It means diary
in German. I don't speak German, but I like that word
much more than the English.
Got mortally clobbered by an algorithms assignment, which is why I haven't been active for the past few days. The good news is I got some help with the linear algebra problem I was stuck on; logistically the proof is not hard at all, it was just a matter of knowing the definitions of things. The key point was that the ideal of a ring homomorphism is its kernel. If I combine that with the proposition from earlier and smooth out some rough edges it should be good to go. I need to do my actual homework though...
First day of classes; not so bad, but it's hard gauging by a single day. Especially since Mondays are a bit of an anomaly, class-schedule wise. Didn't make much progress on math, sadly, but had an amazing run courtesy of Drive like Jehu's Yank Crime. I knew my neurotically intense post-hardcore obsession would be good for something!
I was stuck on Question 32 of Section 3B in Linear Algebra Done Right but decided to devote some time to understanding (part of) a potential solution today. Here is some of the thinking:
Proposition: Any ideal of a ring which has the multiplicative identity is the entire ring.
Proof: Forwards: Let I be an ideal of R. If I = R then the multiplicative identity is an element of I.
Backwards: For a multiplicative identity u, let u-1 be its inverse. For any element of the ring, r, we have r = r(u-1u) = (ru-1)u, which is an element of I by definition of an ideal. Thus I = R. QED.
Now noting that the set of n-by-n matrices with entries in R forms a ring, it's clear if an ideal of such a ring contains the n-by-n identity matrix (the multiplicative identity), then that ideal is the entire ring.
From another point of view, we take the matrix ring as a ring of linear maps from and to a vector space V instead. This allows us to say that an ideal of such a set is either the set itself (using the same logic, now with the identity map instead of the identity matrix) or the set containing the zero map.
Been meeting/talking to more female math people on the internet. While it's
easy to be cynical and turn your nose up at attempts of diversity,
inclusion
, etc, there is something demonstrably comforting about
this. I can't help but be colored by admiration and inspiration.
I recieved this watch in the mail today, an old Soviet thing labeled
ЗВЕЗДА
, "STAR". Unreadable labeling at the bottom of the
watch face, looks like a patrynomic, ending in "ич" but cannot make out
much else. After some reading, it says something like "ГУЗ УГЛИЧ",
which refers to a city called Uglich. Mechanical, and wind-up. Makes a very
small tick-tick-tick
noise I can only hear when I hold it close to my
ear.
I got a watch because I felt uneasy about depending on electronic devices to tell the time. Now it would be more convenient for me to leave the dorm without my phone, which I've wanted to start doing.
Weather is getting warmer and warmer, in the 20s now, though sky was
overcast and dreary. Stuck on a problem about two-sided ideals
.
Which makes sense, as I'm not too familiar with rings.
School is starting again in a few days. Feel just as uncertain about the future as ever.
Keep trying to convince myself that it's ok if I do anything at all in a given day (finally uploaded LADR Chapter 3 Section B) at least I'm not catatonic with depression and accumulated neuroses, as I was over winter.
Today I woke up incredibly late like a total degenerate and
spent 40 minutes of already-precious daylight walking all the way to the
other side of campus, under the hot sun, with my textbook in tow.
A couple days ago, just at the start of the break, I called my boyfriend and we talked for hours. He's actually visiting my campus for a semester next spring (so almost exactly a year from now) in an exchange program.
He's studying biology, specifically genomics---sometimes I wish I knew more about it but I still enjoy it when he talks about his classes because it's the main thing he's passionate about. That, and art.
The funny thing is that he really dislikes math and is ambivalent about computer science. So in that respect, we kind of live in different worlds. He's at a university in China and I sometimes wish that I was the one going to his university rather than the other way around.
Oh, time is getting away from me again.
Usually I have trouble thinking about anything other than running, while I'm running. But sometimes I toy around with a math problem I'm working on, and in the light of day where I feel like I can't get enough air into my lungs, I realise that there is another, simpler way to approach a problem. That always feels good.
On another topic, I wanted to mention how much I enjoy writing my notes with a fountain pen! Someone gifted me a Lamy Safari probably around 5-6 years ago, and I've been using it ever since (I had a Pilot Kakuno, which I really liked using, but I lost the cap for it...). For ink I'm pretty boring, I mainly use the Pilot Iroshizuku Kon-peki blue, although I really want to buy an archival/waterproof ink soon. Sometimes it gets quite rainy here and when my notebook gets wet, the ink will bleed everywhere. I'm thinking of getting the De Atramentis archival ink but if you have any recommendations please feel free to let me know.
Ah, I didn't mean to disappear for a few days. I'm two days into the break and I've been sleeping, running, and burying myself in math textbooks to my heart's content. Linear algebra is endlessly interesting ^_^
Anyways, I was also thinking about tracking my runs here, mainly time and distance, as well as sharing some photos I take with my phone.
I've recently bought into the whole notion of the time you put into
exercise is paid back two, even three-fold in the length of time you
are able to focus
.
Also, as much as I like to write out theorems/lemmas and their proofs longhand in my notebook, I also depend a lot on SRS (spaced-repetition-software). I use Anki to memorize important theorems and other facts that I feel I need to have on hand, quickly. Of course, I make sure to understand the theory behind the cards before I drill them. One of my criticisms about modern education is that we have had such backlash against rote memorization, that it is now unfairly vilified and under-used to the detriment of learning. Memorization has a time and place, sometimes a bigger time and place that we afford it.
We get a short break in the semester starting tomorrow, about a week. I have two difficult classes, one time-consuming class and one very easy class---a nice balance in my opinion. Next semester will be a lot more difficult as I attempt to play catch-up with the Math major requirements. I'm not even sure if I will be able to finish all the requirements before I graduate, but I'm going to give it all I have. But, if I leave college with a computer science degree having taken a lot of math classes (not necessarily get the actual math diploma), there is nothing to complain about. It's just a piece of paper after all.
I can't wait spend the next few days painting and solving math problems to my heart's content. One choice I'm really happy I made is using a more computational linear algebra textbook (Shifrin's) and then pairing it with a more abstract textbook (Axler). Having two points of view of similar topics is really fascinating.
Also, the weather was beautiful today, and it's finally beginning to get warmer. And I managed to hand in that pesky programming assignment, so that's a relief.
I'm not sure if I will keep this page up, but I think I would like a place
to put slightly non-math things on this website, and to keep track of how
exactly I feel, and the details of my days as I study. I'm inspired a bit
by nullspace's
website
and their combination of personal life, math, and creative projects. And also
the website of Vashti. I like
the idea of the qualified self
. Not self-knowledge through numbers (as
in the quantified self) but through details and events.
Today a friend and I were working on a programming assignment (something to do with graphs and shortest paths) and no matter how hard we bashed our heads against the wall about it, we only could make the most incremental, infinitesimal progress while debugging. I'm the type of programmer that can easily get caught up in the minutiae of using debuggers like gdb (or in this case, pdb and jdb), quickly losing sight of the bigger picture. Which is arguably more important than the index-out-of-bounds errors I'm so sensitive to. So, I end up using a lot of time. I feel like I still lack a broader intuition about the correctness of programs; I can't look at a program and tell if it's way off the mark or very close to the mark. I need to dig into it line-by-line, almost surgically.