Mauro Artigiani · @m_artigiani
264 followers · 686 posts · Server mathstodon.xyz

What are good references for beyond the introduction? @ProfKinyon?

#math #grouptheory

Last updated 1 year ago

David Meyer · @dmm
280 followers · 704 posts · Server mathstodon.xyz

More older notes rehabilitation, this time on group theory.

My notes are here: davidmeyer.github.io/qc/groups. The LaTeX source is here: overleaf.com/read/xjmnmzvrgsfk. As always, questions/comments/corrections/* are greatly appreciated.

#texlatex #firstisomorphismtheorem #grouptheory #maths #math

Last updated 1 year ago

David Meyer · @dmm
270 followers · 692 posts · Server mathstodon.xyz

One of my favorite theorems in all of group theory is the beautiful Cayley's Theorem, which is named in honor of British mathematician and lawyer Arthur Cayley. Cayley was born 202 years ago.

Cayley was the first person to define the concept of a group in the modern (and general) way, that is, as a set with a binary operation satisfying certain laws [1]. Before Cayley when mathematicians talked about "groups" they meant permutation groups.

Cayley had many other mathematical accomplishments. For example, Cayley postulated the Cayley–Hamilton Theorem, which states that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3 [2]. Cayley graphs and Cayley tables are also named in his honor.

A few of my notes on Cayley and Cayley's Theorem are here: davidmeyer.github.io/qc/cayley. The LaTeX source is here: overleaf.com/read/nbfyqkwsfmyc.

As always, questions/comments/corrections/* greatly appreciated.

References
--------------
[1] "Arthur Cayley", mathshistory.st-andrews.ac.uk/

[2] "Cayley–Hamilton theorem", en.wikipedia.org/wiki/Cayley%E

#cayleystheorem #grouptheory #maths #math #onthisday

Last updated 1 year ago

Markus Redeker · @mrdk
65 followers · 704 posts · Server mathstodon.xyz

@j2kun So addition and negation, when operating on the 𝑛-bit integers, generate the dihedral group (en.wikipedia.org/wiki/Dihedral) that expresses the symmetries of a \(2^{n-1}\)-gon.

I didn't think of this before. 😃

#grouptheory

Last updated 1 year ago

· @mdrslmr
1 followers · 9 posts · Server qoto.org
Andrew Shields · @AndrewShields
88 followers · 908 posts · Server mas.to
zerology · @zerology
70 followers · 373 posts · Server bayes.club

Ah!
Jamie Mulholland of Simon Fraser University, the one with the book "Permutation Puzzles, A Mathematical Perspective", has the lecture about that topic online!

youtube.com/playlist?list=PLKX

#grouptheory #groups #math #puzzles

Last updated 2 years ago

Jencel Panic · @abuseofnotation
302 followers · 372 posts · Server mathstodon.xyz

From Wikipedia:
"Any group G is the homomorphic image of some free group F"
en.wikipedia.org/wiki/Free_gro
AFAIK the reverse is true as well (provided that you only look at )

Something like:
"If you have a set S and a group F, such that any other group that has S as its set of generators is a homomorphic image of F, then F is the free group for the set S"

#grouptheory #categorytheory

Last updated 2 years ago

David Meyer · @dmm
181 followers · 308 posts · Server mathstodon.xyz

I've been trying to draw this in an easy to look at way. This is what I came up with.

My notes are here: davidmeyer.github.io/qc/linear

As always, questions/comments/corrections/* greatly appreciated.

#grouptheory #linearalgebra

Last updated 2 years ago

David Meyer · @dmm
181 followers · 307 posts · Server mathstodon.xyz

I've been working a bit on some notes about the relationship between linear maps and group homomorphism, as well as how matrices induce linear maps.

My (nascent) notes are here: davidmeyer.github.io/qc/linear.

As always, questions/comments/corrections/* greatly appreciated.

