Latest Posts by bsdndprplplld - Page 8

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 beautiful modernism of Oliver Byrne’s, The First Six Books of the Elements of Euclid, 1847

i was supposed to mention something short about this one medieval guy who invented graphing functions and i just spent like all afternoon just reading about his work with zero words written because it’s all so interesting???

he was a theologian, as many mathematicians were in the past, and the first quantities he graphed were “temperature, pain, and grace” ??

he showed to know about integration by explaining that feeling pain twice as intense for a given amount of time is technically the same as feeling the less intense pain for half the amount of time, because the graphs of both pains across time were rectangles of the same area.

and he classified things as linear or non linear and said that the latter were qualities to describe a soul “occupied by many thoughts and affected by many passions”

it’s always so cool to learn how natural philosophers viewed the world. they draw conclusions that come from their religious or spiritual ideals but that are ultimately the basis of how we understand math or science today.

29 X 2022

another exhausting week finally over! fortunately I have two extra weekend days, so I can rest and do my homework without stressing over it

I found another promising youtube channel about learning. and "insanely difficult subjects" sounds about right when it comes to everything that's happening in math

I wish there was more content about learning math specifically. the tips I see, however good and useful for studying memory-based stuff such as biology or history, don't seem to work for math

for now my best method is to study the theory from the textbook, trying to prove everything on my own or if that fails, working through the proofs, coming up with examples of objects and asking (possibly dumb) questions that I then try to answer. afterwards I proceed to solving exercises

recently I've been studying mainly commutative algebra, in particular the localization

we didn't spend much time discussing local rings so I had to find some useful properties on my own. the whole idea of "local properties" is an interesting one and I definitely want to read more about it

I find it to be much more elegant to study localization through its universal property and exact sequences rather than through calculation on elements. it's funny how you can cheat so many of our homework problems by knowing basics of category theory and a little bit of homological algebra

I wonder if it's possible to learn math using mind maps, never actually tried. here is my attempt at doing that for one of the subjects in complex analysis:

other than studying I had to prepare a presentation for one of my courses

the topics were given to us by the professor so I thought it would be boring and technical, but I got lucky to discuss the possible generalizations of the Jordan theorem

now I'm gonna talk about something more personal

this week has been difficult because my brain doesn't enjoy existing. some days I had so many meltdowns and shutdowns, I could barely think and speak, let alone study difficult subjects in math. it's really disappointing, as I thought it got better after introducing new medication, but apparently I still can't handle time pressure and I break very easily when emotions become overwhelming (which they frequently do). one of the most discouraging parts of a neurodivergent brain is that you can't always say "alright then I'll just work harder" when you see that the situation requires it. you can't, because your brain has a certain threshold of "how much can you take before you snap" and no tips for studying when you're tired can change that. if you try, you'll just have a meltdown and your day is over, the rest of it must be spent regaining your strength and all you can do is hoping that tomorrow will be better

I wish I could always simply enjoy math and see it as an escape route from a confusing world of human interaction and unpredictable emotions, but whenever there is a deadline or grading criteria, I can hardly enjoy it anymore. I know that this is not what it's always gonna be, the further I go the less deadlines and exams we have, so I must wait and one day it might be okey

since june I've been trying to discuss accommodations regarding adhd and autism with my university but the process takes forever and I'm slowly losing hope that I will ever have it easier

nonetheless, I'm willing to do everything to achieve the goal of spending my days alone working on developing some new theory. just a few more years and I might start living the dream

20 X 2022

the past few days were hectic

my grandma's burthday was nice, but very stressful, because until the very last minute I didn't know if I can go home with my mother or if I would have to take the train that would arrive at my city at 5am

I tried to study on my way to the event but unfortunately I didn't do much

annotating categories for the working mathematician was the peak of my abilities

I really enjoy the course btw, which is a bit surprising, because there are so many negative opinions about the teacher. right now we are at abelian categories and probably soon will move on to homological algebra

I spent a long time studying adjunctions but I can say that I understand them pretty well now

maybe a part of the reason why I like category theory so much is that I like drawing and chasing them diagrams

I started doing the second problem set for the analytic functions course. they are much easier than the first one. I managed to solve a half of them today. last time it took me a whole day to solve one problem

for the next few days I plan to

complete the analytic functions homework

commutative algebra homework

category theory homework

abelian categories

localization

analytic functions, differentiation and integration of complex functions

wish me luck and I wish you a pleasant evening

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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13 X 2022

