Latest Posts by bsdndprplplld - Page 9

22 VIII 2022

I will have to give a talk soon, in a few days I'll be attending a student conference. I decided to prepare something about my latest interest, which is knot theory. what makes it so cool for me is that the visual representations are super important here, but on top of that there is this huge abstract theory and active research going on

I decided to talk about the Seifert surfaces. this topic allows to turn my whole presentation into an art project

other than that I'm studying euclidean geometry and unfortunately it is not as fun as I thought it'd be

my drawings are pretty, ik. but there is almost no theory

I had a thought that working through a topic with a textbook is a bit like playing a game. doing something like rings and modules, the game has a rich plot (the theory), and quests (exercises) are there to allow me to find out more about the universum. whereas euclidean geometry has almost no plot, consists almost solely of quests. it's funny cause I never played any game aside from chess and mine sweeper

commutative algebra turned out to be very interesting, to my surprise. I was afraid that it would be boring and dry, but actually it feels good, especially when the constructions are motivated by algebraic geometry

commalg and AG answer the question from the first course in abstract algebra: why the fuck am I supposed to care about prime and maximal ideals?

oh and I became the president of the machine learning club. this is an honor but I'm understandably aftaid that I won't do well enough

I'm stressed about the amount of responsibilities, that's what I wanted to run away from by having the holiday. good thing is I gathered so many study resources for this year that I probably won't have to worry about it anytime soon, or at least I hope so

for the sake of an updates to this, I didn't get 100% on that topology test. I got 85%, which was the third best score. I finally scored the highest possible final grade on that subject, so I'm satisfied. fuck I love algebraic topology so much and I think she loves me

oh and I scored fucking 54% on the analysis test. I think I had a mental orgasm when I found out about that lmao it felt so good. I finished the course with a grade of 4 (idk if it's universal, so 2=the lowest, failed, 5=the highest) which is the best I ever got in the analysis course

28 V 2022

topology and analysis tests are over, both went I think alright

if I don't get 100% from topo I'm going to be very frustrated, because I studied hard and acquired deep understanding of the material – so far as to be able to hold a lecture for my classmate about any topic

analysis ughhh if I get ≥40% I will be overjoyed. but that's just the specifics of this subject, you study super hard and seem to be entirely ready, you solve all of the problems in prep and then best you can do is 40%. my best score so far was 42%, so anything more than that will be my lifetime record lmao, I want this so bad. I solved two problems entirely I think, which should give 40% already, and some pieces from two more, chances are I get 50%, which would be absolutely amazing

here are some pictures from me transforming math into an art project

stokes theorem

topology

I was thinking about how annoying I find what people say to me when I tell them that I'm not happy with how I'm doing at math. their first idea is to tell me how great I am and how all I do is good enough and shit like that. it doesn't help, it just feels like I am not being taken seriously. when I barely pass anything, am I really supposed to believe that everything is actually good? it feels like they skip getting to know my situation and just tell me what they would tell anyone, automatic

when I try to calm myself down and think something that will keep me going I don't try to force myself to be happy, fuck that, not being content with one's achievements is very fine, I believe not being happy all the time is fully natural and all that positivity feels so fake

instead what seems to work is asking myself where the rational threshold of being ok with how I'm doing is. the thing is I will never be satisfied, whatever I have, I always want more. but I can set the limits in advance and that stops me from falling into self-loathing loops

although what has really changed the game for me was getting a few good grades, finally I am achieving something, anything. people tell me that I should learn to be alright without this external reliance on achievements but how am I supposed to do that when the source of my low moods is precisely getting less than I want? I don't understand why I should brainwash myself into thinking that this is actually not what I want. the trick here is to separate the goal-orientedness from the sense of self-worth. the groundbreaking realization of mine was figuring out that I believe I deserve more than I get, that's why I am unhappy. so now that I am getting what I think what I deserve I obviously feel much better

