and at the core is #VectorCalculus and #AbstractAlgebra. This video shows one such connection.

https://youtu.be/Zv9Q7ih48Uc

The LOOPS'23 conference on #loops and #quasigroups just concluded. There were lots of great talks, great Polish food, and great people. This palace in Będlewo, Poland was a neat venue at which to study #AbstractAlgebra!

#conferences #UniversalAlgebra #math #combinatorics

Since I have a fair amount of work from before this venture into social media, I'll share some older things I did sometimes.

My first single-author paper was about multiplayer versions of rock-paper-scissors. You can find a copy on arXiv (https://arxiv.org/abs/1903.07252) which is pretty similar to the version published in the journal Algebra Universalis.

I had the idea for this paper when I was stranded in #Yosemite national park for a month in 2017 after I finished my bachelor's degree. I wanted to explain to my non-mathy friends that I was into #UniversalAlgebra and this is what I came up with. There are a lot of connections with tournaments from #GraphTheory. You can find videos of me talking about this on YouTube too.

#math #combinatorics #algebra #AbstractAlgebra

Évariste Galois was a french mathematician who, as a teenager, solved a 350-year-old problem regarding the condition necessary for a polynomial to be solvable by radicals. His work laid a foundation for a major branch of abstract algebra called Galois theory.

#onthisday in 1832 Galois wrote to a friend accurately predicting that he would die in a duel taking place the next morning. The duel was likely over a woman. In his final letter, Galois describes his work in mathematics and closed with, "Eventually there will be, I hope, some people who will find it profitable to decipher this mess." He was only 20 years old at his death.

#math #galois #abstractalgebra

References
--------------
[1] "Évariste Galois", https://mathshistory.st-andrews.ac.uk/Biographies/Galois

I haven't posted here in so long so let me make a long post about universal side divisors and a generalization of them I'm calling universal side ideals. Some of this I wrote down in a document I made to compile my thoughts on it.

This thread is going to assume that the reader is familiar with basic ring theory. We will have all of the rings discussed here have an identity element. We will focus on commutative rings to make working with ideals much simpler.

Hashtags:
#Algebra #RingTheory #Ring #AbstractAlgebra

1/

Does someone have a more comprehensive version of this "Algebra Ladder"? https://locallytrivial.com/posts/algebra-ladder/

#algebra #mathematics #abstractalgebra

Very good introduction to abstract algebra. Just one remark: why don't such guides cover categories?

https://www.youtube.com/watch?v=IP7nW_hKB7I&list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6

#math #grouptheory #abstractalgebra

#TheMetalDogArticleList
#bravewords.co
ABSTRAKT ALGEBRA Feat. CANDLEMASS, KING DIAMOND Members See Self-Titled Debut Reissued; Includes Three Bonus Tracks
Abstrakt Algebra's highly sought after self-titled debut album has been remastered and reissued featuring three bonus tracks.
https://bravewords.com/news/abstrakt-algebra-feat-candlemass-king-diamond-members-see-self-titled-debut-reissued-includes-three-bonus-tracks

Abstrakt Algebra lineup:

#LeifEdling - Bass
#MatsLeven - Vocals
#MikeWead - Guitar
#SimonJohansson - Guitar
#JejoPerkovic - Drums

#AbstractAlgebra #Candlemass #KingDiamond #metal

I really only have a cursory understanding of the broad strokes of foundational #mathematics - like I did my undergrad #RealAnalysis and #AbstractAlgebra stint but I didn't get to take #Topology and while the joy of getting to engage with #Mathstodon is so real it just makes me wish I could even figure out how to go to #GraduateSchool because #Algebra gives me so much joy, but I'm pretty sure my grades aren't good enough even if I could #ExecutiveFunction some applications. It hurts.

@gramix

Sorry, I'll hijack this post for just a second and add: if anyone can #recommend a good introductory #textbook or online resource for #AbstractAlgebra (say around the 1st year grad level), I'd like to hear it! I've been wanting to dive in for years now.

Good morning! Anyone have cool #Algebra (specifically #AbstractAlgebra ) facts they want to share?

Hey everyone!

My name is Jesse, and I am an undergraduate student of #Mathematics and #ComputerScience. I really enjoy #Algebra the most out of the #math disciplines I've studied. I mainly self-taught myself a good portion of topics from a first year semester of #AbstractAlgebra (#Groups, #Rings, #Fields, and some basics of #GaloisTheory ), I plan to take a #RingTheory course next semester, and I am also trying to learn #UniversalAlgebra currently on the side. Glad to be here!

#introduction

following intro up with some hashtags

Things I do actively!

Programming: #csharp #fsharp #functionalprogramming #idris #clojure #typescript
Gamedev: #bitsy #twine #interactivefiction #pico8 #roguelike #rotjs
Music: #guitar #lute #earlymusic #mbira #livecoding #sonicpi #dungeonsynth

Interests!
Math: #categorytheory #logic #tesselations #theoreticalcomputerscience #polyhedra #abstractalgebra
Nature #ferns #fungi #slimemold #lichen #invertebrates
Other: #bicycling #swordandsorcery

It's been a while since I was excited to read a #mathematics textbook. Yesterday I bought this book from a thrift store. The book is excellently written and helps make #AbstractAlgebra seem more fun and accessible while keeping mathematical rigour. It also includes a great, short history of modern algebra in the first chapter. #math #maths #ModernAlgebra