I dedicated the weekend to meeting with people from the machine learning club, helping my friend through her analysis homework and studying category theory for one of my subjects. then I did mostly the complex analysis homework

here are some wannabe aesthetic notes

my main goal at the time was to truly understand yoneda's lemma and the main intuition I have is that sometimes we shouldn't study the category C, but thw category of all functors from C to Set

after studying for a few hours I can say that the concept became a bit more intuitive

one of the problems in my "putnam homework" was to calculate the product of all differences of distinct n-th roots of unity – or so I thought. for a few days I believed that my solution doesn't work. I ended up with a disgusting fomula interating cosines of obscure angles but the visual intuition is neat, especially for an odd n. aaand that's no surprise since it turns out I'm fucking illiterate. not distinct roots, just differences of distinct roots, so that the whole thing is symmetric and there is no distinction of n odd vs n even

anyway I finally solved it, so that's nice!

I completed 5 out of 10 problems, which was my goal, so I should stop now and do my commutative algebra homework. there is one more exercise I want to solve:

the complex polynomial P with integer coefficients is such that |P(z)| ≤ 2 ∀z∈S¹. how many non-zero coefficients can P have?

I'm almost there with it and it's really cool

ofc the opportunity to include pretty drawings in my homework couldn't be wasted

during my category theory tutorial the professor asked me to show my solution on the blackboard. I was kinda stressed because now is the first time when I have my lectures and tutorials in english and on top of that this is a grad course. that whole morning I was fighting to stay awake, after the blackboard incident I didn't have to anymore

this is what I did

this week is likely to be the hardest out of many proceeding ones, because I won't have the weekend for studying (it's my grandma's birthday) so I need to use the maximum of my time during the week and get as much done as possible. I still need to do two homeworks, and study the theory. I am trying to learn how to prioritize and plan things, this is still a huge problem for me

I found an interesting youtube channel: Justin Sung. he talks about how to study/ how to learn and I like what he says, because it just makes so much sense. it's been a while since I started suspecting that methods such as flash cards or simple note-taking don't work and his content explains very well why they indeed might not work. it's very inspiring to see a professional confirm one's intuition

Iconic Things My Coding Professors Have Said (and it’s only day one)

“that sounds very hacky, but smart”

“i’m not sure where i’m going with this… its quite similiar to my life”

*Entire class and prof spends fifteen minutes trying to solve a problem before eventually giving up* “great work guys, that was some good debugging”

“is this a super big issue?” *longggg dramatic sigh* “… yes”.

Professor 1: “it’s still not working? um… okay, maybe you should… turn off your wifi and turn it back on again?“   Professor 2: "40 years of experience in networking and computing at its finest”

“whenever i’m doing my taxes, i never use the calculator app on my phone, i always just open up a notebook and use python and i think thats very brave of me”

“your life quality with improve when you use python 3 instead of python 2. your skin will improve and you’ll even sleep better”

“so this compiler doesn’t recognise cases, so if you’re really perverse, you could do Apple, aPple, apPle, appLe, applE, but if you do that then i’m going to kick you out”

“so, let’s give an example: "True = False”. Asides from causing the end of the world, much like dividing by 0, this will also cause an error”

“if you want to see my cat, i’ll show her. if you DON’T want to see my cat, too bad, cause I’m going to show you her anyway”

“today we will use three keywords: `if`, `else`, and their weird cousin `elif`.”

“if you want to type something else, like… uh, goodbye world? maybe? is that too dark? i think its too dark, so lets save that for later on in the year… by the way, have you been told about your exams yet?”

Professor : “is everything clear so far? shall i go faster?”   Literally EVERYONE: “no! slower!“   Professor: "Slower?! you can go slow when you’re dead, you won’t need python then!”

