" 'They' Isn't Singular!" Oh Yeah? Show Me Its Multiplicative Inverse Matrix Then.

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

hmmmm idk, this seems like an overgeneralization to me

this whole semester I've been slacking a lot even though I knew I could try harder, but at the same time I felt like even if I give a solid 30% from myself I can still pull it off, so that's what I did. there was no particular reason for it, many times I just didn't feel like studying. I wasn't tired or stressed, if anything I was too relaxed

right now I regret it, while I'm studying for exams I can tell that if I worked more regularly it would be much easier and I would learn much more, but yeah, it seems like I'm going to pass with pretty good grades. however, having had been more systematic I would get better outcomes, especially that I totally had the means to do that. what is this if not pure laziness?

"lazy" is not a negative word in my opinion, or at least it shouldn't be used as such. laziness is when I know I can do better but I choose not to, when I know I can make my future great, but instead I settle for making my future just okay. sometimes there is no underlying reason for it, I simply don't feel like doing more than borderline enough

but that happens sometimes and I think we shouldn't assume that if there is no reason then there must be a hidden reason, because it implies that the natural state of being is working hard and doing your best, which sounds a bit too capitalistic to me. I know for sure that unless there is a reason not to, I will be lazy, and I don't see why this is a bad thing

this was a great read. “Laziness Does Not Exist” by Devon Price

31 VII 2022

finally posting after the exams are over, it was the longest session I have ever experienced, a month of exams. I passed everything and it was a good semester, actually my grades are better than ever before, which comes off as a surprise, I can't believe that it's anything other than luck

now what am I going to do for the holiday huh

next semester I am going to take three courses: analytic functions, commutative algebra and a mix-course of category theory, sheaf theory and homological algebra. then I plan to take algebraic topology, algebraic geometry, number theory and some more abstract algebra, along with writing a bachelor's thesis. this is probably going to be the hardest year so far, I don't know how I am going to survive this, I'm so scared

I was asked to give some lectures on geometry during a math summer camp for people who want to participate in the math olympiad. it's a great opportunity for me to practice giving lectures, as that's what I plan my job to be. moreover, it is my dream to be so good at math that I could prep people for the olympiad, hence that's a fraction of that dream coming true

the problem is I don't know geometry lol last time I did any was like four years ago in high school

thus I play with triangles everyday

other than that I must prepare a talk for a conference, I chose to do one on the knot theory, Seifert surfaces specifically. I started reading about it some time ago and it seems super cool

untangling knots is a perfect thing to do for fun

my plan for the holiday outside of these side-quests is to learn as much as possible for the courses that I'll be taking. the problem with them (besides analytic functions) is that they will be quite technical, detailed and dry, as they are supposed to give the tools necessary to study algebraic topology and geometry. that does sound dreadfully boring, no? that's what scares me, because when I am not interested in what I'm trying to learn everything becomes twice as hard. I asked here and there for advice and people told me to read about algebraic geometry in tandem with commutative algebra, since many constructions have beautiful interpretations and motivations there. sounds like exactly what I need

my bachelor's thesis will be on algebraic or differential topology probably, but I don't know exactly what I want to write about. I was thinking about vector fields on manifolds or de rham cohomology, but the thing with the proseminar on geometric topology (mine) is that it's been planned to give the introduction to the currently researched topics and offer opportunities to work with fresh conjectures and theorems. at least that's how it was described. allegedly geometric topology has this property that undergrads can contribute to the development of new theory, which is very surprising to me ngl, I would guess that this is highly unlikely with any kind of math nowadays and yet here we are

in conclusion, I'm excited but scared

free recall

here I am sitting and trying to learn something from a textbook by making notes and ugh I don't think this is gonna work

what I'm writing down will probably leave my head the second I switch tasks

today I found a cool video about taking notes during lectures and a method called free recall is mentioned there:

to summarize: taking notes during the lecture is ineffective, because it requires dividing attention into writing and processing the auditory input. instead of doing that one should just listen and then try to write down the contents of the lecture from memory. I can believe that – this is how I studied for my commutative algebra exam and the whole process went really fast. I highly recommens this guy's channel, he is a neuroscientist and bases his videos off of research findings

