So The Exponential Function Is Given By

25 II 2023

I had an exam yesterday, one more to go. it was the written part, so 12+ hours of solving problems, exhausting just like before. I completed all of them, but of course I am not sure if my solutions are correct, I will find out on monday. I'm proud of the progress I've made

right now I'm studying for the second part, so the theory-oriented one, I can barely focus because I've already learned those things and now I have to relearn them again

I'm trying to prove all the theorems on my own. partly to see how much I remember, partly to see how much I'm willing to improvize. as they say, if you're using too much memory then you're doing something wrong so I'm hoping to be able to come up with the proofs without memorizing anything new

my technique for studying the theory for the exam is to first test myself on how much I remember by trying to write everything down and note where I'm unsure or don't remember at all. then I read the textbooks starting from the worst topics up to the better ones. when I encounter a long complicated proof I am trying to break it down into steps and give each step a "title" or a short description

for instance, the Baer criterion featured in the photo has the following steps:

only do "extenstions on ideals to R→M ⇒ M injective"

define the poset of extenstions of A → M, A ⊆ B and a contrario suppose there is a maximal element ≠B

use the assumption to define an ideal and a submodule that contradicts the maximality of the extension

it is much easier to fill out the details than to remember the whole thing. this is probably the biggest skill I acquired this semester, next to downloading lecture notes pdfs of random professors I find online lmao

a friend suggested that I could make a post about tips for reading math textbooks and papers. as for papers, I don't have enough experience to give any tips, but I can share how I approach reading the books

a big news in my life is that I got a job. I will be a programmer and I start in march. at first I am going to use mostly python, but in the long run they will have me learn java. I'm excited and terrified at the same time, this semester is gonna kill me

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?

17 IX 2022

for the past few days life was treating me quite aggressively. today I had a terrible migraine, I feel weak and tired in general. doing math in a state like that isn't as pleasant so obviously I didn't do much, prioritized my health instead

during the semester I used The introduction to manifolds by Loring Tu to study analysis and I forgot that there were many nice exercises there that I didn't have time for but promised myself I would try them eventually

so tonight was the night and I studied grassmannians

I had some "results" done on my own, which later confirmed to be true, namely that the grassmannian over ℝⁿ for a 1-dim subspace is equivalent to a projective space of dimension n-1. I'm pretty sure that we are getting the projective of the same dimension for n-1 dim subspaces but I didn't calculate anything for n>3 so I might go back to that one day

it's fun to get hunches like that even if they turn out to be completely obvious to the authors of textbooks lmao

I am finally in the place with studying the theory for homology, commutative algebra and apparently differential topology (as it turned out today), where I have a variety of exercises I can try and that's the good part for me, always helps to get deeper insights and allows me to be more active

a friend asked me for a talk about the zariski topology in the context of algebraic sets and spectra of rings, so I'll see her soon for that. she will give me a personalized lecture about her thesis, which is about general topology. I am not a big fun of general topo but I'm always a slut for lectures about math so am excited for that

I hope my body will get its shit together because I still have to prep my lecture on euclidean geometry and when I don't feel good it's super difficult to motivate myself to do things that are not super exciting. I will never see productivity as a value on its own for this very reason lol I can barely do anything I don't find interesting

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).

15 V 2022

I have a topology test this friday, not gonna lie I'm kinda stressed. this is my favourite subject and I am dedicating a great deal of time to learn it so if I get a low grade it undermines the efficiency of my work. everyone thinks I'm an "expert", but internally I feel like I lied to them. it's ridiculous, because I can solve all the theoretical problems fairly well but the moment I have to calculate something for a specific example of a space I am clueless. and it's about applying theory to problems, right? so what is it worth

other than that tomorrow is a participation round in the integral competition at my university. I am participating. I don't have any high hopes for this, because it's been a while since I practiced integration and I am not motivated to do so because it's not an important skill – wolfram exists. either way could be fun, that's why I decided to go there

I am dreading the fact that I'll have to sit down and learn all the material from the probability theory until the exams. I've been ignoring it completely so far, because it's boring and complicated. the last homework broke me, it's high time to get my shit together

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.

why is deciding on a title for my thesis so hard

can someone please get these hoes under control i'm BUSY

this looks so great! I need to check this out as well

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