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
maybe a littel late for Real’s Math Ask Meme 18, 6 and 3, please?
hi, thanks for the questions!
3: what math classes did you like the most?
tough choice! for the content itself I'd say abstract algebra, commutative algebra, analytic functions and algebraic topology. for the way the class was taught, a course on galois theory I took last semester was probably the best. the pace of the lecture allowed me to learn everything on the spot, not too fast, but not so slow that my mind would wander. the tutorials were also great, because the teacher found the perfect balance between explaining and showing the solutions, and engaging us to think about what should happen next. the courses I mentioned above were also taught well, but the galois theory one was absolutely perfect
6: why do you learn math?
I enjoy the feeling of math in my brain. I can spend hours thinking about a problem and not get bored, which doesn't usually happen with other things. when I finish a study session I feel tired in a good way, like I spent my time and energy doing something valuable and it's very satisfying
18: can you share a good math problem you've solved recently?
given a holomorphic line bundle L over a compact complex manifold, prove that L is trivial iff L and the dual of L both admit a non-zero section
this problem is quite basic, in a sense that you work on it right after getting started with line bundles, but I believe it to be a good problem, because it forces you to analyze the difference between trivial holomorphic bundles and trivial smooth bundles, so it's great for building some intuition
BCC
A minimal figure-eight knot on the body-centered cubic lattice
(source code)
Shortest math paper ever.
And with so much impact! It just disproved a widely accepted theorem from the year 1769 in 5 rows!!!
I'll never publish anything even remotely badass like this! But I want it so much!!!
(Points at the function I'm doing my thesis on) this is my son who has every disease
symbol meaning
= equals
=/= not equals
< left
> right
! LOUD NUMBER
~ worm
π stonehenge
√ right answer
x wrong answer
⋯ soon…
∮ what Exacrly the fuck
∝ fish
∞ fish with 2 heads
↯ lightning
:⇔ he Scream
this is kinda cool, I might do one of these when the semester starts
Studying can be a daunting task, especially when we're not feeling motivated or don't know where to start. Luckily you are on Tumblr, where the Tumblr Studyblr community lives!
A group of individuals who share their study tips, techniques, and challenges to help motivate and inspire others.
As a member of this community, I've compiled a master post of study challenges created by Studyblr bloggers. These challenges aim to help students stay on track, improve their focus, and achieve their academic goals. So you can join in and start achieving your academic potential!
>> 𝐍 𝐨 𝐭 𝐞
If you know any other challenges or you've created ones yourself and want to share them, do message me with the link to the post so I can update the list! I too will be creating some, more coding-related ones as I am a coding studyblr (codeblr) blog! That's all and hope you find a challenge you'd like to start!
@tranquilstudy's Studyblr Challenge - 𝒍 𝒊 𝒏 𝒌
@sub-at-omic-studies' Study Challenge - 𝒍 𝒊 𝒏 𝒌
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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
The beautiful modernism of Oliver Byrne’s, The First Six Books of the Elements of Euclid, 1847
I know your thesis was about something to do with algebraic topology, may I ask what exactly it was about?
(and congrats to you getting your bachelors degree and into a masters program)
(thank you!)
my thesis was about an open question regarding a certain skein module of tangles on 2n nodes. the conjecture is that the module is free and in my thesis I constructed a generating set that is free for n=2,3 (direct calculation) but I have yet to prove that for a general n. if you are interested I can send you the paper in which the question was posed, all the details are explained there and would be hard to write down here without tex lol
⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
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