Life2
no post for 20 days, mb man
So… I don’t really know what to talk about. Well, I have a couple things on my mind but nothing that I think would warrant a solo blog post. Yeah. Oh well, just as a table of contents, I’ll probably talk about future college classes, the lock-in, job interview stuff, and some math.
Yeah, that sounds good. Also, for the longest time, I’ve been wanting to set up some kind of a YouTube channel since that just sounds cool. At the same time, I don’t want to become pretentious (though I probably already somewhat am). Anyways, I’m writing this here so that I’m held accountable by whatever force compels you. Oh, also, I have not set up email for this website yet. I should probably do that. Hold me accountable on that too!!
future college (oh no, the future!)
I am addicted to running degree audits. The software is very outdated and strange, and I don't think the audits even reflect current requirements, but I like it.
Ok, uh, I think I’m coming in with a lot of AP credits. So uh, 2.5 is definitely possible. But also, even with adding a double major in math, 2.5 is still stupidly easy to the point where there’s no reason not to do it. So, I’ve come up with a genius idea! Why don’t I just double major in computer science and biology? Biology with a focus on genetics only has 40 extra hours of upper division biology classes! Completely doable. Originally, I wanted to do Neuroscience (30 extra hours), but I was immediately told that Neuroscience does not permit double majors. Honestly, currently, I have it planned at 3.5 years with a triple major (though I’m not that egotistical as to say that such a feat is possible).
I need a hella high lock-in which I think can only be forced by more classes. If I’m being honest, the way I see time is that time is fluid. There was this thing that I read somewhere that said that tasks explode to take up the time available. Candidly, I’m pretty locked in right now in that I understand all the material being taught in every class at a pretty good level. It’s just I still have a lot of free time which I feel is being wasted. Perhaps that is unhealthy. PERHAPS it is the unproductive time that is most important. Eh, that sounds stupid.
Anyways, my point is that under the 3.5 year plan, I will be stretched pretty thin with a lot of really difficult classes. But at the same time, tasks explode to take up the time available. Therefore, I’ll also cut down on time wasted when I don’t have stuff to do! I’m actually a genius… until my GPA goes down to the single digits.
The other thing is – which is pretty sad about my plan – that there are a lot of cool grad math classes that I want to take in probability and probably topology. Wait, I’m not even past basic, basic math. I think I should slow down. Yeah, but either way, under my 3.5 plan, I will not have time to take those classes because I will need to take classes such as cell biology and genetics lab. Also, there are graduate classes in cancer biology and phylogenetics that I want to take. I will 100% not have time to take those because, right now, Biology is the limiting degree.
Frankly, I’m only really interested in CS theory/algorithms classes or ML (but ML is just math so it’s also theory/algorithms). The main difference for CS though, is that it is a requirement to go choose whatever upper division electives you want to take… so I’m already gonna take a ton of extra algorithms and ML classes. But for math or biology, the requirements are a lot more… strict is the wrong word… but there’s less required choice if that makes sense. What I mean is that CS requires 8 upper division. Math doesn’t even require multiple classes in probability or topology… the math department at UT is fire though. I admire them a lot. I like the CS department too, but the Math department is just built different. Meanwhile, for Biology, you have to take XYZ and then no other choices. I haven’t really talked to the Bio department though the few people in advising who I’ve talked to have all been super helpful, and I can tell that they actually care, which is much more than what I was expecting.