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

28 V 2022

topology and analysis tests are over, both went I think alright

if I don't get 100% from topo I'm going to be very frustrated, because I studied hard and acquired deep understanding of the material – so far as to be able to hold a lecture for my classmate about any topic

analysis ughhh if I get ≥40% I will be overjoyed. but that's just the specifics of this subject, you study super hard and seem to be entirely ready, you solve all of the problems in prep and then best you can do is 40%. my best score so far was 42%, so anything more than that will be my lifetime record lmao, I want this so bad. I solved two problems entirely I think, which should give 40% already, and some pieces from two more, chances are I get 50%, which would be absolutely amazing

here are some pictures from me transforming math into an art project

stokes theorem

topology

I was thinking about how annoying I find what people say to me when I tell them that I'm not happy with how I'm doing at math. their first idea is to tell me how great I am and how all I do is good enough and shit like that. it doesn't help, it just feels like I am not being taken seriously. when I barely pass anything, am I really supposed to believe that everything is actually good? it feels like they skip getting to know my situation and just tell me what they would tell anyone, automatic

when I try to calm myself down and think something that will keep me going I don't try to force myself to be happy, fuck that, not being content with one's achievements is very fine, I believe not being happy all the time is fully natural and all that positivity feels so fake

instead what seems to work is asking myself where the rational threshold of being ok with how I'm doing is. the thing is I will never be satisfied, whatever I have, I always want more. but I can set the limits in advance and that stops me from falling into self-loathing loops

although what has really changed the game for me was getting a few good grades, finally I am achieving something, anything. people tell me that I should learn to be alright without this external reliance on achievements but how am I supposed to do that when the source of my low moods is precisely getting less than I want? I don't understand why I should brainwash myself into thinking that this is actually not what I want. the trick here is to separate the goal-orientedness from the sense of self-worth. the groundbreaking realization of mine was figuring out that I believe I deserve more than I get, that's why I am unhappy. so now that I am getting what I think what I deserve I obviously feel much better

also a funny thing is happening

my title here on tumblr is "you can't comb a hairy ball" – hairy ball theorem, which says that whenever an n-dimensional sphere admits a continuous field of unit tangent vectors, n must be odd. I love how geometric this is, math is full of memes

anyway when I found out about it I was joking that my thesis will be on it. and now it's actually very likely that my first thesis will be about hairy manifolds, I can't wait till I can start writing

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

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

reverse gaslighting where i pretend to know exactly what you are talking about

Person: *breathes*

Graph Theorists: NO NOT THAT KIND OF GRAPH

8 V 2022

I am on my way home from a math conference, the first one in which I participated actively – I prepaired the talk about the Borsuk-Ulam theorem

my lecture was centered around the connection between the classic "continuous" BUT and its combinatorial analog: Tucker's lemma

I wanted to talk about this because I was amazed at how cool and "versatile" this theorem is. there is a whole book about its applications and generalizations, which is btw very well-written, I highly encourage everyone to read it:

my presentation went well, although after practicing it for about a week the topic seemed really fucking boring to me, no wonder

other than that I have another recommendation to make. do you also hate how messy multivariable calculus is? I do. calculations and technical definitions everywhere, and at the end everything comes down to calculating the determinant of some jacobian. bluh. I stumbled upon a book that describes everything from a sort of algebraic perspective, smells a little bit like category theory too. very clean, very satisfying to read:

I have been studying covering spaces recently and I can give some dope motivation for learning about the structure induced by the covering mapping:

I will never forget that the homomorphism induced by the covering projection is injective

that would be it for my mathemathical life. my personal life, which is still closely connected to math, brings me some psychological progress. I no longer get stuck in loops of "oh I'm so bad at math. maybe I'm not? I got a good grade from X. ah but I got a shit grade afterwards". it might be because I didn't fall on my face for a while now, only decent grades, good ideas, a good presentation, this is correct. but I also do not negotiate with myself that this is supposed to be proof that I'm good enough, I just stopped paying attention to these and focused on math instead. and paradoxically when I stopped caring about being good at math I was rewarded with getting better at math???

a coincidence,

a pleasant one, nonetheless.

anyway I will have to take a fall at some point, unavoidable. and it will be the final test of my progress, becauase I used to get very elevated in my sense of self-worth after receiving a single good grade among trash ones and now I'm just ok. not the god, just ok. but back then, at some point I would no longer be god, I would get smacked in the face by some "proof that I'm actually trash" and that would be a fall from a significant altitude. so I'm hoping that the fall will also be less painful now

