30 VIII 2023

i am! obsessed! with this book from the late ming dynasty about scams to watch out for (esp. if you are a traveling merchant). this guy is like, there ARE immortals who can survive without food but you WILL NOT encounter them because they live alone in the mountains and don't talk to anyone. if a monk comes to your house and claims to not need to eat, it's probably because he's secretly eating human fetuses, or something. eunuchs are invariably corrupt and the court system is useless. however, do NOT try to bribe anyone for a better SAT result for your idiot failson; this never works. nuns WILL try to seduce your wife into cheating on you. if your idiot failson does really badly on the SAT, make sure to have his father's remains buried somewhere with A+ fengshui; this is Guaranteed to work (unless your wife is cheating on you).

ok now i might have some kind of super memory??

a week ago i played chess with bf and we didn't finish, so now i arranged the board as i remembered it and i got 13 out of 14 pieces correctly

i mean wow i didn't know i am capable of something like this

might be autism i suspect i might have

anyway now i want to know everything about human memory and take advantage of that

types of mathematical terminology

descriptive

honeycomb

gradient

quiver

computable

less descriptive

centroid

chaos

end

flag

not descriptive

ring

allegory

surreal

group

you know this person, right?

euclidean

abelianization

grothendieck

cartesian

took some non-english word and hoped for the best

eigen

algebra

shtuka

nullstellensatz

i made up a word!

ergodic

functor

adele

logarithm

idk, just give it a generic name

regular

well

admissible

well-admissible

like, specifically, it’s a vague thing

flasque

lax

fuzzy

pseudo

one symbol and a word

*-algebra

D-module

K-theory

†-compact (although that’s going to usually be written “dagger compact”)

just random letters

rg

cwf

Fσ

erf

Me when I need to rotate 720 degrees to return to my original state

Just in case some of you don't know about the websites where you can get your textbooks for free

Every now and then I remember that Malbolge exists and I get to spend the better part of an hour cry-laughing at the world’s worst programming language

already starting off strong, but it gets worse

Wow! Sounds easy and intuitive to use! What’s the “crazy operation” you ask? We’ll get to that later. For now let’s see what a program in this language looks like :)

Thanks! I hate it!

it’s so difficult to work with that the first program was written by another brute force search program

mmmmm delicious base-3 arithmetic, what could go wrong? (For reference, that means this program forgoes the usual “0/1″ values of binary code in favor of a much more fun “0/1/2″ set of values)

ah.

Here’s how the language actually figures out what to do. It’s got 8 “simple” commands that can be executed easily by *checks notes* running the code itself through the modulo operation and taking the result.

As a bonus, on top of all that every single character in your code will now alter what every single other character does. So I hope you’re alright with cracking a cipher every time you add a new letter to your program!

oh god oh fuck.

behold, Malbolge’s primary arithmetic operation and what you’ll be using for most of your math while programming with it :)

This looks specifically designed to be the least logical math operation you could make, and knowing what the rest of Malbolge is I’d wager that’s precisely what happened. I never want to ever use this and it’s my favorite thing I’ve ever seen.

https://en.wikipedia.org/wiki/Malbolge

Anyways here’s the wiki page if you wanna read through it more deeply, I’m gonna sit here holding in my laughter staring at the hello world program again.

meanwhile typical conversations between my friends:

– so what do you do in math?

– differential equations

– ugh I always hated differential equations

– you?

