⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
292 posts
Latest Posts by bsdndprplplld - Page 5
I know we all have different skills and all and it's supposed to be complementary, but, people who can do math are so morbidly funny to me
I figure it must be like
Imagine being like only one of twelve people in your whole city who can read and write
And it's not just because everyone else is uneducated, most of them cannot even learn the sort of things you can learn. Or they could, in theory, but it frustrates them so much that they never make it past grade school reading tops, and they hate every second of it
And it's not a "luxury" skill, either, like your whole society needs the written word to function, and by extension, they need you. They need you for shit like reading labels and instruction manuals and writting 2 sentences letters, and they pay you handsomely for that, which is nice, but also feels absurd
You read a whole series of novels that rock your life and you can't even talk about it to your best friend because anything more complex than a picture book breaks their brain
7 III 2023
it's the second week of the semester and I must say that it's easier than I predicted
statistical data analysis is boring but easy, algebra 2 is easy but probably interesting, so is differential geometry
algebraic topology was funny because ⅓ of the group completed the algebraic methods course, so at first we told the professor to skip half of the lecture (we all know the required part of category theory) and then with every new piece of information he would say "ok maybe this will be the first thing today that you don't know", to which we would reply "naaah we've seen this" lmao. but the course overall will be fun and maybe it's even better that the level of difficulty won't be as high as I though, that would leave more time for my other stuff
the tutorial part of number theory was scary, because the professor wanted us to work in pairs. my autistic ass hates working in groups and the noise in the room was unbearable (everyone was talking about the exercises we were given to solve), so I was on the verge of a meltdown after 30 minutes of this despite ANC headphones. next time I will work by myself from the start. maybe without the requirement of communication it won't be as bad. the course itself will be easy, when it comes to the material. I know nothing about number theory, so the novelty will make it more enjoyable. a few people said that they would prefer the tutorial in the standard form, maybe I won't have to worry about surviving it if there are enough people who want to change it
my birthday is tomorrow and as a gift my parents gave me enough money to buy an ipad, I was saving for it since november. for a few days now I've been testing different apps for note taking, pdf readers and other tools useful for studying. I must say, this is a game changer, I absolutely love it
taking notes itself is less comfortable than on an e-ink tablet, which gives very paperlike experience, but it's better than traditional ones. the upside is that I can use different colors and the whole process is less rigid than on an e-ink
two apps that seem the best for now are MarginNote 3 and GoodNotes
the first one is good for studying something from multiple sources. the app allows to open many pdfs, take pieces from them and then arrange them in a mindmap. it's possible to add handwritten notes, typed notes, photos and probably more that I don't know yet. all of this seems to be particularly useful when studying for exams or in other situations when it's necessary to review a huge chunk of material
the second app is for regular handwritten notes. it doesn't have any special advantages other than I just like the interface lol what I like about taking notes on ipad is that I can take photos and insert them directly into the notebook, which I can't do on the e-ink. it's great for lectures and classes because I don't usually write everything down (otherwise I can't listen, too busy with writing) and even if I do, I don't trust myself with it so I take photos anyway. being able to merge the photos with notes reduces chaos
oh god this is going to be a long post! other news from life is that yesterday I had a meeting with my thesis advisor and we finally picked a topic. some time ago he sent me a paper to try and said, very mysteriously, to let him know if it's not too hard before he reveals more details about his idea. the paper is about symmetric bilinear forms on finite abelian groups, pure algebra, and I was supposed to write about algebraic topology, so I tried to search where this topics comes up, but didn't find anything. it turns out that it's used to define some knot invariant, which I would use to write about the classification of singularities of algebraic curves. in the meantime my advisor had another idea, which is an open problem in knot theory. we decided to try the second one, because there is less theory to learn before I could start writing the paper
to summarize what I'm about to do: there is a knot invariant called Jones polynomial, which then inspires a construction of a certain R-module on tangles and the question asks whether that module is free, if so, what is its rank. now I'm reading the book he gave me to learn the basics and I can't wait till I start working on the problem
Weaving Stereographic Projection
I made a stereographic projection by weaving paper strips!
Here's a Julia package for the computation of the shapes of the paper strips.