“you can’t use functions as your variable names. for example, you can’t call this number "if”. i mean i don’t know why you’d use that as your variable name to begin with, but i’m not here to question your life, i’m here to teach you python”

“it’s probably not the most efficient but its just what came out of me so we’re running with it”

Part 1 | Part 2

Just in case some of you don't know about the websites where you can get your textbooks for free

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

1 X 2022

new month huh

yesterday the commutative algebra teacher sent out the first homework assignment. you know, fuck the holiday, we need that grind

I have a week to solve it but I started yesterday as I was so excited

we need to prove some elementary properties of commutative unitary rings and I am enjoying it, I completed a half of the exercises so far. I can tell that the intuition acquired from studying module theory is paying off. many of the requested properties are the special cases of what I encountered during my module venture, so I feel like I understand them quite well. the problem I come across is how to write it down in a rigorous way, but I guess this is why we're supposed to do those exercises

I just got home from the math camp, it was so exhausting. I am not used to being around people all the time, so I my tolerance for interactions is low. I'm glad I went there tho, because I gained some teaching experience – my lecture, choosing contest problems and then grading the solutions

my university offers jobs as graders, older students can make some extra money checking homeworks of younger ones. the requirement is to have a decent GPA, which I don't have so I'm afraid they won't accept me. I don't know how decent exactly tho, so I'm going to try. in particular I might get bonus points for my extracurricular activities, giving talks at conferences and the grading I did at the camp. I'm so done with being poor, I hope I get in. otherwise I might start looking for some programming jobs, not for this academic year but in general, to find out what I could do at all

a few days ago I found a book that I wish I had found sooner: Vector Analysis, Klaus Janich

these are some of the chapters I needed a few months ago for my analysis course. the book is written like a novel and contains many interesting examples. on the bright side there are chapters about riemannian manifolds and other stuff that I haven't yet had an opportunity to study, so I plan to skim through the topics I already know and stay longer at those new to me

well, the sememster starts on tuesday so I don't have much time for that book, but as a sidequest it seems just right

26 IX 2022

I spent the past few days watching good doctor and doing algebra (mostly). I am trying to get used to working in the library

right now I'm at the math camp for the olympiad where I'm giving a lecture on the power of a point and radical axes

I wish I had been in a more math-oriented highschool, I feel like I missed out on so much. my school was focused on literature and philosophy, I switched to math and physics in my last year. on the one hand it's probably a nice achievement that I've managed to get into the university to study math, on the other hand I could have done so much more

I've been struggling to motivate myself to study lately, because the semester starts next week and I cannot really start anything new right now, but I also don't have anything in particular that I could continue. I decided to just read eisenbud and solve some exercises with homology

when i think about the value of studying math for so many years, i don't really think it comes from the specific subjects i studied. i mean, okay, derivatives and also linear algebra do come up every now and then.

but for the most part, the probability that any specific piece of math knowledge will be relevant for any given problem in life is pretty small. studying math feels less about learning mathematics and more about training that part of your brain that does the math, and you have to learn new parts of math because you have to keep finding new things to train on.

i have some knowledge, sure, but most of it is functionally useless. the real value is in the building of some intuition about how certain types of problems "should" work, and also how to formalize and communicate that intuition to other people (or to a compiler)

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

Nothing but respect for this mathematician's webpage

Hello, lovelies! I’ve gotten a couple of asks about studying so I decided to condense them into one post for you guys! I’m trying to hit a bunch of different topics so if you need an even more specific post you can send an ask! Without any further ado, have some tips! My studyblr is @spacey-scholar​

Prep

First, you always need a good base for your day! Especially if you’re studying a lot.

Make a good full breakfast! Ex. Eggs and Toast, Smoothie and fruit, Pancakes and a cup of juice. 

How’s your hygiene? Do you need to shower, brush your teeth, wash your face, condition your hair? Do it! You’ll be distracted if you feel messy!

Get dressed like it’s a normal day. Staying in PJ’s is okay! But being ready for the day seriously helps focus!

Likewise, your space should be clean. A clean space is a clean mind! Remove dishes, trash, scrap paper, and extra items. Wide down your desk, organize your pens and books. Your space should feel like your space!

Now make a list of what you need to get done! What needs to be done Now, what needs to be done Soon, and what needs to be done Later? 

Order your list how you want your day to go, and don’t put super-tough subjects back to back, or subjects that are similar exercises i.e. reading thirty pages of two different books back to back is no fun.

The Studying

It’s important to buckle down with No Distractions! If you find yourself distracted put your phone away! If you need your phone, put it on Do Not Disturb until you’re done. I also do this at night for better sleep. 

Pick the best technique for you, Pomodoro, reward-based, group studying, etc.

