So, umm, yea…

I still exist, despite not posting for almost a year and a half. Go. Me.

While I still intend to (some day) continue with quandle posts, for the time being I’ll be switching to talking about the work I’m doing this summer (and probably will talk a bit about most of the work I did last summer, which is very tangentially related.)

Kludging an MP3 Bookmark

Suppose you, a run of the mill Linux user, just downloaded a very long mp3 – for example a 10 hour mp3 of Cory Doctorow reading The Hacker Crackdown. Naturally you’re not going listen to this in one sitting; but, you cannot find a media player that implements bookmarking. What do you do?

Well-Definededness

In Algebra, we just finished chapter 10 of Gallian. One of the big theorems in the chapter is the First Isomorphism Theorem – and since I’m a lazy typist I’ll call it FIT from now on. (Isomorphism theorems 2 and 3 are left as exercises.) Skipping over what a group is, what a homomorphism is, what the kernel of said homomorphism is, and what normal subgroups and factors groups are (see, FIT talks about all sorts of cool stuff!), FIT says:

Suppose is a homomorphism. Then ; moreover, the map by is an isomorphism.

One of the points of the proof, since is defined on the cosets of by specifying the image of a representative, is whether or not the map is even well defined for some In particular, will taking different representatives of the coset always have the same image? It turns out that the map is indeed well defined – it’s a rather straightforward argument – but this just brings up another question:

If a map is well defined, does it have the property of well-definededness?

Yay, English!

EDIT: Fixed my accidental interspersing of for

Introduction

So I suppose I should start with the obligatory “Who the hell are you and why should I read this?” post. My name’s Geoff, I’m currently a junior year (I think… long story that I may or may not tell) undergraduate in Theoretical Math at the University of Akron.

I study math because I legitimately enjoy the subject, hard as that may be to believe if you’re not familiar with upper level mathematics. I also study computer science because I like things like programming, operating systems, and databases. Yes, I run Linux. Beyond that… we’ll see where it goes.