Japanese blog post about this: https://note.com/hyrodium/n/n7b7cf03a7d91
me : I love learning new things
Me when it’s time to learn anything new that I’m not instantly good at:
“Netflix and chill?”
No, PDF and cry
but how is this related to adhd? I'd say my ability to have fun is diminished because of the dopamine deficiency, I'm basically constantly bored, and afaik adhd increases the risk of substance abuse disorders, so I don't see the point of bringing up adhd in this context
Me: I don't take alcohol, smoke weed or do any other substances.
Everyone: Omg!! then how do you have fun??
Me: I have ADHD.
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
fields of mathematics
number theory: The Queen of Mathematics, in that it takes a lot from other fields and provides little in return, and people are weirdly sentimental about it.
combinatorics: Somehow simultaneously the kind of people who get really excited about Martin Gardner puzzles and very serious no-nonsense types who don’t care about understanding why something is true as long as they can prove that it’s true.
algebraic geometry: Here’s an interesting metaphor, and here’s several thousand pages of work fleshing it out.
differential geometry: There’s a lot of really cool stuff built on top of a lot of boring technical details, but they frequently fill entire textbooks or courses full of just the boring stuff, and they seem to think students will find this interesting in itself rather than as a necessary prerequisite to something better. So there’s definitely something wrong with them.
category theory: They don’t really seem to understand that the point of generalizing a result is so that you can apply it to other situations.
differential equations: physicists
real analysis: What if we took the most boring parts of a proof and just spent all our time studying those?
point-set topology: See real analysis, but less relevant to the real world.
complex analysis: Sorcery. I thought it seemed like sorcery because I didn’t know much about it, but then I learned more, and now the stuff I learned just seems like sorcery that I know how to do.
algebraic topology: Some of them are part of a conspiracy with category theorists to take over mathematics. I’m pretty sure that most algebraic topologists aren’t involved in that, but I don’t really know what else they’re up to.
functional analysis: Like real analysis but with category theorists’ generalization fetish.
group theory: Probably masochists? It’s hard to imagine how else someone could be motivated to read a thousand-page paper, let alone write one.
operator algebras: Seems cool but I can’t understand a word of it, so I can’t be sure they’re not just bullshitting the whole thing.
commutative/homological algebra: Diagram chases are of the devil, and these people are his worshipers.
chaotic good
Pro-tip: You can use paper twice if you take your notes in pencil first and then write over it in pen.
@shitstudyblr please validate me
To all the people wondering how to do proofs: A good place to start is to read "Book of Proof" by Richard Hammack. Just Google it, it's completely free and available online!
Yes! Also, for people just curious about mathematical proofs, who want to kind of see what they're like I suggest 'Proofs from the book' by Martin Aigner and Günter M. Ziegler. A short summary of this book is some of the most beautiful mathematical proofs from a range of mathematical fields. You may not understand it fully as a layman but it can be an interesting look into proofs.
Here is a free link to the 5th edition of the book
Mathematicians be like:
Def 1.1: A function f is fucked-up iff it is not Lebesgue measurable
Def 1.2: A function is evil iff its graph has non-integer Hausdorff dimension.
Exercise 1: Prove that there exist fucked-up and evil functions
yes, this. taking photos of the blackboard and writing down only the "sketch" of the lecture usually does the trick for me: I have all the details I need but I'm able to actually listen
a thing that i didn’t understand as a student, that many of my students don’t understand, and that i still sometimes struggle to put into practice: taking the most detailed notes is not always the best way to learn the material. trying to write down every single thing a teacher (or other person who is presenting auditory information to you) says is not only slow but it also can easily stop you from being mentally present during the lesson, internalizing the main ideas and how everything fits together, which is what will actually help you learn the material.
Want to learn something new in 2022??
Absolute beginner adult ballet series (fabulous beginning teacher)
40 piano lessons for beginners (some of the best explanations for piano I’ve ever seen)
Excellent basic crochet video series
Basic knitting (probably the best how to knit video out there)
Pre-Free Figure Skate Levels A-D guides and practice activities (each video builds up with exercises to the actual moves!)
How to draw character faces video (very funny, surprisingly instructive?)
