So, to summarize the direction of my most recent mathematical endeavors: I woke up and decided that part of my aspiration was to become a geometric topologist, and I did that despite the fact that topology is (far and away) my worst subject.
That sounds precisely as terrible as it probably is.
Welp, I haven’t been around these parts in a bit. That’s not to say I haven’t been working, though; I’ve just been working through things that don’t necessarily make good reading…
…like math….
Okay, so maybe that’s not entirely true. I have, however, been spending a lot of time on just a couple projects for my advisors and so there hasn’t been an abundance of topics to post about here. I think I’m getting to a point, though, where I can start posting some things here and maybe use that to reconcile the fact that I can’t understand most things I read, etc. We’ll see.
So yea…the semester’s over. It turned out not to be a terrible one for me in the end despite being pretty terrible throughout. The upshot: I managed a 4.0 that semester and ended up with advisors. That’s a victory for sure.
I’ll do my best to come back around these parts in the next day or two and post something of substance. I’d like to try to do some sort of expositing on geometric topology things (foliations, laminations, universal circles) and maybe some Clifford things too; I’d also like to attempt to reconcile my previous goal of learning how to do things from Hatcher.
Maybe I can do all of the above. 🙂
Until next time….
Today is the first day of the eighth week of the semester.
The middle of the semester was officially last Friday.
Some people may read that and deduce that it’s all downhill from here. Any time I hear that phrase to describe midterm, I’m always a bit blown away. Really, it makes me wonder: Is this what downhill feels like?
I really hope there’s more to it than that. Heh.
Anyway, so here’s the usual rundown:
So, I said all that to say: (a) I still exist. (b) Life is hectic. (c) I’m not sure when I’ll get around to posting more of Hatcher 2.1, but I’ll probably be moving on to Hatcher 2.2 here in about…30 seconds. Also, (d) I really need some down-time. And a haircut. And a drink.
I really need a drink.
Goodnight, Monday.
Tomorrow is Day 1 of Week 7.
You thought I’d stopped counting, didn’t you?
Today, I posted a couple more solutions from Hatcher. I also got the okay from Dr. Petersen on my poster for Math Fun Day. I’ll probably post a .pdf image of the poster as the big day gets closer.
For now, I’m going to come study some Riemannian Geometry: I have to (very soon) pick a topic for a presentation in that class, and so it’s getting more and more necessary that make sure I know what’s going on now. Maybe I’ll surprise myself and know a lot.
I don’t expect to surprise myself. 😛
I’m about to have to get ready to meet some friends, but just FYI: I’ve added a couple new Hatcher solutions from section 2.1. I’ve got several more written down, but this surely isn’t a speedy venture. Just FYI.
Woot, progress!
I have another TAing duty starting up in about 20 minutes, but I decided to spend the rest of my time putting something here.
(I spent the time before this doing differential geometry computations on the blackboard)
Things are going. I made it through exam week(s) volume 1 without too much pain (other than the preparation therefor), and though I’m still waiting to hear back on how I performed on my homology exam, I think I managed to do pretty well overall. That’s a plus.
I also managed to finish the rough draft of my poster for FSU’s math fun day! That’s also a plus.
Now, I’ve begun looking to the (near) future. Indeed, I have some presentations coming up and I’m in the process of learning material and picking topics, etc. etc., to try not to put that stuff off until the last minute. Overall, I’m pretty excited: At the end of this semester, I’ll have grown quite a bit as a mathematician and will have done some of the “most meaningful work” of my career in the direction of being a professional mathematizer.
I like it.
I plan on spending some time this weekend putting Hatcher solutions up, as well as trying to finish catching up in do Carmo so I can be prepared for my Riemannian Geometry presentation.
Things right now are pretty not-terrible, though, despite my ceasing to exist here every now and again.
I hope to have some big things to roll out soon. Keep me honest, interwebz!
Peace.
Edit: In all this talk about my career, I forgot the most exciting news to happen in recent weeks! On September 23rd, my son turned the big zero-one! Yep, that means my wife and I managed to raise an amazingly awesome bag of awesomeness for an entire year without killing or seriously maiming him! We’re both as excited as that last sentence seems to convey we would be!
This is a short little thing I’m throwing up here just to say a couple things:
Re: The Last Item: I’ve got some moderating to do here. I’ve gotten a few comments on my Hatcher solutions pointing out that I’m really embarrassingly bad at topology. Rest assured: I’ve received your comments, I know how terrible I am, and I’ll be working to rectify the situation as soon as time permits.
Maybe I’ll have a follow-up to this later this evening.
Peace.
3 weeks.
I’ve officially survived the first three weeks of my second year of grad school (twice, actually). Again, I know keeping count of the days is a terrible thing to do to myself, particularly when there’s been a very small amount of good to come from my weeks thus far, but at this point, I’m sort of using that countdown as some sort of badge of accomplishment. Or something.