| Category | Courses / Notes |
|---|---|
| Planned AP Transfers | RHE 306, HIS 315L, GOV 310L, E 326P, CS 312, M 408C, CH 607, BIO 311D, BIO 311C, CH 301, CH 302, CH 104N, CH 104M, one of the physics path (undecided) |
| First Semester (17 hrs) | CS 314, CS 311, M 427L, M 362K, UGS |
| Additional Credits | Transfer ACC out of some HIS, VAPA; Test out of M 341 |
| Second Semester (18 hrs) | CS 429(H), BIO 325, M 367K, (M 373K or M 365C), BIO 226L, CH 320M |
| Additional Credits | Test out of M 325K (might just take M 328K in this iteration) |
| Third Semester (19 hrs) | CS 439(H), (M 373K or M 365C), CS UDE 1 (math), BIO 370, BCH 369, BIO 320 |
| Fourth Semester (18 hrs) | CS 331(H), CS UDE 2 (math), M 379H, BIO 325T, BIO 344, SDS 328M |
| Fifth Semester (18 hrs) | CS UDE 3 (math), CS UDE 4, CS UDE 5, BIO 350, BIO 325L, BIO 326 |
| Sixth Semester (15 hrs) | CS UDE 6, CS 379H, BIO 320L, BCH 339, BIO 327 |
| Seventh Semester (7 hrs) | CS UDE 7, BIO 379H, MBH 175C |
| Category | Courses / Notes |
|---|---|
| Planned AP Transfers | RHE 306, HIS 315L, GOV 310L, E 326P, CS 312, M 408C, CH 607, BIO 311D, BIO 311C, CH 301, CH 302, CH 104N, CH 104M, one of the physics path (undecided) |
| First Semester (17 hrs) | CS 314, CS 311, M 427L, M 362K, UGS |
| Additional Credits | Transfer ACC out of some HIS, VAPA; Test out of M 341 |
| Second Semester (18 hrs) | CS 429(H), BIO 325, M 367K, (M 373K or M 365C), BIO 226L, CH 320M |
| Additional Credits | Test out of M 325K (M 328K actually sounds interesting) |
| Third Semester (19 hrs) | CS 439(H), (M 373K or M 365C), CS UDE 1 (math), BIO 370, BCH 369, BIO 320 |
| Fourth Semester (19 hrs) | CS 331(H), CS UDE 2 (math), M 379H, BIO 325T, BIO 344, BIO 379H, MBH 175C |
| Fifth Semester (18 hrs) | CS UDE 3 (math), CS UDE 4, CS UDE 5, BIO 350, BIO 325L, BIO 327 |
| Sixth Semester (21 hrs) | CS UDE 6, CS UDE 7, CS 379H, BIO 320L, BCH 339, BIO 326, SDS 328M |
So yeah, those are some pretty different schedules. One of them is the 3.5 year plan I was talking about, and the other one is the 3 year plan I thought of. Depending on how second semester goes (ie. do I feel fine, did I learn everything, is my GPA adequate), I will decide whether to do 3 or 3.5 years. Hell, what will most likely occur is that I get railed during second semester and give up on the triple major and just do CS + Math. I am saying that so that when I do get railed, I am able to laugh it off…hopefully that does not happen.
I mean, I do get that I have not had adequate experience to determine whether I am even capable of surviving in that planned second semester. My current schedule is not particularly rigorous because I am taking the first-first-year CS classes which are a lot easier than other CS classes. Plus, the two ACC classes I’m taking right now aren’t particularly stressful nor is my UGS class. Then, also, CS 311 and M 427L are basically just a review of high school stuff. I still have not seen new material in either class. The professors for CS 311 and M 427L are my favorites by far though. Probably not by far, though you get the point I am attempting to get across.
Ha, now that the glaze is out the way, I can start badmouthing them. Jk, they’re actually cool. Yeah, second semester will be the real test. First semester is kinda just not rigorous enough to be a real marker of college difficulty imo (not to say my classes have easy grade distributions, I may not be getting an A in CS 311 for example). Oh well, hopefully it works out.
I lean towards 3.5 years since it allows me the chance to take grad courses in math and biology (maybe CS too if I discover algorithms are way more interesting than anything else). Oh, I also need to review Linear Algebra. I strongly believe I should be fine without studying since I pseudo took the class twice (once for real, the other because my teacher was the goat), but better safe than sorry. Watch me not get credit for M 341. I’m going to drop a 20 and laugh it off.
