⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
292 posts
Latest Posts by bsdndprplplld - Page 10
30 VII – 1 VIII 2021
done some stuff
sleep: I'm on it, gonna get better soon
concentration: alright
phone time: alright
did some multivar calculus today, didn't do any topo unfortunately, finished the functionality in the coding project, finished the art comission, watched some lectures from MIT
tomorrow going to a different city, gotta wake up early so will be dead all day ugh. plan to do some coding and finish the chapter from the multivar calc book. at the end of it i will find out what the manifold actually is and some of what can be done with it, pretty excited
I have a bet going on with a friend. We need a third opinion. Can one find the square root of 2 in pi? And pi in the root of 2
Gut instinct says no. But when you work with infinities, gut instinct is NOT proof. (And such a gut feeling could have easily been the dodgy dinner I cooked myself last night.)
However I cannot even provide a proof.
I have, however tried to give some insight in another post (it should be the one immediately below this one) to perhaps help/provoke a more concrete argument from someone else :)
What's the beef between engineers and physicists and even mathematicians.
Why physicists mock mathematicians: Because playing 51 dimensional chess against your own brain seems silly to us when there’s a whole cosmos to explore.
Why mathematicians mock physicists: The universe can only be understood because some nerd spent the time playing 51 dimensional chess and in the process they created some useful stuff for the physicists to steal and abuse the hell out of.
Why everyone mocks the engineers: π=e=3 is an abomination before God and those pencil pushing dorks make more money than us so we feel the need to vindicate our $75000 student debt.
“Mathematics is a giant room, full of toys—some of which have very long instruction manuals.”
— Jacob Lurie
30 VII 2021
did some stuff today. found out my cat would die tomorrow if it wasn't for an operation he had today, that didn't feel good but also oh god was he lucky
sleep: better but still trash. yesterday fell asleep between 3 and 4, today planning to go to bed at 3 so in a few minutes
concentration: not as great. couldn't focus because my cat was fucking dying
bo phone time: decent
did some topo today, i think i managed to understand the idea behind the quotient spaces and i really liked it. can't wait to dive deeper tomorrow. other than that i wrote a method that takes a parametric function and provides a partition dividing the curve into k intervals. also i'm almost done with the art comission
sooo tomorrow i plan to finish the code, i want to achieve the functionality that takes a parametric function and draws it with a dashed line. that's why i needed the partition, it's gonna look fucking beautiful. and i need to complete the comission. i hope there will be some time left for quotient spaces, i am very hyped. oh and i forgot i'm drinking tomorrow. so i guess no topo for that gal. eh
ok now i might have some kind of super memory??
a week ago i played chess with bf and we didn't finish, so now i arranged the board as i remembered it and i got 13 out of 14 pieces correctly
i mean wow i didn't know i am capable of something like this
might be autism i suspect i might have
anyway now i want to know everything about human memory and take advantage of that
29 VII 2021
got vaxxed today and spent the rest of the day with bf
sleep: trash. been falling asleep at 4am again, "i'll try to go to bed before 3" my ass
concentration: alright. i'm as always extremely productive and i didn't find it hard to focus recently
no phone time: alright. i'm so immersed in my work that i forget to check the phone and i don't really feel inclined to talk to people or look at social media anyway
didn't do any pure math today, did some applied instead, which was working on SVM with friends from my uni. we got stuck on solving the quadratic programming problem but we're almost done
tomorrow i'm planning to go back to the chapter about operations on topo spaces, finish the art comission I got and finish some functionalities in the digital animation project i'm doing with bf. much finishing, this is how i like things to be
the alphabet is like, there's the "a" region (abc...), for just, things, there's the "f" region (fgh..), for functions, there's the "i" region (ijk...), for indices, there's the "n" region (nm...), for integers, and the "p" region (pq...), for integers that are prime, there's the "t" region (tsr...), for time and progression and other axes that aren't the usual ones, and then there's the "u" region (uv...), for like, i guess open sets and differentiable functions and the such i guess, and then finally there's the "x" region (xyzw...) for just, variables that are more variable-y
there's also o and l but you shouldn't use those
6 Things People Don't Always Tell You About Studying
1. you ace tests by overlearning. you should know your notes/flashcards/definitions basically by heart. if someone asks you about a topic when you’re away from class or your notes and you can answer them in a thorough and and accurate answer, then you’re good, you know the material.