– general topology

– ugh I always hated topology

The curse of a mathematician is to work in a disliked field

I neglected this blog like hell, sorry

I had a lot of work to do, that's kinda what happened. but I would like to go back to posting regularly, so maybe I could write about something people would want to see?

for now my ideas for posts include

more study tips

a quick intro to moduli functors, since a lot of sources are written in a way that requires advanced algebraic geometry. I could explain the basics using (almost) only commutative algebra

updates on my life and what I've been working on

books recommendations

interesting math problems I encountered recently

if you'd like to see any of that, let me know! and feel free to give me more suggestions in the comments

tips for studying math part 2:

studying for an exam but the course is super boring and you don't care about it at all, you just want to pass

start by making a list of topics that were covered in lectures and classes. you can try to sort them by priority, maybe the professor said things like "this won't be on the exam" or "this is super important, you all must learn it", but that's not always possible, especially if you never showed up in class. instead, you can make a list of skills that you should acquire, based on what you did in classes and by looking at the past papers. for example, when I was studying for the statistics exam, my list of skills included things such as calculating the maximum likelihood estimators, confidence intervals, p-values, etc.

normally it is recommended to take studying the theory seriously, read the proofs, come up with examples, you name it, but we don't care about this course so obviously we are not going to do that. after familiarizing yourself with the definitions, skim through the lecture notes/slides/your friend's notes and try to classify the theorems into actionable vs non-actionable ones. the actionable ones tell you directly how to calculate something or at least that you can do it. the stokes theorem or the pappus centroid theorem – thore are really good examples of that. they are the most important, because chances are you used them a lot in class and they easily create exam problems. the non-actionable theorems tell you about properties of objects, but they don't really do anything if you don't care about the subject. you should know them of course, sometimes it is expected to say something like "we know that [...] because the assumptions of the theorem [...] are satisfied". but the general rule of thumb is that you should focus on the actionable theorems first.

now the problem practice. if you did a lot of problems in class and you have access to past papers, then it is pretty easy to determine how similar those two are. if the exercises covered in class are similar to those from past exam papers, then the next step is obvious: solve the exercises first, then work on the past papers, and you should be fine. but this is not always the case, sometimes the classes do not sufficiently prepare you for the exam and then what you do is google "[subject] exercises/problems with solutions pdf". there is a lof of stuff like this online, especially if the course is on something that everybody has to go through, for instance linear algebra, real and complex analysis, group theory, or general topology. if your university offers free access to textbooks (mine does, we have online access to some books from springer for example) then you can search again "[subject] exercises/problems with solutions". of course there is the unethical option, but I do not recommend stealing books from libgen by searching the same phrase there. once you got your pdfs and books, solve the problems that kinda look like those from the past papers.

if there is a topic that you just don't get and it would take you hours to go through it, skip it. learn the basics, study the solutions of some exercises related to it, but if it doesn't go well, you can go back to it after you finish the easy stuff. it is more efficient to learn five topics during that time than to get stuck on one. the same goes for topics that were covered in lectures but do not show up on the past papers. if you don't have access to the past papers you gotta trust your intuition on whether the topic looks examable or not. sometimes it can go wrong, in particular when you completely ignored the course's existence, but if you cannot find any exercises that would match that topic, then you can skip it and possibly come back later. always start with what comes up the most frequently on exams and go towards what seems the most obscure. if your professor is a nice person, you can ask them what you should focus on and what to do to prepare, that can save a lot of time and stress.

talk to the people who already took the course. ask them what to expect – does the professor expect your solutions to be super precise and cuts your points in half for computation errors or maybe saying that the answer follows from the theorem X gets the job done? normally this wouldn't be necessary (although it is always useful to know these things) because when you care about the course you are probably able to give very nice solutions to everything or at least that's your goal. but this time, if many people tell you that the professor accepts hand-wavey answers, during the exam your tactic is to write something for every question and maybe you'll score some extra points from the topics you didn't have time to study in depth.

alright, that should do it, this is the strategy that worked for me. of course some of those work also in courses that one does care about, but the key here is to reduce effort and time put into studying while still maximizing the chances of success. this is how I passed statistics and differential equations after studying for maybe two days before each exam and not attending any lectures before. hope this helps and of course, feel free to add yours!

thank you @dressedsalad @bsdndprplplld and @rooksacrifice for nominations. the last two were my additions (to provide more variety in the choices, not bc I dislike them)