Fun Fact! Did You Know That You Can Gain Extra ‘forbidden Time’ By Staying Up Late In The Night?

27 IV 2022

neglected this place very much, would like to start posting again

may I start with what's new

the last semester was pretty much a failure, I passed everything but my grades were trash. had me seriously doubting my abilities

turns out studying comes easier when I am medicated correctly. I was diagnosed with adhd and asd, so now that I have proper meds and understand my brain a little bit better, things come easier

I fell deeply in love with algebraic topology. there was a notion of excitement about the whole concept of homotopy a few months ago, but now I am fiercely invested in making algebraic topo my field of choice

psychologically I am working on focusing more on the process than the results. it means that my goal is not "to be good at math" but rather to complete this homework, pass that test, etc., in hopes of reducing some of the stress coming from the fear of failure

my current semester is quite boring. ODEs are trivial, yet I have to sit on my ass for a few hours and learn how to solve them. analysis is difficult as always although differential forms are interesting. probability theory is just not my thing. only topology is the light in the tunnel

I don't have any specific plans for the next few days nor do I have any goals. maybe I want to study covering spaces and solve some problems concerning the fundamental group. other than that I need to complete my analysis homework and study de Rham cohomology

here are my category theory notes

in a way. over the last two years or so. mathematics has become the altar at which I pour out my private grief, and transmute it to something like solace. it does not particularly matter to me if I am ever any good at it. what matters is that the effort I apply to it is rewarded by understanding. I have no natural aptitude for it; I am climbing this hill because it was the steepest and least hospitable to me. there is less agony in the gentler slope, but less valor

13 IX 2022

my euclidean geometry journey will be over soon and the start of the semester is so close, it's kinda scary

recently I stumbled upon someone's post with a time-lapse video of their study session. I liked it so much that I decided to make mine

this is me learning about the snake lemma and excision

the excision theorem is the hardest one in homology so far btw, I spent about 4 hours on it and I am barely halfway through. I like the idea of the proof tho, it's very intuitive actually: start simple and tangible, then complicate with each step lmao

I realized two things recently. one of them is that deeply studying theorems is important and effective. effective, uh? in what way? in exams we don't need to cite the whole proof, it suffices to say "the assertion follows from the X theorem"

yeah right, but my goal is to be a researcher, not a good test-taker, researchers create their own proofs and what's better than studying how others did it if I am for now unable to produce original content in math?

the second things is that I learned how to pay attention. I know, it sounds crazy, but I've been trying another ✨adhd medication✨ and after a while I realized that paying attention is exhausting, but this is the only way to really learn something new, not just repeat what I already know. it made me see how much energy and effort it takes to make good progress and that it is necessary to invest so much

I am slowly learning to control my attention, which brings a lot of hope, as I believed that I had to rely on random bouts of hyperfocus, before I started treatment. I am becoming more aware or how much I am focusing at the given moment and I'm trying to work on optimizing those levels. for instance, when I'm reading a chapter in a textbook for the first time, it is necessary to remember every single detail, but wanting to do so consumes a lot of energy, because it means paying constant attention. it is ineffective because most likely I will have to repeat the process a few more times before I truly retain everything. being able to actually pay attention at will sure does feel good tho, as if I had a new part of my brain unlocked

I am solving more exercises for algebraic topology, procrastinating my lecture prep lmao. I am supposed to talk about the power of a point and radical axes, I have a week left and I can't force myself to start, because there is so much good stuff to do instead

I have a dream to produce some original results in my bachelor's thesis. it may be very difficult, because I hardly know anything, that's why I'm calling it a dream, not a goal. the plan is to start writing at the end of the semester, submit sometime in june

I spent last week at the seminar on analysis and oh boi, I will have to think twice next time someone asks if I like analysis. the lecturer who taught me at uni had a different approach than the "classic" one. we did a little bit of differential geometry, Lie groups and de Rham cohomology, those are the things I like. meanwhile at the seminar it was mostly about analytic methods of PDEs, the most boring shit I have ever seen

complex analysis will most likely be enjoyable tho, I'm taking the course this semester

for the next few days I need to force myself to prep that damn geometry lecture. other than that I plan to keep solving the AT exercises and maybe learn some more commutative algebra. I wish everyone a pleasant almost-autumn day 🍁

" 'They' isn't singular!" Oh yeah? Show me its multiplicative inverse matrix then.

13 III 2023

I remember putting it in my bio a while ago that I dream of doing actual research one day. well this is already happening, as I mentioned in some post, my advisor found an open question for me to write my thesis about

the progress for now is that I'm done with most of the reading I need to do to tackle it and I'm slowly moving forward with thinking of ideas for the solution (or at least a partial one)

this is what I want to do for the rest of my life: reading papers and trying to write my own ones

ofc I don't know if I manage to solve the problem or achieve anything at all with it but the process itself is fun

other than that I've been catching up with homeworks and assignments from work. fortunately I found an MIT lecture recordings for statistics so hopefully I might not die from boredom

watching probability and stats lectures from MIT has been my relationship's idea of netflix and chill for a while now, gotta cultivate the tradition

the algtop professor asked us to write down a full detailed solution for an exercises we did in class, because the person presenting was unable to explain it so I sent him mine

I don't know yet if it's correct but I'm pretty sure it is. I wrote this down partly because who doesn't want extra points and partly because I didn't have a chance to present it, the person who did was faster

I like how my life is right now, I want to keep it that way

req'd by @strictly-script

sure we won't?

text: Abelian't

http://proof.ucalgaryblogs.ca/

This is the best resource for studying math that I've found in a while! It's 300+ pages of flawed/incorrect proofs on topics including logic, analysis, and linear algebra. Each flawed proof is followed by a classification of its errors, and a corrected version.

if you don't want to learn tikz but still need them arrows, check out quiver. it's super useful for complicated and unconventional diagrams

Learning LaTex has been a way more pleasant experience than I thought it would be this stuff is way simpler than it looks and the results fuck hard

ofc that's right, thank you for fact checking!

Me duele la cabeza

"numbers don't lie" the real numbers are literally a lie group