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.
I just wanted to drop in and update here. I haven’t been posting much in the last day or two, but not because I haven’t been workin’ it!
Here’s what’s been going on.
Wednesday, I stayed home and had a Clifford Analysis day. I read a solid three or four pages of my professor’s paper before calling it a day.
Because I felt like I hadn’t done enough on the Clifford front, I went to my office Thursday armed with new writing supplies and spent a solid few hours verifying the claims made in the aforementioned three or four pages I’d read. That was a good feeling.
Friday was (differential) geometry day, and I started the day working some “trivial” problems from Spivak’s little book. In the middle of the day, I had a phone interview with Pearson for a potential part-time job; that interview went well and I’m moving on to the second stage of the employment process. I spent some more time in Spivak’s little book before spending the remainder of my evening working problems from Volume One of Spivak’s magnum opus. Those problems are also “elementary” but they’re a bit harder. The challenge was good.
Today is supposed to be algebra day. Because we only recently were in a position to remedy some previously-existing financial woes, however, we spent most of the day split between running errands and spending time out and about with our son. I did take both Eisenbud/Harris and Perrin with me, along with my trusted G2 and Composition Book; very little progress was made, however.
I’m actually about to dip out for the evening here in a few minutes, but depending on how much energy I have tonight, I might buckle in and try to figure out some of this sheaf theory stuff. If I had a fourth Algebraic Geometry Observation published, it would be that transferring between theory and problems which apply said theory is very VERY difficult.
So it’s now creeping into the third (full) week of June. School got out for me during the first (full) week of May. Regardless of how woeful you may consider your abilities in mathematics, I’m sure you can deduce something very clear from these facts:
Summer is about half over.
Generally, that fact in and of itself wouldn’t be too terrible. I mean, big deal: Half the summer’s over, and I’ve been working throughout. How big of a failure can that really be?
In this case, it’s actually a pretty big one.
Despite my having read pretty much nonstop since summer began, I haven’t really made it very far into anything substantial. Compounded onto that is the fact that I’ve had to abandon a handful of reading projects after making what appeared to be pretty not-terrible progress into them because of various hindrances (usually, a lack of requisite background knowledge).
It’s been a pretty frustrating, pretty not successful summer, objectively.
Also, by and large, yesterday was a day consisting entirely of (differential) geometry / topology, so it’s really no surprise that – again – my dreams were all math related and tied to that general realm of theory. More precisely, I spent my entire sleep cycle pondering the Poincaré Conjecture (can we call it the Perelman Theorem yet?) and Ricci Flows. That’s certainly a night well spent.
Unsurprisingly, my day today will be largely similar. I downloaded a bunch of resources concerning the aforementioned topics (Poincaré-Perelman and Ricci Flows), as well as some (more) texts on Riemanninan Geometry (which I started perusing yesterday). Also in the works: A colleague of mine (who I’ll call DW2) and I have decided to work through Atiyah and MacDonald’s Introduction to Commutative Algebra, and I’m pretty sure if I don’t spend a significantly-larger amount of time on my professor’s Clifford paper, I’m going to have zero things about which to ever talk with him…
…then there’s the algebraic geometry stuff I’m working on in Eisenbud and Harris / Dummit and Foote, and the material from the seven or so other books I’m reading through concurrently right now….
Every day I’m huss-uh-lin’….
I have some things I want to write here later – expository things and what not – but for now, it’s just this check-in. Auf Wiedersehen!
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.
Read some pages on Gröbner bases in Dummit and Foote.
Did some tutoring / tutor-related things.
Spent some time figuring out some solutions from Hatcher.
Despite it being 3:30am, my game plan is to be up around 8am to make a trip to campus. While there, I plan to do the usual errand things, and to then lock myself in my office for 5-or-so hours and do some legit math things.
That means I need to take good resources there with me.
"A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." - Paul Halmos