Play music but only if it will not distract you! If you sing along or daydream it’s the wrong music! Classical, Lo-fi, and White noise are all good! My Spotify Here has some good ones.

Use a nice journal (I don’t mean expensive!) and pens/pencils you enjoy using. I like to have a specific journal and color dedicated to each subject. 

Take notes on recorded lectures and classes, if you’re doing online classes right now try to screen record or record the audio! That way if you space out you can play it later and take notes, and you can absorb the lesson better instead of being distracted.

Don’t worry about your notes, stationary, pictures, being beautiful and your grades being perfect. Life doesn’t always look the way it does on Instagram. And the people who spend hours trying to get a good photo of their coffee are not studying! 

Use flashcards! Quizlet is good if you need premade ones! If you can save up and buy them, Barrons AP Flash Cards are the best in my opinion. Very clean, not too long, very durable, and cover all subjects.

Feeling Distracted 

If you catch yourself drifting off and getting into your head, get up and take a quick walk, stretch, or energizer. 

It’s okay if this happens, don’t guilt yourself! practice affirmation. The best and smartest still get distracted. 

If you are drifting, why? Are you hungry? Tired? Thirsty? Bored? Get a snack and some water, take a break and rest, find a way to make your studying more enjoyable. 

Remember that Motivation and Discipline are different things. Sometimes we just won’t be motivated, we won’t want to do it and it will be rather frustrating. But the cure to this is not shaming its discipline. Remind yourself “This may be hard, and I may not want to do this, but I want to reach my goals and If this is what It takes I will make it happen. 

Always do just one more page of you’re tired. One at a time and oh you did it! Maybe just one more? One more? Eh, one more just to finish the train of thought, Oh just- I’m done? Nice!

If you really can’t focus just move on and come back to this subject, you can always ask for help.

Supplementary Things

There are so many apps you can use to study, for free! My favorites are Tide, Quizlet, Focus Keeper, Forest, Flora, Egenda, SpanishDict, Photomath, and Kahn Academy. 

You can also join a study group! You may know one, but if you don’t, there are a lot of online ones! I’m in a study Discord and have been for a while! it helps a lot and motivates me to finish my work!

You can make a studyblr, but don’t do it just for the aesthetics! It’s about studying, and sometimes that gets messy! Sometimes we fail a test, we spill our tea on our notes, we cry because we don’t understand the formula. That’s the part you don’t see!

Having cute stationery can really help, as well as nice organizers and decorations for your space! I don’t have much money so I get a lot of stuff on Amazon or FB Marketplace.

Health

Remember that no matter what you are good enough. It’s okay if you fail, it’s okay if you struggle.

It’s also okay if your path doesn’t go the way you expected! Maybe you go to a different school than expected! Or choose a trade instead! Maybe you take a gap year! Maybe your passion changes! Maybe it changes six times!

Your health is always more important than your school. If you are in pain, mentally or physically, if you are anxious, exhausted, burnt out, talk to your teachers about it! You matter more than a grade.

Your best is good enough! And your best doesn’t look the same as someone else’s best! Don’t compare!

Now go get out there and study!

“Mathematician Henry Segerman demonstrating how a linear 3rd dimensional plane is only a projection of the curved 4th dimensional space time.”

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 🍁

there are two levels to this I think

the first one is how do you know how much time someone spent mastering a skill? and how do you decide how much time is average, how much must be a talent? both those pieces of information can be known or computed, but I don't think anybody performs such an assesment for someone else in a casual conversation before saying "you're so talented"

the secone thing is psychological. it is much healthier to think of oneself as "alright-talentend, very hard-working" than very talented. that's mostly why I reblogged this post, to deal with anxious thoughts "what if I'm not talented enough?"

sometimes it requires talent to be able to master a skill at a certain level at all, we're talking fields medalists and famous classical soloists, but to be ok-good at something it often suffices to be a bit above average and hard working. in general talent usually allows to work faster. being praised for talent is unhealthy, I believe, even when someone who is obviously talented worked super hard to achieve their results

and yes, those who didn't master any skill can be very discouraged to try when there is a narrative that it's all about talent. thinking of it as "mainly hard work" spares the question of "am I talented enough?" and inspires to just go and try

