The long, hard road to updates

So since coming back around here last week, I’ve been working on an update.

Of course, I’d be lying if I said I’d been working non-stop on an update, but I have, in fact, been working on one. I’d say I’m a solid 75% finished with it now, even though it’s (a) not going as quickly as I’d expected and (b) probably not going to be written the way I’d anticipated. Oh well; such is life, I guess.

I’m down to my last seven days of Wolfram employment, and to say I’m a sad robot is understatement of the year. I’m hoping the hustle and bustle of a new school term with new responsibilities and opportunities and excitements will curb that somewhat, but at this point, I’m not 100% convinced.

Among new things that have happened in the last week:

• FSU made office assignments for the new year. Apparently I’m staying put. As much as I’d have liked a new office (you know, since my CEILING COLLAPSED AND DESTROYED ALMOST EVERYTHING I HAD THERE(!!!)), I don’t like the hassle that comes with doing something new. I’ll already be doing enough new things; figuring out a new office situation isn’t something I want to add to that list.
• Fall schedules have been entered. I’m officially taking the third semesters of abstract algbera (field theory + categories, I think) and topology (advanced algebraic topology), as well as a course on complex manifolds (taught from an algebraic geometry perspective, I’d guess) and Riemannian manifolds. I’m excited. Sincerely.
• I’ve gotten my change of residency file 95% compiled. Monday will be the day to finish it off and submit it.
• I’ve finally started training for my new gig with Pearson. I’m less than thrilled with the progress so far. We’ll see.

Otherwise, things have been kinda the same: I’ve been doing a lot of Wolfram stuff, I’ve been taking more time away to hang with my family, and I’ve been somehow managing to not think about the nervousness I’ll invariably feel when new TA responsibilities, etc., pick up.

Things are good, I’d say, even though I’ve got a lot of things I need to start doing otherwise. I need to start reading the books potential advisers have suggested; I need to start doing more independent research; I need to start getting back in school mode.

For the first time in a really really long time, I’m enjoying being in not-school mode. I wonder if this is that changing tide I always heard so much about.

Anyway, expect a new content entry soon enough. And maybe some to follow that one. We’ll see.

Peace.

Doors closing, opening

So it’s been a hectic few days around these parts, in part because of things happening on the work front and in part because tomorrow is the first day back to school for me after a six week hiatus. It’s bittersweet, really.

By and large, the learning part of school makes me happy; I guess that’s a given since it’s a career thing for me, now. Tethered to that aspect are the things that are less-pleasant, among which are miscellaneous other duties, etc. I’ll be taking one class which, for all intents and purposes, seems like it’s going to be amazing; I’ll also be spending around 8 hours per week doing TA duties, and trying to split the remainder of my time between continuing the work I’ve been doing throughout the summer, balancing work-at-home things, and seeing about an internship that may be beginning soon.

Lots of things to keep me busy; I’m not sure I’ll necessarily be enjoying it all, though.

In other news:

I spent today being mostly idle on the math front. My plan was to have a carryover of yesterday’s supposed Algebra day since yesterday was spent mostly idle on the math front, as well. Today consisted of lots of not feeling well, running errands, and sleeping randomly. After all that subsided, I tried to work some of the exercises in Eisenbud and Harris only to be re-re-re-reminded of how important it’s going to be for me to get a good book that incorporates category theoretic ideas into some kinds of examples so I can see how to use ideas instead of just read them.

Seriously, though: I’ve read the handful of equivalent definitions of direct limits about 300,000 times, and I’ve scoured the internet to see how people respond to other people asking how to compute them, and still: I have no idea what I’m actually trying to do. I’m not sure how many times someone has to read and reread the same four pages on sheaf theory before something clicks, but I’m starting to grow anxious.

Maybe I need to start looking in other resources.

Besides that, I’ve got nothing: Failed attempts at Eisenbud/Harris solutions and lots of time spent being unmotivated. Nicht gut.

Good night, everybody.

Category Theory: Moving Up, Out

I remember my very first encounter with Category Theory.

I was in my fourth semester (a spring semester) as a master’s student: I had passed my two mandatory abstract algebra classes my first two semesters there and had passed my comprehensive exams during the Fall (my third semester). As was custom, then, I spent my third and fourth semesters taking random “advanced topics” courses aimed at potential doctoral students, and one of the sequences I took was the algebra sequence.

My first semester doctoral-level (or 7000-level as was colloquial there) algebra class was over the classification of finite simple groups and was by far the most difficult class I’d ever taken at the time. Apparently, being a student who doesn’t remotely have the sufficient background and being in a class run by a professor who has unimaginably-greater background – who teaches as if the audience consists of peers – makes for a difficult time. I squeaked out an A.

In the second semester of 7000-algebra, however, things were far less directed. Long story short, it was a potpurri of material, some from algebraic topology, some from homological algebra, and some – about 1/3 of the course, I’d say – from category theory. That was my very first exposure to an area I didn’t otherwise know existed and I remember thinking, This is the most abstract thing that’s ever been devised, and also, There’s no way this will ever be far-reaching outside the realm of mathematics.

I’ve since realized that the first assertion isn’t really true – unsurprisingly since my exposure to other areas has increased drastically since leaving there – but apparently, the second one isn’t either. To be more precise, I stumbled upon this article online which describes a number of non-math areas that have been benefiting – and will continue to benefit – from the use of category theoretic ideas.

It’s really quite amazing to see, but in and of itself is unsurprising given the fact that category theory itself was devised to provide unity among the wide variety of subdisciplines of mathematics. As a pure mathematician, I always tried to find a balance between being interested in too broad a range of topics and being too narrow with my scope; the spread of category theory invites us all to analyze that aspect of ourselves. To borrow a quote from David Spivak’s exposition (available on the arXiv),:

It is often useful to focus ones study by viewing an individual thing, or a group of things, as though it exists in isolation. However, the ability to rigorously change our point of view, seeing our object of study in a different context, often yields unexpected insights. Moreover this ability to change perspective is indispensable for effectively communicating with and learning from others. It is the relationships between things, rather than the things in and by themselves, that are responsible for generating the rich variety of phenomena we observe in the physical, informational, and mathematical worlds.

Here’s to you, category theory!

The Half-Week That Never Was

As I type this, it’s 2:45am on a Wednesday. I haven’t been around these parts since Sunday night (actually, 3:30am Monday morning), so one would think I’d have accumulated a ginormous list of professional doings to post proudly about here.

I regret to inform: That is not the case.