#grouptheory #linearalgebra #math

Last updated 2 years ago

Adz · @adz
1 followers · 1 posts · Server mathstodon.xyz

A weird thing: For considering \( (\mathbb Q, +) \) as a group, one must consider the knowledge of the whole operations \( +,-,*,\div \) since one can say that 1 has just the inverse -1 and that \( 1-\frac{2}{2} \neq 0\), but then one would be thinking about \( \mathbb Q \) as a weird alphabet.

#grouptheory

Last updated 2 years ago

Seth Axen 🪓 :julia: · @sethaxen
716 followers · 498 posts · Server bayes.club

I wrote a blog post on how to work out the injectivity radii of the unitary groups. If you like getting results in differential geometry and group theory with (mostly) just linear algebra, this one's for you! sethaxen.com/blog/2023/02/the-

#diffgeo #grouptheory #linearalgebra

Last updated 2 years ago

JordiGH · @JordiGH
826 followers · 21616 posts · Server mathstodon.xyz

Anyone know anything about solving a 7x7x7 Rubik's cube?

I've got three centres down and I am looking for a hint (and just a hint!) if this is on the right track.

If I should be doing something else, I would appreciate a gentle nudge in another directions.

#grouptheory #rubikscube

Last updated 2 years ago

Jencel Panic · @abuseofnotation
245 followers · 52 posts · Server mathstodon.xyz

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

youtube.com/watch?v=IP7nW_hKB7

#abstractalgebra #grouptheory #math

Last updated 2 years ago

· @crsnq
19 followers · 65 posts · Server mathstodon.xyz

Relational PK-Nets for Transformational Music Analysis
by Alexandre Popoff, Moreno Andreatta, Andree Ehresmann
arxiv.org/abs/1611.02249

#grouptheory #musictheory #categorytheory

Last updated 2 years ago

egri-nagy · @egrinagy
10 followers · 17 posts · Server mathstodon.xyz
Adel Ardalan · @adel
18 followers · 4 posts · Server neuromatch.social


I am a postdoc at the Princeton Neuroscience Institute, working with Tim Buschman and my brilliant lab mates on transformational geometry in the brain. We ask what are various classes of transformations brains utilize to compute for different tasks, in different contexts and with different objectives. Our main tools consist of linear algebra, differential geometry and group theory. 📐

#introduction #neuroscience #workingmemory #grouptheory #braingeometry #geometry

Last updated 2 years ago

Holly A. Gultiano · @axoaxonic
15 followers · 64 posts · Server mathstodon.xyz

There's actually not much on used for the same, all I could find in a (brief) search was the defunct International Society for Group Theory in Cognitive Science

web.archive.org/web/2017061821

the only name i recognize on there are Michael Leyton, and Jean Petitot (who uses things like for neurogeometry). Eloise Carlton's work seems cool: sciencedirect.com/science/arti "Psychologically simple motions as geodesic paths I. Asymmetric objects"

#contactgeometry #grouptheory

Last updated 2 years ago

Jacob Something · @jkanev
34 followers · 27 posts · Server fediscience.org

Playing with a Rubik's Cube I noticed —

when starting at a certain state, doing a few twists and repeating these over and over again, you will allways come back to the state you started in.

I'm not sure whether this is interesting or trivial. Is this provable?

#howtosurviveboringmeetings #grouptheory #cube #rubiks

Last updated 2 years ago

Hi! I'm Null (they/them), a , , and and nerd. I am a bit of a bard (in the jack-of-all-trades sense, the musical sense, the cheery Wandersong bard personality sense, the preferred D&D class sense, among probably other senses). My current interests include , , , , , , , , , , .

#musictheory #accessibility #puzzlehunts #indiegames #linguistics #sushi #calligraphy #cartoons #origami #functionalprogramming #grouptheory #programming #math #musician #digifu #gamedev #trans #nonbinary #introduction

Last updated 2 years ago