2. if you don’t understand something, it will end up on the test. so just don’t disregard and hope that this specific topic won’t be on the test. give it more attention, help, and practice. find a packet of problems on that one concept and don’t stop until you finish it and know it the best.
3. sometimes you just need that Parental Push. you know in elementary school, they would tell you “ok now it’s time for you to do your homework! you have a project coming up, start looking for a topic now!” ONE of your teachers might be like this. be thankful for it and follow their advice! these teachers are the best at always keeping you on track with their calendar. if not a teacher, then have one of your friends be that person that can keep you accountable for the things you promised you would do.
4. you just need to kick your own ass. seriously. i know it sucks and its hard to study for two things at once. BUT. I DONT CARE IF IT’S HARD. you need to do it and at least do it to get it over with because you can’t keep putting things off. If you do, you will eventually run out of time and you will hate yourself. force yourself to do it. i made myself sign up for june ACT even though there’s finals because if i didn’t, i probably never would. like do i think i’m gonna be ready in one month? probably not, SO I BETTER GET ON IT AND START STUDYING!
5. do homework even if it doesn’t count. if you actually try on it, then you will actually do so much better on the tests, it’s like magic.
6. literally just get so angry about procrastinating that you make yourself start that assignment. I know how hard it is to kick the procrastination habit. I have to procrastinate. So I make myself start by thinking about my deadlines way early. I think, “oh i have a presentation in three weeks (but it really takes 2 weeks to do), i’ll be good and start today.” when that doesn’t happen, you say you’ll do it tomorrow, and this happens for like the next four days. I get so mad at myself for not starting when i am given a new chance to do so with every passing day. By that time, you actually have exactly how much time you need for it AND you were able to procrastinate the same way you usually do ;)
my love for topology is a very concave function with a very positive derivative
tietze theorem is fucking beautiful urysohn's lemma is pretty and separation axioms are cute
aand i animated some riemann integration today:
i could've chosen different partitions or a different function in order to achieve more frames but i like this anyway
i ended up not doing topo yesterday and made an animation of a lipschitz function instead:
i'm kinda proud of it even though it's messy. had so much fun with it. maybe i'll do some more today
but i want to do that topo content i planned to do so we'll see. i also need to do some coding and finish an art comission
ok i get it now, most people need plans and structures so then they can study what they're really into in the future
btw today i'm doing operations on topo spaces, i love that already
i gotta say i don't buy all them planning strategies and tips that require more effort than just sitting and doing the work
i mean that might help some people but i find that when i am doing something important to me i need no plans nor do i need motivation, i also don't procrastinate, everything falls into its right place
and if achieving something takes so much effort in preparation, is this even supposed to be a thing? idk, maybe that's the reason why i have no external proof of my work lol
i gotta say i don't buy all them planning strategies and tips that require more effort than just sitting and doing the work
i mean that might help some people but i find that when i am doing something important to me i need no plans nor do i need motivation, i also don't procrastinate, everything falls into its right place
and if achieving something takes so much effort in preparation, is this even supposed to be a thing? idk, maybe that's the reason why i have no external proof of my work lol
An Overview of Note-Taking Styles
Note-taking is one of the most essential skills a student should master. It allows you to record and review information to be used in the future. But what’s the best way to do so? Here’s an overview of note-taking styles that can help you maximize your learning!