I think the biggest change I made was giving up, I abandoned all hope. nooow here is the moment when people interrupt me with "nooo that's horrible don't give up you're a great person you just have to notice that"

fuck off you don't understand shit

I'm doing better now precisely because I stopped hoping that one day I'll stop feeling worthless, that one day something great will happen that will prove once and for all that I'm meant for something great. I can't stand this anymore, I am disgusted by the fact that deep down I still believe that I'm supposed to be the best and that I can't enjoy anything unless I am winning. I want to puke when I'm reminded that everything I do serves the purpose of winning the negotiations I have with myself about what my actual value is

my self-hatred runs much deeper now than ever before and I have no more patience for self-victimization, no more room for "allowing myself to feel". fuck off, all I feel is rage. I want to be able to do things without the prospect of a reward, my goal is to enjoy things, not the sense of being good at doing things

so that's what I'm doing, I made peace with the fact that I will probably never feel good about myself and that I have no chance at achieving the greatness I crave. and I must say I started respecting myself more, turns out I am actually able to do things without the promise of being the best at them, the vision of bringing value to the world motivates me. and fuck the western culture with its oh you must love yourself you are a great person. no, you don't have to do that and you have no way of knowing what kind of person you are, nobody has ever defined it in a strict formal sense, people just use this phrase to trigger the feel-good in others

I am aware that all of this sounds really bad, but I don't care, it works. and my math will be better like that because now that I stopped crying over being trash I have more time to study

I just hope that the fall won't be as painful

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

→ 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

daaamn girl are you a graph?

cause you're very edgy

→ 30 VIII 2021

not much has happened really

concentration: 4

doing topo as usual, stopped doing as much analysis, just enjoying my break from coding with abstract ideas

reading books about math became sort of a comfort thing for me. i fell in love with just sitting there and trying to imagine everything. i wish i could be payed for studying math, i would be a fucking billionaire at this point

→ 25 VIII 2021

ok so it's been very busy for me for the past few days. we made the yt video with bf and i finally moved out from my parents

concentration: 4 (recently)

i did some topo but not in a very by-the-book way, more like just reading some interesting stuff in various places. homotopy is super fascinating and visual, i love it. other than that i read about other basic concepts such as compact spaces, connected spaces and axioms of countability. i used to read about the aforementioned axioms a while ago and think "why would you even define something like this why does it matter" but after reading topology by jänich i have the intuition that the first axiom is strongly related to the convergence of sequences, hence knowing that the space is first-countable might be useful for evaluating things like the continuity of mappings and compactness

now, i also have a book called elementary concepts of topology by alexandroff and i can't stop reading it, i'm on the page 20 out of 60 since yesterday. and i think i might finish it today but i'll see. i also want to study 1-dimensional manifolds today or tomorrow

i've been working on it with my boyfriend for a while now and–

our first video is up!

i hope you enjoy it and subscribe to our channel

https://youtu.be/-X2BBtRI1Xw

13-16 VIII 2021

much work recently gotta code

gonna monitor only my focus now, define the scale such that 1 means "can't concentrate at all" and 5 means "hyperfocus". today was

focus: 2

i am not doing as much math as i'd like to as i have to focus on the python project i'm doing with bf. anyway, we can say that i did cartesian products of topo spaces, i do have some basic understanding of the concepts now. i started compact spaces. i also need to read some stuff on connectedness and put extra time into analyzing examples of what i've been learning about. so that's the next thing on my schedule, after i'm done with compact and connected spaces

but hey i have 1.5 month of the holidays left and i learned most of the theory planned for me on analysis and half of what i'm supposed to learn on topo. doing good

other than that i decided to write down the structure of how i study:

i find it to be a good way for studying math, it goes brrr like this:

general idea → details, connections and applications

i gained some followers already, i hope you guys enjoy this and possibly find it helpful. moreover, i'm very interested in your custom study algorithms if you have any

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

Inflating regular pentagon through underlying stars. The sequence of side lengths is essentially Fibonacci.

Square is a rhombus, regular hexagon can be tessellated with three equal rhombuses, and every regular polygon with even number of sides can be rhombi-tessellated.

uhh probably the worst math feeling is when you're so excited about proving something and you talk about it to someone who does math with you and they say oh but it's trivial

some experimentation with colors, i tried the inverse:

looks neat tho i think i won't stick to that, as my previous notes are black on white and the inverse is taken by changing the template and the marker color uhh they're gonna be incompatible

7-9 VIII 2021

did math and coding nothing special really

sleep: good

concentration: good

phone time: good

reading about measure theory. here is a great book:

everything is so well explained here. i wish i could do more math than i have time for but i guess it's fine, it's holidays, i will wreck my brain completely anyway when october comes

tomorrow more measure theory and topo

It's always funny when a math book or a paper starts out with like a foreword/introduction type thing but it calls itself an "Apologia"

Like "Sorry i wrote a new book, this is why i thought i had to do it. Please forgive me."

