I Got 55 And It Seems To Me That The Majority Of My Answers Were Heavily Influenced By Asd

god I hate when people do that. bonus points for "so the exam was super easy. what did you get?"

Hi ppl who are nosy and want to know ur grades so they can judge how smart u are are annoying as fuck

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 ;)

17 IX 2022

for the past few days life was treating me quite aggressively. today I had a terrible migraine, I feel weak and tired in general. doing math in a state like that isn't as pleasant so obviously I didn't do much, prioritized my health instead

during the semester I used The introduction to manifolds by Loring Tu to study analysis and I forgot that there were many nice exercises there that I didn't have time for but promised myself I would try them eventually

so tonight was the night and I studied grassmannians

I had some "results" done on my own, which later confirmed to be true, namely that the grassmannian over ℝⁿ for a 1-dim subspace is equivalent to a projective space of dimension n-1. I'm pretty sure that we are getting the projective of the same dimension for n-1 dim subspaces but I didn't calculate anything for n>3 so I might go back to that one day

it's fun to get hunches like that even if they turn out to be completely obvious to the authors of textbooks lmao

I am finally in the place with studying the theory for homology, commutative algebra and apparently differential topology (as it turned out today), where I have a variety of exercises I can try and that's the good part for me, always helps to get deeper insights and allows me to be more active

a friend asked me for a talk about the zariski topology in the context of algebraic sets and spectra of rings, so I'll see her soon for that. she will give me a personalized lecture about her thesis, which is about general topology. I am not a big fun of general topo but I'm always a slut for lectures about math so am excited for that

I hope my body will get its shit together because I still have to prep my lecture on euclidean geometry and when I don't feel good it's super difficult to motivate myself to do things that are not super exciting. I will never see productivity as a value on its own for this very reason lol I can barely do anything I don't find interesting

some more animation: how secant-teenager becomes tangent-adult

also! it illustrates a well-known inequality of a differentiable convex function and its tangents & the monotony of slopes

I'm reblogging this to compare it later with 1.A from Hatcher's Algebraic Topology. in that chapter he defines the topology on a graph if anyone else wants to check it out

Intuitively, it seems to me that graphs should be some sort of finite topological space. I mean, topology studies "how spaces are connected to themselves", and a graph represents a finite space of points with all the internal connections mapped out. That sounds topological to me! And of course many people consider the Seven Bridges of Königsberg problem to be the "beginning" of topology, and that's a graph theory problem. So graphs should be topological spaces.

Now, I vaguely remember searching for this before and finding out that they aren't, but I decided to investigate for myself. After a bit of thought, it turns out that graphs can't be topological spaces while preserving properties that we would intuitively want. Here's (at least one of the reasons) why:

We want to put some topology on the vertices of our graph such that graph-theoretic properties and topological properties line up—of particular relevance here, we want graph-theoretic connectedness to line up with topological connectedness. But consider the following pair of graphs on four vertices:

On the left is the co-paw graph, and on the right is the cycle graph C_4.

Graph theoretically, the co-paw graph has two connected components, and C_4 has only one. Now consider the subgraph {A, D} of the co-paw graph. Graph theoretically, it is disconnected, and if we want it to also be topologically disconnected, it must by definition be the union of two disjoint open sets. Therefore, in whatever topology we put on this graph, {A} and {D} must be open. The same argument shows that {B} and {C} must be open as well. Therefore the topology on the co-paw graph must be the discrete topology.

Now consider the subgraph {B, D} of C_4. It is disconnected, so again {B} and {D} must be open. Since {A, C} is also disconnected, {A} and {C} must be open. So the topology on C_4 must again be the discrete topology.

But these graphs aren't isomorphic! So they definitely shouldn't have the same topology.

It is therefore impossible to put a topology on the points of a graph such that its graph-theoretic properties line up with its topological properties.

Kind of disappointing TBH.

15 V 2022

I have a topology test this friday, not gonna lie I'm kinda stressed. this is my favourite subject and I am dedicating a great deal of time to learn it so if I get a low grade it undermines the efficiency of my work. everyone thinks I'm an "expert", but internally I feel like I lied to them. it's ridiculous, because I can solve all the theoretical problems fairly well but the moment I have to calculate something for a specific example of a space I am clueless. and it's about applying theory to problems, right? so what is it worth

other than that tomorrow is a participation round in the integral competition at my university. I am participating. I don't have any high hopes for this, because it's been a while since I practiced integration and I am not motivated to do so because it's not an important skill – wolfram exists. either way could be fun, that's why I decided to go there

I am dreading the fact that I'll have to sit down and learn all the material from the probability theory until the exams. I've been ignoring it completely so far, because it's boring and complicated. the last homework broke me, it's high time to get my shit together

hey guys quick question

hey be nice to me im just a teenage girl who has legally been an adult for years

7 X 2022

my first week is over. I'm tired and I can tell already that it will be a hard semester. I have already spent more than 15 hours on my complex analysis homework and I solved 1 problem out of 10, ugh

this subject is gonna give me major impostor syndrom lmao I know that these problems are putnam level difficulty but it's frustrating to have spent the whole day on something and fail. and I'm not kidding, I have a book on problem solving techinques for putnam and the exercises there are easier than those we do in class

one could say I'm bragging but it doesn't mean anything if I can complete only 1 of 10 problems which is a trivial corollary from Vieta's and took me about 4 hours to realize anyway

algebra homework was relatively easy, I discussed it with a few people who also take the course and together we completed the whole thing

for now I still have the motivation to try to look good so this week I've been pulling off dark academia aesthetic

I am afraid of my brain because it likes to give me meltdowns right when I need my cognitive performance to be reliable. I spent the whole holiday working on coping skills so I could spend less time sitting on the floor and crying

I spend most of the time with my boyfriend studying together. having a body double really helps