I Finally Tried Mindmaps To Keep Track Of The 200 Kinds Of Morphisms And Another 100 Kinds Of Sheaves

12 XII 2022

I have a test at the end of this week so I am mostly grinding for that, kinda ignoring other things along the way, planning to catch up with them during the christmas break

the new update for my tablet's OS brought the option to insert pictures into the notes, so now I can paste the problem statements directly from the book. I am not sure if this is actually efficient but it surely looks better and the notes are more readable

(I can't vouch for the correctness of those tho lol I just started learning about the Rouché's theorem)

I have been trying to keep up with the material discussed in lectures on commutative algebra and agebraic methods. with each lecture there is a set of homework problems to solve and I predefined a standard for myself that this week it's alright if I don't do the homework because grinding for the test is more important

I made some pretty notes on valuation rings

during the break I need to study finite and integral ring maps and valuation rings for commutative algebra course; resolutions, derived functors and universal coefficients theorem for algebraic methods course. I feel pretty good about the test that's coming up. sure, you can never be too prepared but so far I've been able to solve a good part of the problems I tried, so I should be ok

I got 55 and it seems to me that the majority of my answers were heavily influenced by asd

I took a test on like where you are on the ‘nonverbal intimacy scale’ and the average female score is 102 and male is 93.8 and I got 56 lolololol

here it is if ya want (reblog/reply w/ what you get!!)

What's the beef between engineers and physicists and even mathematicians.

Why physicists mock mathematicians: Because playing 51 dimensional chess against your own brain seems silly to us when there’s a whole cosmos to explore.

Why mathematicians mock physicists: The universe can only be understood because some nerd spent the time playing 51 dimensional chess and in the process they created some useful stuff for the physicists to steal and abuse the hell out of.

Why everyone mocks the engineers: π=e=3 is an abomination before God and those pencil pushing dorks make more money than us so we feel the need to vindicate our $75000 student debt.

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

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

Okay I’m currently furious that migraines are often so blindly easy to treat and I had to find this out myself at the age of 26 when I’ve been to a neurologist since I was 11 lol so I’m about to teach you two neat and fast little tricks to deal with pain!

The first is the sternocleidomastoid muscle, or the SCM muscle.

This big red section is responsible for pain around the eye, cheekbone, and jaw, as well as some temple pain. Literally all you have to do is angle your head down a little, angle it away from the side that hurts, and then you can gently pinch and rub that muscle. I find it best to start at the bottom and travel upwards. The relief is so immediate! You can increase pressure as you feel comfortable doing so.

Here is a short and easy video showing this in action

The second is a fast and easy stretch that soothes your vagus nerve, which is the nerve responsible for calming you down. The vagus nerve, for those unfamiliar, is stimulated by deep breathing such as yawning, sighing, singing, or taking a deep breath to calm your anger in a tense situation.

You can stretch this out by sitting up as straight as possible (this does not have to be perfect to work) and interlacing your fingers. Put your hands on the back of your head with your thumbs going down the sides of your neck and, while keeping your face forward, look all the way to one side with just your eyes. Hold that until you feel the urge to breathe deeply or yawn, or until you can tell there’s a change. Then do the same thing on the other side. When you put your arms down, you should clearly be able to turn your head farther in both directions. If the first session doesn’t get rid of your migraine, rest and repeat as many times as necessary. I even get a little fancy with it and roll my eyes up and down along the outer edge sometimes to stretch as much as I can.

If you need a visual here’s a good video on it. I know some of the language they use seems questionable but this is real and simple science and should not be discarded because it’s been adopted by the trendy wellness crowd!

I seriously cannot believe I didn’t hear a word of this from any doctor in my life. Additionally, if you get frequent recurring migraines, you may want to see a dietician. Migraines can be caused by foods containing histamines, lectin, etc. and can also be caused by high blood pressure in specific situations such as exercise, stress, and even sex.

If any of this information helps you I’d love to hear it btw! It’s so so fast and easy to do. Good luck!

Artificial intelligence makes accurate sheep counting.

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

remember if you ever want to read an article for free and the subscription ad prevents you from reading the entire article DO NOT

Reload it and immediately turn off your Internet access (data/WiFi if you are using a phone)

Reload it and click the 'X' next to the return icon on the top left of your window (if you are on desktop)

Reload the page, type 'Ctrl+ A' and 'Ctrl+ C' and paste everything onto an open document

this has worked for me 97ish % everytime hope this works for u too