“Mathematician Henry Segerman Demonstrating How A Linear 3rd Dimensional Plane Is Only A Projection

saving this for self-care and for anyone who might need this

also, I can add: squint your eyes hard and then looking at something far away. it's supposed to help your eyes relax and a bonus simple grounding exercise!

from my personal experience, once you start paying attention to how different it feels on your eyes to look at something far away as opposed to something close, you can relax your eyes without needing an object to look at. now when I'm going to bed I imagine a tree far away and I feel my eyes relaxing, it helps with me fall alseep faster. it might be a placebo ofc, I know nothing about eyes, but it is still a good trick for falling asleep regardless of the supposed effect of it on the eyes

We need like “unclench your jaw” posts but for eye strain. Like

Go look at something 20ft away for 20 seconds.

ah yes my boy tom cardy. everyone must listen to him, he's the best

I need everyone to see this ABSOLUTE MASTERPIECE

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

when K ⊆ L is a finite extension by one element, say α with the minimal polynomial f, we can write 0 → (f) → K[x] → L → 0, where (f) is the kernel of evaluation at α. this is quite disappointing and very basic, but I haven't found anything better really. when there are finitely many intermediate fields between K and L for an extension L/K, L can be expressed as an extension by one element (Artin's theorem), which is still very specific

I didn't know about the group extensions, it makes the category of fields even more disgusting. I was hoping that the algebraic closure can be expressed as a colimit but of course not, not in the general case at least. but maybe at least some type of extensions can be realized as such? that's a nice thing to ponder. I'm pretty sure it will fail like every other request I had for this abomination of a category

I wonder what is typically done to make working with this category more pleasant. passing to Grp with the Galois group is one idea, the other I guess would be working with vector spaces or algebras? that would make sense considering that integral and finite ring maps are a thing and the field automorphisms play a role in the integral closure of ℤ in ℚ[√d]

on a sidenote, I laughed at the "lower body" and it reminds me how funny it is to talk about kernels in Polish. kernels and testicles are the same word

I've always thought 'splitting field' was a very cool sounding term. The Galois theorists did good with that one

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

omg that's the most beautiful thing I've seen today

Chapter 2 of commutative algebra!

" 'They' isn't singular!" Oh yeah? Show me its multiplicative inverse matrix then.

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?

What math classes did you do worst in?

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?

Do you think you’re good at math? Do you expect more from yourself?

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?

How did you solve it?

Can you share any problem solving tips?

Have you ever taken a competitive exam?

Do you have any friends on Tumblr that also do math?

Will P=NP? Why or why not?

Do you feel the riemann zeta function has any non-trivial zeroes off the ½ line?

Who is your favorite Mathematician?

Who is your least favorite Mathematician?

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?

Would you date someone who’s better than you at math?

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?

Are you a Formalist, Logicist, or Platonist?

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?

Do you have a favorite sequence? Is it in the OEIS?

What inspired you to do math?

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?

30 I 2023

in a fortnight I will have two oral exams and one problem-based exam

the first oral will be for complex analysis and we are supposed to choose three topics from which the professor will pick one and we'll have a chat. I chose meromorphic functions, Weierstrass function and modular function. I have already received my final score from homeworks, which is 73%. combined with 74% and 100% from tests, I am aiming for the top grade

the rest of exams will be for algebraic methods. a friend who already took this course told me that when someone is about to get a passing grade, they get general questions and the professor doesn't demand details of proofs. when I asked him if we are supposed to know the proofs in full detail or if it suffices to just be familiar with the sketch, he told me that if I will only know the sketch I will sit there until I fill in all the details. lmao that sounds like he wants me to get a top grade. ok challenge accepted

so it seems like I have a chance to ace everything. if I achieve this and do it again next semester I can apply for a scholarship. studying for the sole purpose of getting good grades doesn't feel right, the grades should come as a side effect of learning the material. buuut if I can get paid for studying then I might want to try harder, I enjoy being unpoor

the next two weeks will be spent mostly grinding for the algebraic methods exams, this is what I'm doing today

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