Another drawing character faces video
Literally my favorite art pose hack
Tutorial of how to make a whole ass Stardew Valley esque farming game in Gamemaker Studios 2??
Introduction to flying small aircrafts
French/Dutch/Fishtail braiding
Playing the guitar for beginners (well paced and excellent instructor)
Playing the violin for beginners (really good practical tips mixed in)
Color theory in digital art (not of the children’s hospital variety)
Retake classes you hated but now there’s zero stakes:
Calculus 1 (full semester class)
Learn basic statistics (free textbook)
Introduction to college physics (free textbook)
Introduction to accounting (free textbook)
Learn a language:
Ancient Greek
Latin
Spanish
German
Japanese (grammar guide) (for dummies)
French
Russian (pretty good cyrillic guide!)
me when Čech cohomology
i love math. i hate math. i can do it all day, everyday. i cannot solve a single question. it's my favorite subject. I would rather kms than open the book. it's beautiful and everything makes sense and it's the best. it's fucking useless and nothing is logical and it's the worst. it's the loml. it's my arch nemesis.
this is kinda cool, I might do one of these when the semester starts
Studying can be a daunting task, especially when we're not feeling motivated or don't know where to start. Luckily you are on Tumblr, where the Tumblr Studyblr community lives!
A group of individuals who share their study tips, techniques, and challenges to help motivate and inspire others.
As a member of this community, I've compiled a master post of study challenges created by Studyblr bloggers. These challenges aim to help students stay on track, improve their focus, and achieve their academic goals. So you can join in and start achieving your academic potential!
>> 𝐍 𝐨 𝐭 𝐞
If you know any other challenges or you've created ones yourself and want to share them, do message me with the link to the post so I can update the list! I too will be creating some, more coding-related ones as I am a coding studyblr (codeblr) blog! That's all and hope you find a challenge you'd like to start!
@tranquilstudy's Studyblr Challenge - 𝒍 𝒊 𝒏 𝒌
@sub-at-omic-studies' Study Challenge - 𝒍 𝒊 𝒏 𝒌
@wecandoit’s Study Challenege - 𝒍 𝒊 𝒏 𝒌
@cheereader's The “Back To College” Study Challenge - 𝒍 𝒊 𝒏 𝒌
@myhoneststudyblr's The Studyblr Community Challenge - 𝒍 𝒊 𝒏 𝒌
@ddaengstudies' Wabi-Sabi Studyblr Challenge - 𝒍 𝒊 𝒏 𝒌
@hayley-studies' 30-Day Study Challenge - 𝒍 𝒊 𝒏 𝒌
@ddaengstudies' Zoomester Studyblr Challenge - 𝒍 𝒊 𝒏 𝒌
@cheereader's Summer Studying Challenge: Southern Hemisphere Edition - 𝒍 𝒊 𝒏 𝒌
@cheereader's Horrortober Challenge - 𝒍 𝒊 𝒏 𝒌
@caramelcuppaccino's Autumn Studying Challenge - 𝒍 𝒊 𝒏 𝒌
@myhoneststudyblr's Winter Studying Challenge - 𝒍 𝒊 𝒏 𝒌
@ddaengstudies' Winter Wonderland Studyblr Challenge - 𝒍 𝒊 𝒏 𝒌
@stu-dna's January Study Challenge - 𝒍 𝒊 𝒏 𝒌
@planningforpatience's February Study Love Challenge - 𝒍 𝒊 𝒏 𝒌
@littlestudyblrblog’s March Study Challenge - 𝒍 𝒊 𝒏 𝒌
@smallstudyblrsunite's The June Challenge - 𝒍 𝒊 𝒏 𝒌
@stu-dna’s October Study Challenge - 𝒍 𝒊 𝒏 𝒌
@alfalfaaarya’s 21-Day Productivity Challenge - 𝒍 𝒊 𝒏 𝒌
@work-before-glory's G's Productivity Challenge - 𝒍 𝒊 𝒏 𝒌
@moltre-se-s' 30 Day Langblr Challenge - 𝒍 𝒊 𝒏 𝒌
@drunkbloodyqueen’s The language challenge - 𝒍 𝒊 𝒏 𝒌
@caramelcuppaccino's 20 Language Learning Challenge - 𝒍 𝒊 𝒏 𝒌
@prepolygot’s Langblr Reactivation Challenge - 𝒍 𝒊 𝒏 𝒌
@xiacodes' 5in5weeks Coding Challenge - 𝒍 𝒊 𝒏 𝒌
@friend-crow's Tarot Study Challenge - 𝒍 𝒊 𝒏 𝒌
Lagrange Markipliers or something idk I forgot all my multivariable calc.