"Wow you're so naturally talented!" "You truly are gif-" biting you biting you biting you biting you die die die die I didn't work for thousands of hours to get called naturally talented fuck you fuck you fuck you I wasn't a particularly gifted beginner I just didn't stop doing it aaaaaaaaaaaaaaaaaaa

"Wow you're so naturally talented!" "You truly are gif-" biting you biting you biting you biting you die die die die I didn't work for thousands of hours to get called naturally talented fuck you fuck you fuck you I wasn't a particularly gifted beginner I just didn't stop doing it aaaaaaaaaaaaaaaaaaa

10 IX 2022

today I need some extra motivation to study because I didn't sleep well these past few days and it has drastic effects on my productivity, energy, motivation and what have you

also I am struggling to make the choice as to what I should do today

yesterday I started solving some basic exercises from hatcher's textbook

Δ-complex structures are becoming more intuicitve with time. take my solutions with a grain of salt, I am just starting to learn about these things and won't vouch for them lmao

some more complicated objects (the last one is an example of a lense space)

I decided to study commutative algebra today

so far I'm enjoying it. not as much as algebraic topology (which will always be my number 1) but it has its beauty

right now I'm at hom and tensor functors, the structures are fairly complicated, but pretty, and they look like they need to be studied in stages, with repetition and breaks, to fully grasp what's going on

my sensory issues are terrible today and I'm exhausted and hyperactive at the same time uh

I'll try working through a lecture on commutative algebra and give an update on how it went later

update: I studied for a while, but it wasn't going great so I decided to take a nap instead. god knows I tried

I want you all to know that an Arab Muslim from Tunis proposed the Theory of Evolution near 600 years before Charles Darwin even took his first breath. Don’t let them erase you.

5 IX 2022

maybe once a month is a bit too seldom to post? I kinda want to form a habit of romanticizing my academic life, I see all those studyblr accounts with beautiful photos of their desks and notes and I'm pretty sure those images exist in their minds as well

maybe one day I will be considered studyspo lol

I'm just starting to work on some geometry problems for today, haven't yet decided what I will focus on, but there is this one problem that haunted me when I tried to sleep yestarday:

given a triangle ABC with ∠A = 60°, let P be a point in the interior of ABC such that ∠APB = ∠APC = 120°. prove that ∠APX = 90°, for X being the circumcenter of ABC

it's supposed to be solved using spiral similarity, which is a composition of a rotation and homothety. there was another problem that was listed as "spiral similarity exercise", but I proved it with angle chasing exclusively, creating some nasty drawings in the process

other than geometry I'm studying homology, at the moment the basics of homological algebra, such as the first proofs by diagram chasing and exact sequences

I made some notes for exact sequences induced in homology

my perspective on doing math is slowly changing I think, I feel inspired to search for problems that I would like to solve. I noticed that I have this mental block: before I start doing math for real, I need to learn all the theory. which is absurd, you can never learn all the theory

sure, obtaining truly groundbreaking results requires years of learning theory and mastering tools if you want to specialize in algebraic topology and geometry, but the mindset I have creates the comfort zone of "play safe, just read your textbook, no challenges for now" and I'm starting to see beyond that

right now I'm taking my first steps into understanding that reading textbooks and learning how to solve basic exercises is not enough. they are just methods that are supposed to help my creativity and curiosity do their thing. essentially what I've been doing so far is not math, merely the preparation to do math in the future. no wonder I've been feeling so bored recently, all I'm doing is just learning basic tools. the idealist in me is asking to be unleashed

I feel like I'm about to see something much bigger than me

this looks so great! I need to check this out as well

25 VIII 2022

I found the most beautiful math book I have ever seen

it covers the basics of algebraic topology: homotopy, homology, spectral sequences and some other stuff

one of the authors (Fomenko) was a student when this book was being published, he made all the drawings. imagine being an artist and a mathematician aaand making math art

just look at them

other than those drawing masterpieces there are illustrations of mathematical concepts

I'm studying homology right now, so it brings me joy to know that this book exists. I don't know how well it's written yet, but from skimming the first few pages it seems fine

I just finished watching a lecture about exact sequences and I find the concept of homology really pretty: it's like measuring to what extent the sequence of abelian groups fails to be exact

