7 III 2023
7 III 2023
it's the second week of the semester and I must say that it's easier than I predicted
statistical data analysis is boring but easy, algebra 2 is easy but probably interesting, so is differential geometry
algebraic topology was funny because ⅓ of the group completed the algebraic methods course, so at first we told the professor to skip half of the lecture (we all know the required part of category theory) and then with every new piece of information he would say "ok maybe this will be the first thing today that you don't know", to which we would reply "naaah we've seen this" lmao. but the course overall will be fun and maybe it's even better that the level of difficulty won't be as high as I though, that would leave more time for my other stuff
the tutorial part of number theory was scary, because the professor wanted us to work in pairs. my autistic ass hates working in groups and the noise in the room was unbearable (everyone was talking about the exercises we were given to solve), so I was on the verge of a meltdown after 30 minutes of this despite ANC headphones. next time I will work by myself from the start. maybe without the requirement of communication it won't be as bad. the course itself will be easy, when it comes to the material. I know nothing about number theory, so the novelty will make it more enjoyable. a few people said that they would prefer the tutorial in the standard form, maybe I won't have to worry about surviving it if there are enough people who want to change it
my birthday is tomorrow and as a gift my parents gave me enough money to buy an ipad, I was saving for it since november. for a few days now I've been testing different apps for note taking, pdf readers and other tools useful for studying. I must say, this is a game changer, I absolutely love it
taking notes itself is less comfortable than on an e-ink tablet, which gives very paperlike experience, but it's better than traditional ones. the upside is that I can use different colors and the whole process is less rigid than on an e-ink
two apps that seem the best for now are MarginNote 3 and GoodNotes
the first one is good for studying something from multiple sources. the app allows to open many pdfs, take pieces from them and then arrange them in a mindmap. it's possible to add handwritten notes, typed notes, photos and probably more that I don't know yet. all of this seems to be particularly useful when studying for exams or in other situations when it's necessary to review a huge chunk of material
the second app is for regular handwritten notes. it doesn't have any special advantages other than I just like the interface lol what I like about taking notes on ipad is that I can take photos and insert them directly into the notebook, which I can't do on the e-ink. it's great for lectures and classes because I don't usually write everything down (otherwise I can't listen, too busy with writing) and even if I do, I don't trust myself with it so I take photos anyway. being able to merge the photos with notes reduces chaos
oh god this is going to be a long post! other news from life is that yesterday I had a meeting with my thesis advisor and we finally picked a topic. some time ago he sent me a paper to try and said, very mysteriously, to let him know if it's not too hard before he reveals more details about his idea. the paper is about symmetric bilinear forms on finite abelian groups, pure algebra, and I was supposed to write about algebraic topology, so I tried to search where this topics comes up, but didn't find anything. it turns out that it's used to define some knot invariant, which I would use to write about the classification of singularities of algebraic curves. in the meantime my advisor had another idea, which is an open problem in knot theory. we decided to try the second one, because there is less theory to learn before I could start writing the paper
to summarize what I'm about to do: there is a knot invariant called Jones polynomial, which then inspires a construction of a certain R-module on tangles and the question asks whether that module is free, if so, what is its rank. now I'm reading the book he gave me to learn the basics and I can't wait till I start working on the problem
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Real’s Math Ask Meme
What math classes have you taken?
What math classes did you do best in?
What math classes did you like the most?
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Are there areas of math that you enjoy? What are they?
Why do you learn math?
What do you like about math?
Least favorite notation you’ve ever seen?
Do you have any favorite theorems?
Better yet, do you have any least favorite theorems?
Tell me a funny math story.
Who actually invented calculus?
Do you have any stories of Mathematical failure you’d like to share?
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Do other people think you’re good at math?
Do you know anyone who doesn’t think they’re good at math but you look up to anyway? Do you think they are?
Are there any great female Mathematicians (living or dead) you would give a shout-out to?
Can you share a good math problem you’ve solved recently?
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Do you feel the riemann zeta function has any non-trivial zeroes off the ½ line?
Who is your favorite Mathematician?
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Do you know any good math jokes?
You’re at the club and Andrew Wiles proves your girl’s last theorem. WYD?