14 II 2023
so yesterday would be the last of my exams but I decided to retake both the written and the oral part. the grade I would get is 4, so not the highest possible, still pretty good especially for the standards of that course (it's one of the most difficult), but I am not satisfied
it was the professor who suggested I retake the exams, which surprised me, I was mentally prepared to finish being only half-happy about my results and his reactions, strangely enough, inspired me to try harder. he wouldn't offer it if he didn't think I could do better, right?
if he gave me a 5 with my written exam points I would feel like an impostor, because I don't think I am fluent enough with the topics to receive the best grade. to be graded 4 and not being effered the chance to try again would make me feel that it's done, I was just too slow and I can't do anything else to fix it (at least on paper, but we're talking symbolics now) and him giving me a second chance meant to me that he believes in my potential yet doesn't want to give me a participation trophy, instead he made it about earning the reward that I know I deserve
he achieved the aurea mediocritas with this and the most absurd part of it all is that he of all people was to give me this inspiration. half of the students I talk to think that he is pure evil, the majority of the other half think he is an inconsiderate asshole lmao
so in two weeks I'm trying the exam again. in the meantime I will have a party with friends (small – 5 people + my boyfriend's cat) and then I will be grading the math olympiad. afterwards my another grind of algebraic methods shall commence and this time please let me not fuck it up
"based and purple pilled" with deleted vowels. the first adhd medication I tried was life changing, I could finally study and function (half-)properly, and the pills are purple, hence my version of "based and red pilled", which I probably don't have to explain
Guys please reply to this with what your url means or references I’m really curious
Okay I’m currently furious that migraines are often so blindly easy to treat and I had to find this out myself at the age of 26 when I’ve been to a neurologist since I was 11 lol so I’m about to teach you two neat and fast little tricks to deal with pain!
The first is the sternocleidomastoid muscle, or the SCM muscle.
This big red section is responsible for pain around the eye, cheekbone, and jaw, as well as some temple pain. Literally all you have to do is angle your head down a little, angle it away from the side that hurts, and then you can gently pinch and rub that muscle. I find it best to start at the bottom and travel upwards. The relief is so immediate! You can increase pressure as you feel comfortable doing so.
Here is a short and easy video showing this in action
The second is a fast and easy stretch that soothes your vagus nerve, which is the nerve responsible for calming you down. The vagus nerve, for those unfamiliar, is stimulated by deep breathing such as yawning, sighing, singing, or taking a deep breath to calm your anger in a tense situation.
You can stretch this out by sitting up as straight as possible (this does not have to be perfect to work) and interlacing your fingers. Put your hands on the back of your head with your thumbs going down the sides of your neck and, while keeping your face forward, look all the way to one side with just your eyes. Hold that until you feel the urge to breathe deeply or yawn, or until you can tell there’s a change. Then do the same thing on the other side. When you put your arms down, you should clearly be able to turn your head farther in both directions. If the first session doesn’t get rid of your migraine, rest and repeat as many times as necessary. I even get a little fancy with it and roll my eyes up and down along the outer edge sometimes to stretch as much as I can.
If you need a visual here’s a good video on it. I know some of the language they use seems questionable but this is real and simple science and should not be discarded because it’s been adopted by the trendy wellness crowd!
I seriously cannot believe I didn’t hear a word of this from any doctor in my life. Additionally, if you get frequent recurring migraines, you may want to see a dietician. Migraines can be caused by foods containing histamines, lectin, etc. and can also be caused by high blood pressure in specific situations such as exercise, stress, and even sex.
If any of this information helps you I’d love to hear it btw! It’s so so fast and easy to do. Good luck!