6 VIII 2021

went back home

sleep: good, finally, although it's already almost 3 and i'm still up so i gotta go be unconscious for a few hours soon

concentration: fine

phone time: fine

did some measure theory, only this today and i'm in love, shit's fucking amazing

tomorrow i'll probably do more measure theory and possibly some coding

mood: filling an open set with dyadic cubes and pretending this is studying measure theory

4-5 VIII 2021

did much topo and walked

sleep: weird. 5 hours. woke up at 3:30, at least right now it seems i might finally fix my circadian rythm

concentration: not good. too little sleep

phone time: good

almost done with operations on topo spaces and did some measure theory today. i love it so much, it's so new and yet so intuitive

tomorrow gonna take a peek at some art probably and possibly finish the operations on topo spaces, hoping to jump right into connected spaces and maybe do some more measure theory. kinda gave up with multivar calc boring af lol

Zero to the power of anything is zero. Anything to the zeroth power is one. So what is zero to the zeroth power?

The world's most cited mathematicians would seem to be in disagreement about the issue

also i'm having a quarrel with my parents, i'm afraid they will disown me or kick me out

they are anti-vax and full-blown conspiracy theorist and my mother found out i took a covid vax

the fact that my father believes the earth is flat makes me so motivated to become a full-time scientist, being the very thing they hate. then they could not undermine what i say with "what the fuck do you know, you're just a student"

my father likes you only if you agree with him and he literally tells me every time we talk that i am stupid and should go fuck myself. not that i don't say the same things to him, i do, i hate the fact that this is how this relationship works

i am aware that doing things to prove something to someone is not the way to go but up to this point it was just my goal, one of many, to be a scientist, now it feels like a necessity

i'm conducting an experiment on how to study the theory effectively

there are i guess two main ways:

(1) read and take notes simultaneously

(2) read first, then take notes

so for the first one, there is the risk of going passive with the note-taking, writing down the symbols without focusing on their meaning. for the second one there is the risk of zoning out and just reading the symbols, again, losing their meaning

the problem seems to be that the processing of sheer symbols and processing their meanings might be disjoint and their natural tendency seems to be so

from my recent actions i noticed that (1) doesn't work for me as effectively as (2)

it might be that when i don't plan to write something down right away, i am more inclined to remember these things short-term as "i won't be able to check it later so remember it now in order to understand what comes next", and when i'm taking notes simultaneously it's "i have it written down anyway so i can take a peek anytime"

so now i'm testing the strategy of

read → try to understand the idea and memorize the elements → why all the elements are important → understand the construction in more detail and write it down

this is how i imagine my mind working:

it means that at first i start to remember the elements as points of its own but simultaneously my brain builds its idea on how they interact and then i notice the inner structure of how the elements are connected with each other in less obvious ways

this idea is cool to visualize how i imagine my thinking, because it shows how learning the topic reduces possible permutations and paths. i have this problem that when i start learning something new i see so many possibilities of what can happen to the elements that i can't discern between crucial and additional stuff. in order to use the knowledge i need to provide some structure

thus the main goal of optimized learning is to take the leap from "i memorized the elements" to "i understand their structure" as fast as possible

and so the strategy (2) might be more effective as it forces the memorization of the elements first and then it is easier to provide structure for them, where i would be defining order on something that's already in my mind. whereas (1) strikes at memorization and structuring simultaneously, it is too difficult for me to see at first in which direction the topic is going, i must know the next point

in a few days i will focus on how "the point" can be defined in this and how to characterize the connections

honestly tho this is some sorta pseudo graph theory and pseudo topology and i don't believe this could be as straightforward. otherwise nobody would ever post any study tips and we would have a field of study called "learning optimazation", this would be too big to go unnoticed. i wish it was so easy to just know how brain works and be able to build such an algorithm that would optimize the desired processes lmao

i wish i was a σ-field or something

side not is, i love this kind of thinking and i love to analyze how the thinking works, especially when it can me algorithmized or structured in some ways. the moment i see something is structured or algorithmic it becomes interesting to me

2-3 VIII 2021

it's 4am currently, i woke up after a 5hour nap and i don't plan to sleep anymore, time for topo

sleep: weird but going in the right direction i guess

concentration: fine

phone time: good

i am currently dragging myself through some of the most important theorems in multivar calculus i believe. inverse function theorem, implicit function theorem, diffeomorphisms and stuff. the proofs are quite simple but very long hence exhausting, my least fav kind of proofs. right now i'm doing topo

tomorrow (or rather today) i'm planning to do more topo and possibly finish my notes from that calculus chapter