I will try to do this with textbooks and after a while I'll share how it felt and if I plan to keep doing it. the immediate advantage of this approach is that it gives raw information for what needs the most work and what can be skipped, which is often hard to see when trying to evaluate one's knowledge just by thinking about it. another thing that comes to mind is the accountability component – it is much easier to focus on the text while knowing that one is supposed to write down as much as possible after. kinda like the "gamify" trick I saw in the context of surviving boring tasks with adhd

I'll use this method to study differential geometry, algebraic topology, galois theory and statistics. let's see how it goes

10 IX 2022

today I need some extra motivation to study because I didn't sleep well these past few days and it has drastic effects on my productivity, energy, motivation and what have you

also I am struggling to make the choice as to what I should do today

yesterday I started solving some basic exercises from hatcher's textbook

Δ-complex structures are becoming more intuicitve with time. take my solutions with a grain of salt, I am just starting to learn about these things and won't vouch for them lmao

some more complicated objects (the last one is an example of a lense space)

I decided to study commutative algebra today

so far I'm enjoying it. not as much as algebraic topology (which will always be my number 1) but it has its beauty

right now I'm at hom and tensor functors, the structures are fairly complicated, but pretty, and they look like they need to be studied in stages, with repetition and breaks, to fully grasp what's going on

my sensory issues are terrible today and I'm exhausted and hyperactive at the same time uh

I'll try working through a lecture on commutative algebra and give an update on how it went later

update: I studied for a while, but it wasn't going great so I decided to take a nap instead. god knows I tried

30 I 2023

in a fortnight I will have two oral exams and one problem-based exam

the first oral will be for complex analysis and we are supposed to choose three topics from which the professor will pick one and we'll have a chat. I chose meromorphic functions, Weierstrass function and modular function. I have already received my final score from homeworks, which is 73%. combined with 74% and 100% from tests, I am aiming for the top grade

the rest of exams will be for algebraic methods. a friend who already took this course told me that when someone is about to get a passing grade, they get general questions and the professor doesn't demand details of proofs. when I asked him if we are supposed to know the proofs in full detail or if it suffices to just be familiar with the sketch, he told me that if I will only know the sketch I will sit there until I fill in all the details. lmao that sounds like he wants me to get a top grade. ok challenge accepted

so it seems like I have a chance to ace everything. if I achieve this and do it again next semester I can apply for a scholarship. studying for the sole purpose of getting good grades doesn't feel right, the grades should come as a side effect of learning the material. buuut if I can get paid for studying then I might want to try harder, I enjoy being unpoor

the next two weeks will be spent mostly grinding for the algebraic methods exams, this is what I'm doing today

→ 3 IX 2021

such a weird day today. i finished complete spaces and then moved on to preparing for the math conference i'm going to on sunday. there is a lot of high level stuff so i won't be able to learn everything, of course, but i'm doing my fav thing ever and enjoying it thoroughly. that is, switching from a topic to a topic in the spare of 15 minutes and reading a bit about anything until it stops being ✨super exciting✨

this amounts to a total of 8 hours of math and i am not done yet. love it, absolutely love to waste time like that

concentration: fucking ∞

tomorrow i'm doing an algebra speedrun with bf and two of our friends. this is an experiment aiming at seeing how much information we are able to pack into our heads in one sitting. we haven't studied abstract algebra before. then in a few as i mentioned i am going to a math conference, with bf and our other friend. excited about that too. i fucking love math

Artificial intelligence makes accurate sheep counting.

oh i just saw, congrats on the bachelors!! im still in calc 3, i thought itd be less mundane but it is actually killing now to the point where i cant even open our stewart text. all my friends in decent math programs are doing more fun and general versions this course. i just cant wait to not use this awful book anymore (all our work is based on the books problems and methodology). all this is to say your progress is inspiring. hopefully i get to a point where i can also be having fun around structures and such, i just have to finish grinding through the filter of "do a bunch of this and don't worry about what it really means, btw good luck problem solving on your exams with 0 neither provided intuition nor rigor". i hope blogs like this stick around!

thank you for the nice message!

I'm so sorry to hear that this is how they teach you math, something like this takes away all pleasure and satisfaction. I didn't have calc 3 as such at my university, we would generally focus on theory and understanding from the start. however, we did have some courses where the mindset was like you just described and it was torture. I hope it changes for you soon so that you can finally enjoy some beautiful math!

BCC

A minimal figure-eight knot on the body-centered cubic lattice

(source code)