Energy Management
A human-based organization method
click on images for better resolution; images also available here (link to google drive)
Other posts that may be of interest:
Getting stuff done: How to deal with a lack of motivation
Flexible time-blocking: A more breathable way to get things done
The ABCDE Method
gonna list my general goals, not necessarily what theorems i want to learn but rather some global "fix your life" things. gonna post about it every week to keep myself accountable
(1) wake up at 9 instead of 12. go to sleep at 1 instead of 4. if my current circadian rythm is here to stay, it's gonna be a fucking nightmare in november. first goal is to start going to sleep between 2 and 3
(2) concentrate on lectures. my focus is really bad when it comes to listening to someone. i have some interesting lectures downloaded and want to use them as training. first goal is to be able to actively listen to one for 30 minutes, then I can have a break for a zone-out
(3) get used to not checking my phone every damn 20 minutes. first goal is to have two 1-hour intervals daily of not checking it
probably will add some more soon
Pick a point inside a triangle and drop perpendicular projections onto the sides. These define another triangle. Repeat, with the same point but within the new triangle. Do the same thing once more. The fourth triangle now has the same angles as the first one, although it’s much smaller and it’s rotated.
Complex Number Grapher
https://jutanium.github.io/ComplexNumberGrapher/
This grapher is really fun to play around with!
A normal function takes in a number, x, and outputs another number, y. But a complex function takes in a complex point on a plane (a+bi) and outputs another complex point. Without 4 dimensions, it would be impossible to graph a complex function :(
The creator of this project instead uses complex domain coloring which they explain much better than I have here so you should 100% go and check it out!
Look at this cool function I got:
f(z)=(sin(z^3))^((cos(z))/2)
I got a proof wrong on an exam. No points.
Then, I thought about it for fifteen minutes outside of the exam, wrote it down, nailed it.
I showed a classmate and told him what happened. He looked frustrated. He’d clearly had this happen before, too (haven’t we all?). He said, “Don’t you hate it when that happens?”
I almost said yes. What the h*ck!? No. No, I do not hate it when I can fathom a deeply abstracted concept in mathematics. I never hate that. I the opposite of hate that. Expecting myself to immediately understand topics like this is unrealistic. I’m proud of being able to do it at all. Who cares if I did it in the exam or within the next hour? I DID IT. It’s mine now. I can do it whenever I want. Missing points on that problem doesn’t take the knowledge out of my brain. How dare I be taught that my knowledge is useless because I didn’t have it right at that moment. It’s just as good now.
Education is not about the arbitrary numeric number ascribed to your ability to do things quickly in an arbitrary, restricted time interval. Education is about being able to do progressively more things, to understand progressively complex things.
Tenacity and challenging yourself far beyond your limits is a hundred times more important than getting good grades. Because, when you’re one of .4 percent of the population who possess complete knowledge on a very complex topic, nobody cares how long it took you to do it, or how well you did it the first time you tried.
Grades don’t discover new mathematics. Mathematicians do (even the ones who failed a basic topic in mathematics because their base way of thinking was too complex). Grades don’t advance medical research. Scientists do (even the ones who had to apply for their PhD programs 3 times in a row before they got accepted). Grades don’t make science fiction into real-world technologies. Engineers do (even the ones who dropped out of school because they wanted to build things, not talk about building things).
Knowledge is power. Skills are power. Grades are constructs. Never trade actual understanding for a semblance of understanding.
welcome ✨
i'm a math student, currently persuing master's degree. this semester I'm taking courses on complex manifolds, category theory, equivariant cohomology and representation theory
my bachelor's thesis was about my partial result in the knot/link theory. right now I'm finishing that proof and hoping to publish it when (if?) I'm done. my interests include algebraic and geometric topology and the goal for this year is to get to know some algebraic geometry
I post updates of how I'm doing, photos of my ugly notes and sometimes share some study methods that proved to be useful to me
oh and math is my special interest, I take it way too seriously lol
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my posts with study tips:
tips for studying math
tips for studying math part 2: you have an exam but the course is boring