September

A monoid? Oh, you mean a monad on a one point set in the bicategory of spans of sets?

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

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

hey netizens! i'm not sure how many people are aware, but youtube's been slowly rolling out a new anti-adblock policy that can't be bypassed with the usual software like uBlock Origin and Pi-Hole out of the gate

BUT, if you're a uBlock Origin user (or use an adblocker with a similar cosmetics modifier), you can add these commands in the uBlock dashboard (under My Filters) to get rid of it!

youtube.com##+js(set, yt.config_.openPopupConfig.supportedPopups.adBlockMessageViewModel, false) youtube.com##+js(set, Object.prototype.adBlocksFound, 0) youtube.com##+js(set, ytplayer.config.args.raw_player_response.adPlacements, []) youtube.com##+js(set, Object.prototype.hasAllowedInstreamAd, true)

reblog to help keep the internet less annoying and to tell corporations that try shit like this to go fuck themselves <3

Theory Time

The reason endermen don’t like it when you look at them is because they communicate telepathically with one another by locking eyes! Humans are absolutely not designed to do this so when we look at them we are accidentally projecting all of our thoughts into them at the same time and it hurts :(

you really can't

wha?

please explain what this message means or else the curiosioty will kill me

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 ;)

The only thing that this university computer-science in-class-use file is dangerous to is my mental health, and the only thing it harms is my soul, but thanks for looking out for me google :)

tips for studying math

I thought I could share what I learned about studying math so far. it will be very subjective with no scientific sources, pure personal experience, hence one shouldn't expect all of this to work, I merely hope to give some ideas

1. note taking

some time ago I stopped caring about making my notes pretty and it was a great decision – they are supposed to be useful. moreover, I try to write as little as possible. this way my notes contain only crucial information and I might actually use them later because finding things becomes much easier. there is no point in writing down everything, a lot of the time it suffices to know where to find things in the textbook later. also, I noticed that taking notes doesn't actually help me remember, I use it to process information that I'm reading, and if I write down too many details it becomes very chaotic. when I'm trying to process as much as possible in the spot while reading I'm better at structuring the information. so my suggestion would be to stop caring about the aesthetics and try to write down only what is the most important (such as definitions, statements of theorems, useful facts)

2. active learning

do not write down the proof as is, instead write down general steps and then try to fill in the details. it would be perfect to prove everything from scratch, but that's rarely realistic, especially when the exam is in a few days. breaking the proof down into steps and describing the general idea of each step naturally raises questions such as "why is this part important, what is the goal of this calculation, how to describe this reasoning in one sentence, what are we actually doing here". sometimes it's possible to give the proof purely in words, that's also a good idea. it's also much more engaging and creative than passively writing things down. another thing that makes learning more active is trying to come up with examples for the definitions

3. exercises

many textbooks give exercises between definitions and theorem, doing them right away is generally a good idea, that's another way to make studying more active. I also like to take a look at the exercises at the end of the chapter (if that's the case) once in a while to see which ones I could do with what I already learned and try to do them. sometimes it's really hard to solve problems freshly after studying the theory and that's what worked out examples are for, it helps. mamy textbooks offer solutions of exercises, I like to compare the "official" ones with mine. it's obviously better than reading the solution before solving the problem on my own, but when I'm stuck for a long time I check if my idea for the solution at least makes sense. if it's similar to the solution from the book then I know I should just keep going

4. textbooks and other sources

finding the right book is so important. I don't even want to think about all the time I wasted trying to work with a book that just wasn't it. when I need a textbook for something I google "best textbooks for [topic]" and usually there is already a discussion on MSE where people recommend sources and explain why they think that source is a good one, which also gives the idea of how it's written and what to expect. a lot of professors share their lecture/class notes online, which contain user-friendly explenations, examples, exercises chosen by experienced teachers to do in their class, sometimes you can even find exercises with solutions. using the internet is such an important skill

5. studying for exams

do not study the material in a linear order, instead do it by layers. skim everything to get the general idea of which topics need the most work, which can be skipped, then study by priority. other than that it's usually better to know the sketch of every proof than to know a half of them in great detail and the rest not at all. it's similar when it comes to practice problems, do not spend half of your time on easy stuff that could easily be skipped, it's better to practice a bit of everything than to be an expert in half of the topics and unable to solve easy problems from the rest. if the past papers are available they can be a good tool to take a "mock exam" after studying for some time, it gives an opoortunity to see, again, which topics need the most work

6. examples and counterexamples

there are those theorems with statements that take up half of the page because there are just so many assumptions. finding counterexamples for each assumption usually helps with that. when I have a lot of definitions to learn, thinking of examples for them makes everything more specific therefore easier to remember

7. motivation

and by that I mean motivation of concepts. learning something new is much easier if it's motivated with an interesting example, a question, or application. it's easier to learn something when I know that it will be useful later, it's worth it to try to make things more interesting

8. studying for exams vs studying longterm

oftentimes it is the case that the exam itself requires learning some specific types of problems, which do not really matter in the long run. of course, preparing for exams is important, but keep in mind that what really matters is learning things that will be useful in the future especially when they are relevant to the field of choice. just because "this will not be on the test" doesn't always mean it can be skipped

ok I think that's all I have for now. I hope someone will find these helpful and feel free to share yours