Hey, im second semester math undergrad, do you recomend any book for calculus?
hi, unfortunately for first year analysis/calculus I used mostly the resources given by the professors, however, when I did use textbooks I really liked Walter Rudin:
as far as I know, many people recommend Apostol's book, which looks very good and if I was to choose a textbook for myself right now I would definitely try this one:
other than textbooks, if you like learning math from videos check out this channel:
Michael Penn is a teacher at a university and he's great at explaining theory and solutions of problems
11 II 2023
in two days I have my last exam and I have absolutely zero motivation to study for it
yesterday I had an oral complex analysis exam and I did very well, the professor said that I will most likely receive the top grade. my partial scores from this course add up to 80%, so if the oral one was for 100%, it yields 84% total. that sounds like a top grade to me although we haven't received the official report yet
I also had an algebraic methods exam a few days ago and it went ok, I completed 4.5 out of 6 problems. I probably have no chance for a top grade from this course because the professor is very strict with how many points qualify for that and I am not even close to what the best people had. this is why I have zero motivation to study for the oral exam from this course, if there was a chance to score a 5 (the top grade) then I would care, but if my options are 3.5, 4 or 4.5, I don't really see the difference
well, the difference lies in maybe applying for a scholarship after this academic year, but honestly that "goal" is just here to distract myself from feeling judged all the time. somehow I don't care about money as much as an abstract number supposedly rating my abilities so thinking of it as "try harder so you might get paid for it" feels less pressing than "try harder so you'll have higher abstract numbers and you can feel good about yourself"
jesus I fucking hate grades, I wish it was kept secret from me how much points I actually have, only receive feedback on the correctness of my solutions and the information if I am passing or not. I can never be satisfied with I am doing. last year I would see it as a success to score 4's at everything, now it feels like a failure because I already scored some 5's, so that's my new bottom line. and I know that if I did ace everything, I would be happy for about 5 minutes and then move on to picking up twice as many courses for the next semester because "it would be too easy otherwise"
grades, no matter what I'm getting, fuck with my self esteem so deeply. it brings out the worst insecurities, fears and memories, this is when I am thinking my darkest thoughts. I have no one to talk to about this and I am angry at myself for perceiving it this way. I wish these things didn't matter to me but they do, I don't even know why, it feels like a trap
I don't want people to tell me that "I'm great no matter what grades I'm getting" or that "I will do it, because I'm smart". I actually don't know what I want, and it sucks to put my friends into the situation where no matter what they say it's "the wrong line". ughhh I want this semester to be over so I can go back to only caring about learning as much as possible
my thesis advisor (I think that's what you call the thesis boss) sent me a paper to read and I'm curious what topic he picked for me. I will gladly read it right after I'm done with exams
" 'They' isn't singular!" Oh yeah? Show me its multiplicative inverse matrix then.
tips for studying math
I thought I could share what I learned about studying math so far. it will be very subjective with no scientific sources, pure personal experience, hence one shouldn't expect all of this to work, I merely hope to give some ideas
1. note taking
some time ago I stopped caring about making my notes pretty and it was a great decision – they are supposed to be useful. moreover, I try to write as little as possible. this way my notes contain only crucial information and I might actually use them later because finding things becomes much easier. there is no point in writing down everything, a lot of the time it suffices to know where to find things in the textbook later. also, I noticed that taking notes doesn't actually help me remember, I use it to process information that I'm reading, and if I write down too many details it becomes very chaotic. when I'm trying to process as much as possible in the spot while reading I'm better at structuring the information. so my suggestion would be to stop caring about the aesthetics and try to write down only what is the most important (such as definitions, statements of theorems, useful facts)
2. active learning
do not write down the proof as is, instead write down general steps and then try to fill in the details. it would be perfect to prove everything from scratch, but that's rarely realistic, especially when the exam is in a few days. breaking the proof down into steps and describing the general idea of each step naturally raises questions such as "why is this part important, what is the goal of this calculation, how to describe this reasoning in one sentence, what are we actually doing here". sometimes it's possible to give the proof purely in words, that's also a good idea. it's also much more engaging and creative than passively writing things down. another thing that makes learning more active is trying to come up with examples for the definitions
3. exercises