Uh, row reduction. Uh, matrix multiplication. Uh, change of basis. Uh, eigenvalues, inverses, PDEs, R2 matrices, determinants, jacobians, linear transformations, geometry. Uh, what else is in Linear? I guess linear systems? I also asked somebody in my CS 311 professor’s office hours, and he told me some stuff I didn’t know – examples being: LU decompositions, SVD decomposition, Block matrices, least squares. I don’t know, there’s a lot of Linear stuff. OH… ChatGPT has a lot of stuff when I ask it about Linear topics.
| Topic | Typical Contents |
|---|---|
| Vectors and Vector Spaces | Definitions, linear combinations, span, linear independence, basis, dimension |
| Matrices | Matrix operations, types of matrices (diagonal, identity, symmetric), matrix multiplication, transpose, inverse |
| Systems of Linear Equations | Solving Ax = b, Gaussian elimination, row-reduced echelon form, consistency, rank |
| Determinants | Definition, properties, computing via cofactor expansion, applications to invertibility |
| Eigenvalues and Eigenvectors | Characteristic polynomial, diagonalization, spectral theorem, applications to linear transformations |
| Linear Transformations | Kernel, image, matrix representation, change of basis |
| Inner Product Spaces | Dot product, length, orthogonality, projections, Gram-Schmidt process |
| Orthogonalization and Orthogonal Matrices | Orthogonal bases, QR decomposition, orthogonal transformations |
| Diagonalization and Jordan Form | Diagonalizable matrices, Jordan canonical form, generalized eigenvectors |
| Applications | Systems of differential equations, computer graphics transformations, least squares problems, PCA |
Ok, I know most of this, it’s just probably review rank (rank nullity theorem I kinda forgor). And then also some new stuff like cofactor expansion? + spectral theorem? + gram-schmidt process? + QR decomposition? plus Jordan canonical form? + least squares problems? + whatever PCA is. Oh that’s kinda a lot. Hopefully, it’s just stuff I forgot at some point or never actually remembered the named version. Oh, there was something I saw in my Linear textbook in high school about Taylor series with matrices. That was cool. Probably not on here though. Also, I did not understand that in high school. Anyways, that’s about it for college.
This is the Linear Algebra book my high school teacher taught from. Junior year was quite stressful and difficult since the abstraction was a concept I had not encountered yet. However, looking back, I am all the better a thinker for it.
Oh, I got points taken off of my Discrete test for using set notation. Ik, actually crazy. I even asked my TA if I could use it on my quiz and he responded sure. Well, now he’s denying it so idk. I’m pretty sure I did not hallucinate. Though, imma be honest, if a bunch of people gaslight me, I’ll probably fall for it. Also, set notation is actually crazy. Like I can’t do $n \in Z$. Crazy.
The lock-in
A CS section problem. I think I can share this. I don't see why not. If this gets me in trouble, I would be quite surprised since everybody has access to these plus the problem is not even difficult. Anyways, I put this image here because the rainbow looks cool. I wonder why that happens...
So, I don’t really know what to put here cause I kinda talked about the lock-in already. My printer is flashing orange because there’s no toner. Plus I can’t even replace it because we don’t have extra toner. Hopefully, it does not take up a number akin to 700 watts flashing orange. Is that how power is calculated? idk.
This section will be about my future plans. Oh that’s a good section idea. If you can’t tell, I write these on the fly…that probably made about 90% of the audience leave. As my high school English teacher said, if you can’t be bothered to care about your work, why should I? I think he said that. I don’t really remember.
I want to double major in math for sure because math is super cool. The current math research (though I don’t understand most of it) I’m doing with my mentor, a graduate student, as part of the Directed Reading Program has been the most fulfilling experience in all of college for sure, and probably all of high school as well. Maybe in my whole life. I mean, it’s definitely not my happiest experience… probably… because that would be sad.
For any college people out there, I’d advise applying to a Directed Reading Program. You will learn very interesting stuff and meet cool people. Either way, that’s why I want to do a math degree. I already plan on taking a lot of ‘deep’ math classes in pure math so, at that point, why not just take one extra class and get a math degree.
