Also I Don't Get What "bad Representation" Is Supposed To Mean. Given A Number Of Symptoms And Creating

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

can someone please get these hoes under control i'm BUSY

Astronaut sculpture from an ex-physicist (Source/Credit)

that sounds a bit like mystery flesh pit national park

I’m Christian and respect the order of creation as God intended it but I’m not gonna lie if I could take a massive vat of agar and grow an alive shopping mall made out of red blood and meat and feed it living human bodies to make it expand larger with more shops and amenities, Without hesitation, Without question I would do exactly that

oh, you misunderstood. when i said "applications" i didnt mean real world applications, i meant ways to use this in the context even more abstract nonsense

13 X 2022

I dedicated the weekend to meeting with people from the machine learning club, helping my friend through her analysis homework and studying category theory for one of my subjects. then I did mostly the complex analysis homework

here are some wannabe aesthetic notes

my main goal at the time was to truly understand yoneda's lemma and the main intuition I have is that sometimes we shouldn't study the category C, but thw category of all functors from C to Set

after studying for a few hours I can say that the concept became a bit more intuitive

one of the problems in my "putnam homework" was to calculate the product of all differences of distinct n-th roots of unity – or so I thought. for a few days I believed that my solution doesn't work. I ended up with a disgusting fomula interating cosines of obscure angles but the visual intuition is neat, especially for an odd n. aaand that's no surprise since it turns out I'm fucking illiterate. not distinct roots, just differences of distinct roots, so that the whole thing is symmetric and there is no distinction of n odd vs n even

anyway I finally solved it, so that's nice!

I completed 5 out of 10 problems, which was my goal, so I should stop now and do my commutative algebra homework. there is one more exercise I want to solve:

the complex polynomial P with integer coefficients is such that |P(z)| ≤ 2 ∀z∈S¹. how many non-zero coefficients can P have?

I'm almost there with it and it's really cool

ofc the opportunity to include pretty drawings in my homework couldn't be wasted

during my category theory tutorial the professor asked me to show my solution on the blackboard. I was kinda stressed because now is the first time when I have my lectures and tutorials in english and on top of that this is a grad course. that whole morning I was fighting to stay awake, after the blackboard incident I didn't have to anymore

this is what I did

this week is likely to be the hardest out of many proceeding ones, because I won't have the weekend for studying (it's my grandma's birthday) so I need to use the maximum of my time during the week and get as much done as possible. I still need to do two homeworks, and study the theory. I am trying to learn how to prioritize and plan things, this is still a huge problem for me

I found an interesting youtube channel: Justin Sung. he talks about how to study/ how to learn and I like what he says, because it just makes so much sense. it's been a while since I started suspecting that methods such as flash cards or simple note-taking don't work and his content explains very well why they indeed might not work. it's very inspiring to see a professional confirm one's intuition

when K ⊆ L is a finite extension by one element, say α with the minimal polynomial f, we can write 0 → (f) → K[x] → L → 0, where (f) is the kernel of evaluation at α. this is quite disappointing and very basic, but I haven't found anything better really. when there are finitely many intermediate fields between K and L for an extension L/K, L can be expressed as an extension by one element (Artin's theorem), which is still very specific

I didn't know about the group extensions, it makes the category of fields even more disgusting. I was hoping that the algebraic closure can be expressed as a colimit but of course not, not in the general case at least. but maybe at least some type of extensions can be realized as such? that's a nice thing to ponder. I'm pretty sure it will fail like every other request I had for this abomination of a category

I wonder what is typically done to make working with this category more pleasant. passing to Grp with the Galois group is one idea, the other I guess would be working with vector spaces or algebras? that would make sense considering that integral and finite ring maps are a thing and the field automorphisms play a role in the integral closure of ℤ in ℚ[√d]

on a sidenote, I laughed at the "lower body" and it reminds me how funny it is to talk about kernels in Polish. kernels and testicles are the same word

I've always thought 'splitting field' was a very cool sounding term. The Galois theorists did good with that one

september

I decided to start posting monthly, I hope it will help me keep it regular during the semester, it may also bring more structure into my posts

I gave my talk at the conference, I was surprised with the engagement I received, people asked a lot of questions even after the lecture was over. it seemed to be very successful in a sense that so many people found the topic interesting

what I need to do the most in the next 3 weeks is learn the damn geometry. sometimes I take breaks to study algebraic tolology, I did that yesterday

you guys seem to enjoy homology so here is me computing the simplicial homology groups of the projective plane. I tried to take one of these aesthetic photos I sometimes see on other studyblrs but unfortunately this is the best I can do lmao

my idea for mainly reading and taking notes only when it's for something really complicated seems to be working. I focus especially on the problem-solving side of things, because as I learned the hard way, I need to learn the theory and problem-solving separately. what I found is that sitting down and genuinely trying to prove the theorems stated in the textbook is a good way to get a grasp of how the problems related to that topic are generally treated. sometimes making one's own proof is too difficult, well, no wonder, experienced mathematicians spend months trying to get the result, so why would I expect myself to do that in one sitting. then I try to put a lot of effort into reading the proof, so that later I can at least describe how it's done. I find this quite effective when it comes to learning a particular subject. I will never skip the proof again lmao

in a month I'll try to post about the main things I will have managed to do, what I learned, what I solved, and hopefully more art projects

mood: filling an open set with dyadic cubes and pretending this is studying measure theory