I Love Reading Stuff On Abstract Geometry Because There'll Be Some Extremely Complicated Construction

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!

remember if you ever want to read an article for free and the subscription ad prevents you from reading the entire article DO NOT

Reload it and immediately turn off your Internet access (data/WiFi if you are using a phone)

Reload it and click the 'X' next to the return icon on the top left of your window (if you are on desktop)

Reload the page, type 'Ctrl+ A' and 'Ctrl+ C' and paste everything onto an open document

this has worked for me 97ish % everytime hope this works for u too

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

i've been working on it with my boyfriend for a while now and–

our first video is up!

i hope you enjoy it and subscribe to our channel

https://youtu.be/-X2BBtRI1Xw

gonna list my general goals, not necessarily what theorems i want to learn but rather some global "fix your life" things. gonna post about it every week to keep myself accountable

(1) wake up at 9 instead of 12. go to sleep at 1 instead of 4. if my current circadian rythm is here to stay, it's gonna be a fucking nightmare in november. first goal is to start going to sleep between 2 and 3

(2) concentrate on lectures. my focus is really bad when it comes to listening to someone. i have some interesting lectures downloaded and want to use them as training. first goal is to be able to actively listen to one for 30 minutes, then I can have a break for a zone-out

(3) get used to not checking my phone every damn 20 minutes. first goal is to have two 1-hour intervals daily of not checking it

probably will add some more soon

hey be nice to me im just a teenage girl who has legally been an adult for years

The only thing that this university computer-science in-class-use file is dangerous to is my mental health, and the only thing it harms is my soul, but thanks for looking out for me google :)

25 XII 2022

this chunk of the semester is finally over, sweet jesus I'm so exhausted. I'm getting the well-deserved rest and later catching up with all the things I put on my to-do list that I kinda learned but not really

the test I had last week went fine. frankly I expected more from it after solving more than 50 problems during my prep, but I scored 74%, which is objectively great and more than I predicted after submitting my solutions

here is my math plan for the break:

in algebraic methods I started falling behind a few weeks ago when I missed two lectures while being sick. they were about resolutions, derived functors and group homology and afterwards I wasn't really able to stay on top of my game like before. high time to get back on track. in commutative algebra I was doing ok, but there are some topics I neglected: finite and integral maps and Noether's normalization. for complex analysis everything is great until we introduced the order of growth and recently we've been doing some algebraic number theory, which btw is a huge disappointment. don't get me wrong, I understand the significance of Riemann's ζ, but the problems we did all consisted of subtle inequalities and a lot of technical details. I am doing mainly algebraic stuff to avoid these kind of things lol

when we were doing simplicial sets I stumbled upon some formulas for the simplicial set functor and its geometric realization and I thought it to be a nice exercise to probe them, so here it is:

I won't know if this proof actually works until I attend office hours to find out, but I am satisfied with the work I put into it

I already started making some notes on the derived functors

other than that I have this nice book that will help me prepare for writing my thesis, so I'd like to take a look at that too

as for the non-math plans, I am rewatching good doctor. my brain has this nice property that after a year has passed since finishing a show I no longer remember anything, the exponential distribution is relatable like that. this allows endless recycling of my favourite series, I just need to wait

I wish you all a pleasant break and I hope everyone is getting some rest like I am

Theory Time

The reason endermen don’t like it when you look at them is because they communicate telepathically with one another by locking eyes! Humans are absolutely not designed to do this so when we look at them we are accidentally projecting all of our thoughts into them at the same time and it hurts :(

6 Things People Don't Always Tell You About Studying

1. you ace tests by overlearning. you should know your notes/flashcards/definitions basically by heart. if someone asks you about a topic when you’re away from class or your notes and you can answer them in a thorough and and accurate answer, then you’re good, you know the material. 

2. if you don’t understand something, it will end up on the test. so just don’t disregard and hope that this specific topic won’t be on the test. give it more attention, help, and practice. find a packet of problems on that one concept and don’t stop until you finish it and know it the best. 

3. sometimes you just need that Parental Push. you know in elementary school, they would tell you “ok now it’s time for you to do your homework! you have a project coming up, start looking for a topic now!” ONE of your teachers might be like this. be thankful for it and follow their advice! these teachers are the best at always keeping you on track with their calendar. if not a teacher, then have one of your friends be that person that can keep you accountable for the things you promised you would do. 

4. you just need to kick your own ass. seriously. i know it sucks and its hard to study for two things at once. BUT. I DONT CARE IF IT’S HARD. you need to do it and at least do it to get it over with because you can’t keep putting things off. If you do, you will eventually run out of time and you will hate yourself. force yourself to do it. i made myself sign up for june ACT even though there’s finals because if i didn’t, i probably never would. like do i think i’m gonna be ready in one month? probably not, SO I BETTER GET ON IT AND START STUDYING! 

5. do homework even if it doesn’t count. if you actually try on it, then you will actually do so much better on the tests, it’s like magic. 

6. literally just get so angry about procrastinating that you make yourself start that assignment. I know how hard it is to kick the procrastination habit. I have to procrastinate. So I make myself start by thinking about my deadlines way early. I think, “oh i have a presentation in three weeks (but it really takes 2 weeks to do), i’ll be good and start today.” when that doesn’t happen, you say you’ll do it tomorrow, and this happens for like the next four days. I get so mad at myself for not starting when i am given a new chance to do so with every passing day. By that time, you actually have exactly how much time you need for it AND you were able to procrastinate the same way you usually do ;)