I think – I think is not a good way to describe getting a whole other degree, but I digress – I think I want to pursue a Biology degree because I want to do cancer and phylogenetics research. I think. I think is definitely not a good way to describe that large a commitment. But, I also rather enjoy ‘real’ natural sciences on top of already having a lot of leeway in my degree, so I see no reason not to pursue a Biology degree.
Bro, I’m actually gonna end up homeless on the street from trying to do too much. Like this is the fig thing. Yk,
“I saw my life branching out before me like the green fig tree in the story. From the tip of every branch, like a fat purple fig, a wonderful future beckoned and winked. One fig was a husband and a happy home and children, and another fig was a famous poet and another fig was a brilliant professor, and another fig was Ee Gee, the amazing editor, and another fig was Europe and Africa and South America, and another fig was Constantin and Socrates and Attila and a pack of other lovers with queer names and offbeat professions, and another fig was an Olympic lady crew champion, and beyond and above these figs were many more figs I couldn’t quite make out. I saw myself sitting in the crotch of this fig tree, starving to death, just because I couldn’t make up my mind which of the figs I would choose. I wanted each and every one of them, but choosing one meant losing all the rest, and, as I sat there, unable to decide, the figs began to wrinkle and go black, and, one by one, they plopped to the ground at my feet.”
- Sylvia Plath
I wrote a short story based on that quote’s idea and feeling in high school. It was very cool. I might link it at the bottom if I feel like it. Edit: I did end up linking it at bottom.
CS is pretty easy to say why I like it. Uh, I applied to it in high school, and it is pretty fun + the people are cool so I will pursue it. I mean, I am attracted to algorithms and ML, so like yeah. I’m gonna be honest, I was kinda peer pressured in high school (not overtly) to major in CS. Parents, friends, girls I liked. Yeah, not overtly though. I am really enjoying my CS classes right now though. Data structures is fun and the programming assignments are actually surprisingly invigorating to think about and code. The exams are not particularly interesting, but they are bearable. So, I will definitely finish my CS degree because CS is fun + job prospects are best (oh wait, that is a big reason) + classes are cool + professors are great + CS people are nice. Or… maybe I take computer architecture and operating systems and just give up.
Though, then again, I really liked the Digital Electronics class I took in high school where we built an arithmetic logic unit (LALU). I have a soft spot for learning about the stack and heap and RAM and how instructions are loaded in. That part was great – learning about how loops, conditionals, and methods actually work in assembly. Yeah, I will probably be very engaged in comp arch and OS.
Job (unemployed)
me
I’m a yapper, but I’m getting kinda tired of typing. I had a couple job interviews. I think I did fine though I will not hold out hope for a freshman summer internship. I candidly will say that I believe I vibed really well with my first interviewer, and I got to talk a lot about stuff that I don’t really get to talk about all that often. I was able to elaborate on my work at ARL (within reason) plus talk about my current math research (if you can call my level of understanding research). That felt really cathartic and great.
I’m not holding out hope for a freshman summer internship though. What I really want is to learn more about how industry operates and how production gets shipped out. What I mean is that I have a ton of research experiences (perhaps not as complex as somebody pursuing a PHD or something, but still experiences), but I’ve never actually worked at a real company trying to generate profits. My second interviewer was chill, but at the same time, we only talked for 20 minutes and he told me at one point that there were 40-60 people interviewing. That is pretty stiff competition. The company sounds really fun to work at, and they also seem very geared towards positive EV outcomes. Jesus, that sounds nerdy. I mean, most companies want to generate positive EV outcomes. There is also apparently a chess culture which sounds like a perfect match for me. At the same time though, I learned my lesson from college applications, so I will not hold my breath.
Is stiff the right word? I believe it’s correct, though it also sounds strange.
Math
messy
Alright, my favorite part. I get to share two really cool math problems. Jesus, I’m excited.
The first one is a math problem that my M 427L professor gave in a Putnam prep club (I am getting a 0 on the Putnam exam, but it’s fine). The problem goes as follows:
You have a rectangle R that is parallel to the x and y axes. This rectangle is formed of a bunch of subrectangles. Prove that if each subrectangle has at least one side of integer length, then the whole rectangle R has at least one side of integer length.
