Tags » Group Theory

So I promised you symmetries...

Hello again and welcome! Following from my first post about group theory I figured I aught to give you a better overview by giving examples which will form a foundation for further study. 1,827 more words

Group Theory

Group theory: a (continually updated) summary

Hello again!

I realise that I have mentioned many things, and so this post aims to summarise what is covered in the other posts on group theory. 386 more words

Group Theory

So you want to know about a group, eh?

Not sure quite how I’m going to say this but, everything you’ve been told about maths is a lie. Maybe I should be more specific…maths is not about being a human calculator or remembering facts about numbers. 625 more words

Group Theory

Every subgroup of order 74 in a group of order 148 is normal

Every subgroup of order 74 in a group of order 148 is normal



We will prove a much general claim: if index of a subgroup is 2, then that subgroup must be normal. 72 more words

College Mathematics Corner

Starting out

“I wonder how many of these first posts look the same?” might be the sort of question a mathematician asks which others wouldn’t, or maybe it’s because of xkcd’s… 89 more words

Group Theory

Not all finitely-presented groups are fundamental groups of closed 3-manifolds

In our previous note Amalgamated products and HNN extensions (IV): Markov properties, we saw that for every and for every finitely-presented group , there exists a -dimensional closed manifold whose fundamental group is . 1,254 more words


Row Reduction Over A Field

We’re quite eager to get to applications of algebraic topology to things like machine learning (in particular, persistent homology). Even though there’s a massive amount of theory behind it (and we do plan to cover some of the theory), a lot of the actual computations boil down to working with matrices. 1,804 more words


Emi reblogged this on Pathological Handwaving.