The Only Thing That This University Computer-science In-class-use File Is Dangerous To Is My Mental Health,

7 XI 2022

I think I found an advisor and a topic for the bsc thesis! or rather they found me

one of the teachers that prepares us for writing our theses approached me and started asking about homology I mentioned during our presentation, he wanted to know what courses I took and how familiar I am with that stuff. I told him that I know a bit about homology only from self-study but I enjoyed everything from algebraic topo so far and I would be happy to write about something from that. "ok then I'll find the right topic for you" was his response. then he suggested I read Groups of Homotopy Spheres by Milnor and Kervaire and write about surgery theory. I was sold the moment I heard that name, it's almost as funny as writing about the hairy ball

so there she is, very high level, very complicated. I barely skimmed the first half of that 34-page paper, it's gonna take a lot of work before I learn the basics necessary to even comprehend what is going on. it feels good to be noticed tho, I'm so happy to start writing asap

other than that my mood hasn't been in a great place, because commutative algebra is super hard and I am struggling to find the right resources to study. the last thing we did was tensor product and I've been procrastinating actually studying it by making pretty notes lol

I found a textbook that seems decent. the theory is very thoroughly explained here and there are plenty of exercises ranging from easy to difficult ones

recently I've been trying a new method of tracking, which is instead of writing to-do lists, I write down what I did each day, here is what it looks like for now:

I find it much less anxiety-inducing than the to-do approach because I know damn well what I need to do and writing down what I actually completed feels much better than crossing things off of the list

this week I hope to study the tensor product, representable functors (yoneda is still not done with me) and probably start the complex analysis homework. if I have time I will study the prerequisites for the Milnor's paper

The proof is left as an exercise to the IRS

well, google, one of them is a giant fuckin red dog

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

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)

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 ;)

Here’s a long but important comic for you <3

Accepting ourselves the way we are means we allow ourselves the things we need to make life a little easier. You don’t have to fight it, it’s ok have different needs to others. You are worthy of kindness, so be kind to you <3

love from the sad ghost club <3

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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.

oh and there is the dual thing: sometimes you just know that the professor hates the subject. like when I was taking one of the analysis courses, where the lecture was with one professor and the tutorials were with a different one

at the lectures we were two months into measure theory while at the tutorials haven't even started doing exercises on that topic, but oh it was fine, still plenty of time, he knows what he's doing – we thought, like fools. then the midterm was announced, two weeks left, we still haven't started measure theory. then it was one week left, so the professor tried to solve some lebesgue integrals with us, but he got so bored with each example that he hasn't finished a single one. at this point we just hoped that maybe measure theory just won't be on the midterm, it was too late to do anything. well, unfortunately, the midterm consisted mostly of measure theory problems, it made sense because that was the main content of the course

the professor was clearly very passionate about hating measure theory

One of the really amusing things about college is that if you pay attention you sometimes can discern some of your professor's favorite pet concepts.

For instance, in my Topology course this semester, the Zariski topology has come up at least once in every single homework set so far, and in multiple lectures.

And okay, that's not that weird. The Zariski topology is a really important object in a LOT of fields, especially algebraic geometry. And discussing it at length is a really pedagogically sound move because the Zariski topology is a good example of a topology with a very well motivated structure (the closed sets are the algebraic sets!) that still very naturally gives rise to a lot of strange features, like the way all open sets in the standard topology are Zariski-dense. It was quite effective at startling me out of the complacency of unconsciously basing my intuition of how topologies behave entirely on the standard topology on the reals. So my professor bringing up Zariski so often doesn't necessarily mean he has any special affection for it.

except...

My professor writes many of the homework problems himself. Not all of them - the less interesting ones he lifts from the textbook- but some. Well, every single Zariski topology question I've encountered so far is an original from this guy. I know because the all the questions he writes personally have paragraphs of commentary contextualizing why he thinks the problem is interesting and where the ideas in the problem are going later in the course. And well- let's just say the asides on the Zariski topology have been copious indeed

AND THEN there's the way he talks about the Zariski topology in class! It's with this blend of enthusiasm and fascination only comparable to the way I've seen tumblrites talk about their blorbos. Like hey! Come behold this sgrungy little guy! Isn't he fucked up? Isn't he marvelous? And I look and I can only conclude YEAH that is indeed a spectacular specimen, he's so strange, I want to put him in a terrarium and study him (and then I get to! In my homeworks!)

Anyways. It makes me really happy picking up on how excited my professor is to share this topology with us. I'm kind of baffled that people assume math is a boring field full of boring people when there exist folks like my professor who get this passionate about a topology!

10-12 VIII 2021

finished the basics of the measure theory and god am i in love

sleep: ok

concentration: good

phone time: good

yeah so now i know what a measurable set and a measurable function is, i'm on my way to lebesgue integration. however, i don't have the intuition for measurable functions yet, just the basics. there are those two theorems that i merely vaguely understand and idk barely can touch them. one of them is lusin, the other one is frechet. they seem very important as they deal with continuity of a function in the context of measurability. and do we love continuous functions my dude yes we do

tomorrow i plan to solve some problems concerning measurable functions and then do topo. i must admit, measure theory devoured me entirely recently and i had a break from topo. gotta fix that. and possibly do some coding