1 X 2022

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

(I'm reblogging this for later to really look into all the amazing accounts I follow)

Let's get a new mathblr roll call going! There's an older version but it's got a decent number of inactive people on it so let's start fresh. Reblog and/or reply tagging yourself and any other good math accounts!

Math shitposters! Math academia aesthetic blogs! Math studyblrs! Unthemed blogs owned by people who happen to be math fans! CS, stats, physics and other math-adjacent dorks too if they like hanging out with the math crowd! I want them all!

the human experience is so crazy. at any time i want, for free, i can comprehend the beauty and the horror of my own fragile existence, the cosmic insigificance and personal significance of my experiences, the impossibly vast yet laughably tiny boundaries of my own consciousness, and feel sick to my stomach with anticipation for everything i have yet to understand and grief for everything i have yet to lose.

Quatrefoil Knot

omg so that's why so many empty blogs follow me. I've been blocking them at first assuming that they were bots, but at some point the usernames started sounding way too normal-human-like, so I stopped, my instinct told me something else was going on. lemme just unblock all the empty blogs now, damn, I'm so sorry to everyone who wanted to follow me but was blocked out of habit!!

fun fact!! it turns out that now when u make a new blog, tumblr forces you to follow 3-4 people before you can change your icon or modify your blog in any way!! this, of course, means that, yes, some of the "potential bots" many of us have been automatically blocking could have possibly been genuine new users who were only just seconds in to having an account!!! tumblr is literally screwing new users over!!!!

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

everybody cries doing their math hw, those who claim they don't just haven't met that hw yet

this unlocked some ancient pain lol

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 🍁

You think math should relate to the real world? What are you, some kind of physicist? Get the fuck out of here

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