Possible rectangle R configurations
I was unable to solve this. I was able to solve every other problem on that sheet (something I should probably not be proud of), but I was not able to solve that one even after thinking about it for about a month. The M 427L professor gave a breathtaking solution though.
\(\int_0^a \frac{1}{\pi} \cos (\pi x) dx = 0\)
if and only if $a \in Z$. That is some crazy intuition to figure that out. The way I think you approach that is by trying to find things that only integer length items have. If $a \in Z$, then it is true that such an integral equals 0, and if such an integral equals 0, $a \in Z$.
We can extend that integral to the rectangle by making it a double integral (M 427L is vector calc, so vector calc, yay!). Truthfully, vector calc is surprisingly interesting given that most of the material is review. My professor is cracked at lecturing though.
\(\int_0^a \int_0^b \frac{1}{\pi^2} \cos (\pi x) \cos (\pi y) dx dy = 0\) if and only if $a \in Z$ or $b \in Z$. So beautiful. Wow. Isn’t that just crazy?
Then, the reasoning becomes trivially simple. All you say is that, since all the subrectangles that make up R must be 0 for this integral, the entire rectangle R must be 0 for this integral (since you can split integrals up into smaller versions). Thus, since the entire rectangle R must be 0 for this integral, we know that at least one of its sides must be 0 (as the integral is if and only if). SO BEAUTIFUL.
Second problem that I wanted to find an answer for was a derivation of the sum of consecutive squares. You can prove it pretty easily with induction, but that’s a ‘fake’ proof because there’s no intuition.
My M 427L professor came in clutch again. There’s this really nice Minecraft video explaining the concept (https://www.youtube.com/watch?v=IkWDBFPK7ZU), but you can also prove it using iterated integrals. Just watch the Minecraft video. It is worth it, trust me.
Anyways, then I was curious as to whether there was a formula for the sum of consecutive nth powers. The answer is that there is, but it is scuffed beyond belief. In fact, I still do not understand that formula. Maybe I’ll ask around and figure it out. This guy explains it well: https://www.johndcook.com/blog/2016/12/31/sums-of-consecutive-powers/.
$[ \sum_{k=1}^{m} k^n = \frac{1}{n+1} \sum_{j=0}^{n} \binom{n+1}{j} B_j \, m^{\,n+1-j} ]$
$B_j$ are Bernoulli numbers. Either way, this week has been great for math. I just feel great because I also made progress on hyperbolic mapping stuff for my own math work.
To conclude, I will conclude, by saying that in conclusion…
Shoot, I normally end these on a depressing note. Alright, I got this. I know how to end this on a depressing note.
I was thinking about the people I talked to in high school and realized that I will never see any of them who didn’t go to UT Austin again. That’s pretty depressing.
There are also one friend I have that’s out of state who I used to talk with a lot online (mainly talked in person before). Now, we’ve kinda stopped too.
Man, friendships suck. Too much feeling. I don’t quite like it. But, at the same time, it’s gratifying to talk to people. Maybe, I just start talking to random people and use that to get my need for social interaction. There’s no commitment that way.
Oh shit, I write these by copying the past post. That section is rather depressing. Though I think it is also depressing to think that I will never see my high school associates again. Well, it’s only really depressing when I think about 2-3 people. Oh well, you lose people, you gain people. Life is what it is.
I played in the CCL and threw multiple positions (THE GOAT)
Friend recommended me this Manhwa (or manhua, idk the difference man) 1-2 years ago. At the time, I said nah, that story sounds rather similar to a power fantasy. But... I started reading it, and it is kinda fire. I even started reading the light novel for The Beginning After the End. I have a CS 314 test next Wednesday. Hopefully, I don't just waste this weekend reading the light novel... though I probably will!
Link to short story: https://docs.google.com/document/d/15dgu1Z_JK39bW1HDocJZwZTVLO9kdLFJ-3sdBltvgLs/edit?tab=t.0