31 VII 2022
31 VII 2022
finally posting after the exams are over, it was the longest session I have ever experienced, a month of exams. I passed everything and it was a good semester, actually my grades are better than ever before, which comes off as a surprise, I can't believe that it's anything other than luck
now what am I going to do for the holiday huh
next semester I am going to take three courses: analytic functions, commutative algebra and a mix-course of category theory, sheaf theory and homological algebra. then I plan to take algebraic topology, algebraic geometry, number theory and some more abstract algebra, along with writing a bachelor's thesis. this is probably going to be the hardest year so far, I don't know how I am going to survive this, I'm so scared
I was asked to give some lectures on geometry during a math summer camp for people who want to participate in the math olympiad. it's a great opportunity for me to practice giving lectures, as that's what I plan my job to be. moreover, it is my dream to be so good at math that I could prep people for the olympiad, hence that's a fraction of that dream coming true
the problem is I don't know geometry lol last time I did any was like four years ago in high school
thus I play with triangles everyday
other than that I must prepare a talk for a conference, I chose to do one on the knot theory, Seifert surfaces specifically. I started reading about it some time ago and it seems super cool
untangling knots is a perfect thing to do for fun
my plan for the holiday outside of these side-quests is to learn as much as possible for the courses that I'll be taking. the problem with them (besides analytic functions) is that they will be quite technical, detailed and dry, as they are supposed to give the tools necessary to study algebraic topology and geometry. that does sound dreadfully boring, no? that's what scares me, because when I am not interested in what I'm trying to learn everything becomes twice as hard. I asked here and there for advice and people told me to read about algebraic geometry in tandem with commutative algebra, since many constructions have beautiful interpretations and motivations there. sounds like exactly what I need
my bachelor's thesis will be on algebraic or differential topology probably, but I don't know exactly what I want to write about. I was thinking about vector fields on manifolds or de rham cohomology, but the thing with the proseminar on geometric topology (mine) is that it's been planned to give the introduction to the currently researched topics and offer opportunities to work with fresh conjectures and theorems. at least that's how it was described. allegedly geometric topology has this property that undergrads can contribute to the development of new theory, which is very surprising to me ngl, I would guess that this is highly unlikely with any kind of math nowadays and yet here we are
in conclusion, I'm excited but scared
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4-5 VIII 2021
did much topo and walked
sleep: weird. 5 hours. woke up at 3:30, at least right now it seems i might finally fix my circadian rythm
concentration: not good. too little sleep
phone time: good
almost done with operations on topo spaces and did some measure theory today. i love it so much, it's so new and yet so intuitive
tomorrow gonna take a peek at some art probably and possibly finish the operations on topo spaces, hoping to jump right into connected spaces and maybe do some more measure theory. kinda gave up with multivar calc boring af lol
“Netflix and chill?”
No, PDF and cry
the alphabet is like, there's the "a" region (abc...), for just, things, there's the "f" region (fgh..), for functions, there's the "i" region (ijk...), for indices, there's the "n" region (nm...), for integers, and the "p" region (pq...), for integers that are prime, there's the "t" region (tsr...), for time and progression and other axes that aren't the usual ones, and then there's the "u" region (uv...), for like, i guess open sets and differentiable functions and the such i guess, and then finally there's the "x" region (xyzw...) for just, variables that are more variable-y
there's also o and l but you shouldn't use those
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
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
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
well, google, one of them is a giant fuckin red dog
The beautiful modernism of Oliver Byrne’s, The First Six Books of the Elements of Euclid, 1847
The Washington Post's Mensa Invitational invited readers to take any word from the dictionary, alter it by adding, subtracting, or changing one letter, and supply a new definition.
Here are the winners:
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bsdndprplplld reblogged this · 2 years ago
⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
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