The coming weeks are going to be very very stressful and busy and stressful. Besides my usual load of stuff (I’m enrolled in 6 classes, I have a reading class in algebraic geometry starting up on Tuesday, I’m TAing for 1 lecture and 7 labs, and I’m trying to pick advisors / plan presentations I’ll need to give some timem soon), I also thought it was a good idea (remind me why?!) to make a poster to present at FSU’s upcoming Math Fun Day. That particular endeavor shouldn’t be especially difficult, but it requires time and time, ladies and gentlemen, is precisely what I have zero of.
Daunting is the adjective that comes to mind.
Also daunting is / was / has been the thought of continuing my goal to do all the problems in Hatcher. As you may recall, I spent the first half of summer slaving to acquire the information needed for the Chapter 0 exercises, only to have my plan for Chapter 1 totality derailed by that little piece of awesome that was my Wolfram internship. Long story short: The obsessive-compulsive part of me wants to not move forward until I hash out a Chapter 1 plan, but the This will benefit me in the class I’m taking now which, subsequently, hinges on my ability to understand Chapters 2 and 3 of Hatcher part wants to press forward.
I’m pleased to announce that the second guy won out.
In particular, my Hatcher Solutions page is showing signs of progress. It didn’t take as long as I’d predicted it to take to build that framework, and due to a random, unforeseen bout of sleeplessness at 3am this morning, I had precisely the opportunity needed to seize the moment. Right now, all those are empty pages, but I’m pleased to report that I seem to have accumulated approximately six solutions; if everything goes as planned, I’ll be taking time to update by including those as soon as possible.
In the meantime, I’m going to continue to hash out what to do about this paper. And what to do about the professors I’m emailing regarding potential advisor-hood. And what to do about the fact that I severely cut my weekend work time by spending yesterday ballin’ out of control in celebration of my wife’s birth. And what to do about….
Au revoir, internet. I bid thee well.
Oh, I just remembered: I have my first exam of the semester Friday. It’s on field theory. I’m less than pleased. 
This is going to be an entry about my algebraic topology class.
My previous topology classes were taught by someone who’s amazing <i>as a mathematician</i>. Most people in the class would agree, however, that this person was someone who was terrible as an instructor: Somehow, I made it through a graduate sequence of coursework despite receiving terrible grades throughout. This happened despite my spending 50+ hours a week on every homework assignment and slaving until I was on the verge of breakdown week in and week out. Somehow, I got a B.
My topology experience thus far is certainly not one of my finest achievements.
Fast forward to now and I’m in an algebraic topology class taught by someone who’s amazing. Amazing. Not amazing <i>insert quantifier here</i>, no – this person is simply amazing. And this topic is beautiful. And this class is hard.
This class is hard, too, despite the fact that we have no continual responsibilities. Indeed, we have zero homework whatsoever: Not required problems to turn in, not required problems to keep, not even suggested problems for our benefit. We simply have <i>zero homework</i> in this class. That’s a huge relief after last semester.
What we <i>do have</i>, though, are exams. We have three of them, and I have zero doubt now (nor have I had doubt at any point this semester) that my ass will be kicked by each and every one.
As a result, I’m working hard.
A week-ish ago, I spent some time going through the preliminary parts of the stuff we’re talking about (homology theory). I did examples, I spent lots of time drawing pictures, and I didn’t stop until I got it.
That’s right: A week-ish ago, I <i>got it</i>.
Today, however, I’m sitting in my office, frustrated and almost-defeated, blogging to you all and mourning the fact that a lot has apparently changed in the last week-ish.
Today, I just don’t get it.
If I were to make a list here cataloging the number of screw-ups I made trying to solve one problem over the course of about 20 hours, I’d be (a) making a really long list and (b) really <i>really</i> embarrassed.
I’m really <i>really</i> embarrassed right now.
Finally, after re-reading and re-re-reading Hatcher, I found source 1 of my confusion. Later, after consulting the online resources of mathematicians greater than myself (case in point here), I found the remaining sources of my confusion.
The upside is that now I’m no longer confused. On the other hand, the fact that I was as confused as I was (and about such basic material as that happened to be) makes me really <i>really</i> uneasy moving forward.
I need an intervention.
In the meantime, I’m going to try to dust myself off, hit the salt mines yet again, and lose my frustrations in the never-ending cycle of Lana del Rey that’s been permeating through my office for the past couple hours.
3 weeks, 2 days.
So right now, it’s 10:23pm.
I’m sitting in my dimly-lit home office, basking in the warmth permeating out of my powerhouse Sun workstation, and partaking in a strangely-appropriate combination of Hatcher’s algebraic topology (stuff from Chapter 2) and Portishead.
This just in: I’d apparently forgotten that Portishead was a band, and I’d also apparently never learned that they’re really really good.
I’m not saying I’m suddenly a topologist because of it, but the experience is definitely way better.
Just thought I’d share.
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