25 II 2023
I had an exam yesterday, one more to go. it was the written part, so 12+ hours of solving problems, exhausting just like before. I completed all of them, but of course I am not sure if my solutions are correct, I will find out on monday. I'm proud of the progress I've made
right now I'm studying for the second part, so the theory-oriented one, I can barely focus because I've already learned those things and now I have to relearn them again
I'm trying to prove all the theorems on my own. partly to see how much I remember, partly to see how much I'm willing to improvize. as they say, if you're using too much memory then you're doing something wrong so I'm hoping to be able to come up with the proofs without memorizing anything new
my technique for studying the theory for the exam is to first test myself on how much I remember by trying to write everything down and note where I'm unsure or don't remember at all. then I read the textbooks starting from the worst topics up to the better ones. when I encounter a long complicated proof I am trying to break it down into steps and give each step a "title" or a short description
for instance, the Baer criterion featured in the photo has the following steps:
only do "extenstions on ideals to R→M ⇒ M injective"
define the poset of extenstions of A → M, A ⊆ B and a contrario suppose there is a maximal element ≠B
use the assumption to define an ideal and a submodule that contradicts the maximality of the extension
it is much easier to fill out the details than to remember the whole thing. this is probably the biggest skill I acquired this semester, next to downloading lecture notes pdfs of random professors I find online lmao
a friend suggested that I could make a post about tips for reading math textbooks and papers. as for papers, I don't have enough experience to give any tips, but I can share how I approach reading the books
a big news in my life is that I got a job. I will be a programmer and I start in march. at first I am going to use mostly python, but in the long run they will have me learn java. I'm excited and terrified at the same time, this semester is gonna kill me
gonna list my general goals, not necessarily what theorems i want to learn but rather some global "fix your life" things. gonna post about it every week to keep myself accountable
(1) wake up at 9 instead of 12. go to sleep at 1 instead of 4. if my current circadian rythm is here to stay, it's gonna be a fucking nightmare in november. first goal is to start going to sleep between 2 and 3
(2) concentrate on lectures. my focus is really bad when it comes to listening to someone. i have some interesting lectures downloaded and want to use them as training. first goal is to be able to actively listen to one for 30 minutes, then I can have a break for a zone-out
(3) get used to not checking my phone every damn 20 minutes. first goal is to have two 1-hour intervals daily of not checking it
probably will add some more soon
me : I love learning new things
Me when it’s time to learn anything new that I’m not instantly good at:
I'm glad I never encoutered anyone with such serious mindset while I was studying programming because now I wouldn't have as much fun writing branchless things in python, which is completely useless in highlevel languages but I just can't resist
I feel like some people are too serious with learning how to program. “I gotta be the best in this and that and build this and that to impress this employer” blah blah, that kills the fun out of programming. I see a lot of people (bashing people on Twitter again and actually a few people on here too, oops) making programming such a serious topic and you can’t have fun in it. Besides the proper syntax, documentation, best practises whatever, people in the tech community have putting up “rules” about how you should program and what to learn and if you fall out of that, you get ridiculed for it. Literally making it less fun.
Someone said that there’s no point in learning jQuery because JavaScript alone can do all that jQuery can and more.
So? I’m still going to learn it for fun? I’m having a blast with SCSS and jQuery, I don’t care 🤷🏾♀️ and I’ll learn the other frameworks and libraries that suits me because I want to. I don’t care if the entire tech community stops using a technology - if it interests me, I’m still going to learn it~!
Also no hate or anything to that person who said that to me - I completely understand your POV on jQuery! 💗✨ When I first read comment, I was a bit down like “oh what’s the point then…” but slapped myself and was like “I’m not learning for them or anyone. This library is cool and I like it so I’m still gonna use it”
Moral of the story: just do you. Do what makes you happy, code what you happy. Don’t be so serious all the time and make stupid dumb programs or games or websites whatever. Have fun in such a hard subject!!!
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
"based and purple pilled" with deleted vowels. the first adhd medication I tried was life changing, I could finally study and function (half-)properly, and the pills are purple, hence my version of "based and red pilled", which I probably don't have to explain
Guys please reply to this with what your url means or references I’m really curious
2 IV 2023
oh god the programming task for today was so annoying. I was supposed to process the MIT database with ECG records, and the annotation part of it was hell. after three hours I finally did it but the anger I felt at that time put me seconds away from throwing my laptop out of the window lmao
a recent success is that I calculated the rank of the module that I am working with, the problem is almost solved! when I told my advisor about it he looked so happy, he said that maybe he should start looking for another problem for me to ponder, it was so satisfying. I have a thing for mentors. at each point in my life for which I had a mentor who would teach me my special interest the progress I was making improved significantly and those were always the happiest times of my life. I am not sure if my advisor will stay with me to further show me a way into the research, but it certainly feels like a possibility
today I did some algebraic topology and differential geometry, I'm trying not to fall behind with the material even when I don't feel like studying
next week the easter starts, so I will probably have to visit my family. it's an interesting feeling to see my sister all grown up, there is still the image in my head of when she was barely a teenager and we didn't have much to talk about. now she is almost 18 and the significance of the age difference is nearly gone. when she start university it will be even less noticeable as she will understand what I mean by "fuck my life it's exam session season" lol
for about a week I've been trying to eat more healthy food, it's going fine so far. my biggest problem is that I'm eating way too much sugar but undereating in the general sense at the same time. I'm trying to incorporate more fruits and vegetables into my diet, as well as different kinds of nuts. it's so important to be properly nourished for math and yet I neglect it so much
yesterday I had a conversation with my friend and he said that his vision for doing math is working on some huge open problem such as RH. obviously you do you, but this sounds like such a depressive idea to me lol. chances of solving something like this are almost non-existent, that's such a waste of time to work on something like this for 10, 20, 50 years and make no progress. I mean, it certainly would feel nice to prove or disprove something like RH, but I'm perfectly fine with reading papers and answering all the questions I can anwer, which might not be huge and famous but I'm pretty sure creating those small pieces of theory will be useful to somebody one day
Very funny when mathematicians call weird edge cases "pathological".
Mathematician looking at a function that's continuous everywhere but differentiable nowhere: yeah that function has something wrong with it.
You think math should relate to the real world? What are you, some kind of physicist? Get the fuck out of here
Thank you, /r/ProgrammerHumor, I love you endlessly.
Redditors competing to make the worst volume sliders possible...
⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
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