I'm trying to find my way of taking notes. time and again I catch myself zoning out and passively writing down the definitions, so right now I avoid taking notes until it's with a goal of using the writing as a tool for acquiring understanding. I'm trying to create the representations of objects and their basic relations in my mind at first, then maybe use the process of note-taking to further analyze less obvious properties and solving some problems

I will post more about it in the future, we'll see how that goes

september

I decided to start posting monthly, I hope it will help me keep it regular during the semester, it may also bring more structure into my posts

I gave my talk at the conference, I was surprised with the engagement I received, people asked a lot of questions even after the lecture was over. it seemed to be very successful in a sense that so many people found the topic interesting

what I need to do the most in the next 3 weeks is learn the damn geometry. sometimes I take breaks to study algebraic tolology, I did that yesterday

you guys seem to enjoy homology so here is me computing the simplicial homology groups of the projective plane. I tried to take one of these aesthetic photos I sometimes see on other studyblrs but unfortunately this is the best I can do lmao

my idea for mainly reading and taking notes only when it's for something really complicated seems to be working. I focus especially on the problem-solving side of things, because as I learned the hard way, I need to learn the theory and problem-solving separately. what I found is that sitting down and genuinely trying to prove the theorems stated in the textbook is a good way to get a grasp of how the problems related to that topic are generally treated. sometimes making one's own proof is too difficult, well, no wonder, experienced mathematicians spend months trying to get the result, so why would I expect myself to do that in one sitting. then I try to put a lot of effort into reading the proof, so that later I can at least describe how it's done. I find this quite effective when it comes to learning a particular subject. I will never skip the proof again lmao

in a month I'll try to post about the main things I will have managed to do, what I learned, what I solved, and hopefully more art projects

mathematicians, constantly: god I’m so tired of people telling me how much they hate math whenever i mention what im into

me: yeah it’s fucked up. i do probability theory, what about you

them: oh man I hate probability theory

25 VIII 2022

I found the most beautiful math book I have ever seen

it covers the basics of algebraic topology: homotopy, homology, spectral sequences and some other stuff

one of the authors (Fomenko) was a student when this book was being published, he made all the drawings. imagine being an artist and a mathematician aaand making math art

just look at them

other than those drawing masterpieces there are illustrations of mathematical concepts

I'm studying homology right now, so it brings me joy to know that this book exists. I don't know how well it's written yet, but from skimming the first few pages it seems fine

I just finished watching a lecture about exact sequences and I find the concept of homology really pretty: it's like measuring to what extent the sequence of abelian groups fails to be exact

I'm trying to find my way of taking notes. time and again I catch myself zoning out and passively writing down the definitions, so right now I avoid taking notes until it's with a goal of using the writing as a tool for acquiring understanding. I'm trying to create the representations of objects and their basic relations in my mind at first, then maybe use the process of note-taking to further analyze less obvious properties and solving some problems

I will post more about it in the future, we'll see how that goes

types of mathematical terminology

descriptive

honeycomb

gradient

quiver

computable

less descriptive

centroid

chaos

end

flag

not descriptive

ring

allegory

surreal

group

you know this person, right?

euclidean

abelianization

grothendieck

cartesian

took some non-english word and hoped for the best

eigen

algebra

shtuka

nullstellensatz

i made up a word!

ergodic

functor

adele

logarithm

idk, just give it a generic name

regular

well

admissible

well-admissible

like, specifically, it’s a vague thing

flasque

lax

fuzzy

pseudo

one symbol and a word

*-algebra

D-module

K-theory

†-compact (although that’s going to usually be written “dagger compact”)

just random letters

rg

cwf

Fσ

erf

today I learned that for a surface with boundary, which I believe we can say a straw is, the genus is equal to that of a 2-manifold obtained from attaching disks to the boundary. hence the straw has genus equal to that of a 2-sphere, which is 0, therefore a straw has 0 holes

also a straw is not homotopic to a torus I think, but rather to S¹, as it's a product of S¹ and a closed interval, which is contractible. a torus has the fundamental group S¹×S¹, thus they cannot be homotopy equivalent. buuut that requires the straw to be infinitely thin so maybe I'm too idealistic for this claim to hold and it is in fact equivalent to a torus

lmao I love math but I can't stop laughing at the fact that it took me two years of university to be able to have this discussion

I’m really into internet discourse but only pointless and stupid internet discourse like how many holes there are in a straw (it’s 2)