You’re at the club and Grigori Perlman brushes his gorgeous locks of hair to the side and then proves your girl’s conjecture. WYD?
Who is/was the most attractive Mathematician, living or dead? (And why is it Grigori Perlman?)
Can you share a math pickup line?
Can you share many math pickup lines?
Can you keep delivering math pickup lines until my pants dissapear?
Have you ever dated a Mathematician?
Would you date someone who dislikes math?
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Have you ever used math in a novel or entertaining way?
Have you learned any math on your own recently?
When’s the last time you computed something without a calculator?
What’s the silliest Mathematical mistake you’ve ever made?
Which is better named? The Chicken McNugget theorem? Or the Hairy Ball theorem?
Is it really the answer to life, the universe, and everything? Was it the answer on an exam ever? If not, did you put it down anyway to be a wise-ass?
Did you ever fail a math class?
Is math a challenge for you?
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Are you close with a math professor?
Just how big is a big number?
Has math changed you?
What’s your favorite number system? Integers? Reals? Rationals? Hyper-reals? Surreals? Complex? Natural numbers?
How do you feel about Norman Wildberger?
Favorite casual math book?
Do you have favorite math textbooks? If so, what are they?
Do you collect anything that is math-related?
Do you have a shrine Terence Tao in your bedroom? If not, where is it?
Where is your most favorite place to do math?
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Do you have any favorite/cool math websites you’d like to share?
Can you reccomend any online resources for math?
What’s you favorite number? (Wise-ass answers allowed)
Does 6 really *deserve* to be called a perfect number? What the h*ck did it ever do?
Are there any non-interesting numbers?
How many grains of sand are in a heap of sand?
What’s something your followers don’t know that you’d be willing to share?
Have you ever tried to figure out the prime factors of your phone number?
If yes to 65, what are they? If no, will you let me figure them out for you? 😉
Do you have any math tatoos?
Do you want any math tatoos?
Wanna test my theory that symmetry makes everything more fun?
Do you like Mathematical paradoxes?
👀
Are you a fan of algorithms? If so, which are your favorite?
Can you program? What languages do you know?
are you a girl?
I am, but I thought that was obvious given that I have a picture of me in my icon.
I have a bet going on with a friend. We need a third opinion. Can one find the square root of 2 in pi? And pi in the root of 2
Gut instinct says no. But when you work with infinities, gut instinct is NOT proof. (And such a gut feeling could have easily been the dodgy dinner I cooked myself last night.)
However I cannot even provide a proof.
I have, however tried to give some insight in another post (it should be the one immediately below this one) to perhaps help/provoke a more concrete argument from someone else :)
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
30 VII 2021
did some stuff today. found out my cat would die tomorrow if it wasn't for an operation he had today, that didn't feel good but also oh god was he lucky
sleep: better but still trash. yesterday fell asleep between 3 and 4, today planning to go to bed at 3 so in a few minutes
concentration: not as great. couldn't focus because my cat was fucking dying
bo phone time: decent
did some topo today, i think i managed to understand the idea behind the quotient spaces and i really liked it. can't wait to dive deeper tomorrow. other than that i wrote a method that takes a parametric function and provides a partition dividing the curve into k intervals. also i'm almost done with the art comission
sooo tomorrow i plan to finish the code, i want to achieve the functionality that takes a parametric function and draws it with a dashed line. that's why i needed the partition, it's gonna look fucking beautiful. and i need to complete the comission. i hope there will be some time left for quotient spaces, i am very hyped. oh and i forgot i'm drinking tomorrow. so i guess no topo for that gal. eh
Please fund my research in finding fewer applications of mathematics. I'm going to start my project with trying to find fewer uses of trigonometry, so that ideally we can eliminate the need for remembering trigonometric identities. Then I'm going to move on to researching fewer uses for integration by parts, because that tends to get real tedious real fast. With your unending financial support, I believe I can return mathematics to the purity and simplicity it has always yearned for.
oh, you misunderstood. when i said "applications" i didnt mean real world applications, i meant ways to use this in the context even more abstract nonsense
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)
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
this is going to be difficult -> i am capable of doing difficult things -> i have done everything prior to this moment -> this difficulty will soon be proof of capability
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⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
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