many textbooks give exercises between definitions and theorem, doing them right away is generally a good idea, that's another way to make studying more active. I also like to take a look at the exercises at the end of the chapter (if that's the case) once in a while to see which ones I could do with what I already learned and try to do them. sometimes it's really hard to solve problems freshly after studying the theory and that's what worked out examples are for, it helps. mamy textbooks offer solutions of exercises, I like to compare the "official" ones with mine. it's obviously better than reading the solution before solving the problem on my own, but when I'm stuck for a long time I check if my idea for the solution at least makes sense. if it's similar to the solution from the book then I know I should just keep going
4. textbooks and other sources
finding the right book is so important. I don't even want to think about all the time I wasted trying to work with a book that just wasn't it. when I need a textbook for something I google "best textbooks for [topic]" and usually there is already a discussion on MSE where people recommend sources and explain why they think that source is a good one, which also gives the idea of how it's written and what to expect. a lot of professors share their lecture/class notes online, which contain user-friendly explenations, examples, exercises chosen by experienced teachers to do in their class, sometimes you can even find exercises with solutions. using the internet is such an important skill
5. studying for exams
do not study the material in a linear order, instead do it by layers. skim everything to get the general idea of which topics need the most work, which can be skipped, then study by priority. other than that it's usually better to know the sketch of every proof than to know a half of them in great detail and the rest not at all. it's similar when it comes to practice problems, do not spend half of your time on easy stuff that could easily be skipped, it's better to practice a bit of everything than to be an expert in half of the topics and unable to solve easy problems from the rest. if the past papers are available they can be a good tool to take a "mock exam" after studying for some time, it gives an opoortunity to see, again, which topics need the most work
6. examples and counterexamples
there are those theorems with statements that take up half of the page because there are just so many assumptions. finding counterexamples for each assumption usually helps with that. when I have a lot of definitions to learn, thinking of examples for them makes everything more specific therefore easier to remember
7. motivation
and by that I mean motivation of concepts. learning something new is much easier if it's motivated with an interesting example, a question, or application. it's easier to learn something when I know that it will be useful later, it's worth it to try to make things more interesting
8. studying for exams vs studying longterm
oftentimes it is the case that the exam itself requires learning some specific types of problems, which do not really matter in the long run. of course, preparing for exams is important, but keep in mind that what really matters is learning things that will be useful in the future especially when they are relevant to the field of choice. just because "this will not be on the test" doesn't always mean it can be skipped
ok I think that's all I have for now. I hope someone will find these helpful and feel free to share yours
good point! I should add to my list the golden rule of asking yourself "does this thing that I'm currently trying actually work for me". in the meantine I had a conversation with a friend who said that for her not caring about the aesthetics of notes decreases the effectiveness of studying, my perspective definitely isn't The Only Correct One
the best method is the one that works. it's perfectly okay to benefit from notes, from making them pretty, it's also perfectly okay to limit the notes. it was a surprising discovery for me that taking notes doesn't help with my learning, because my whole life I've been told to always take notes. but of course this isn't going to work for everyone, thank you for pointing this out
tips for studying math
I thought I could share what I learned about studying math so far. it will be very subjective with no scientific sources, pure personal experience, hence one shouldn't expect all of this to work, I merely hope to give some ideas
1. note taking
some time ago I stopped caring about making my notes pretty and it was a great decision – they are supposed to be useful. moreover, I try to write as little as possible. this way my notes contain only crucial information and I might actually use them later because finding things becomes much easier. there is no point in writing down everything, a lot of the time it suffices to know where to find things in the textbook later. also, I noticed that taking notes doesn't actually help me remember, I use it to process information that I'm reading, and if I write down too many details it becomes very chaotic. when I'm trying to process as much as possible in the spot while reading I'm better at structuring the information. so my suggestion would be to stop caring about the aesthetics and try to write down only what is the most important (such as definitions, statements of theorems, useful facts)
2. active learning
do not write down the proof as is, instead write down general steps and then try to fill in the details. it would be perfect to prove everything from scratch, but that's rarely realistic, especially when the exam is in a few days. breaking the proof down into steps and describing the general idea of each step naturally raises questions such as "why is this part important, what is the goal of this calculation, how to describe this reasoning in one sentence, what are we actually doing here". sometimes it's possible to give the proof purely in words, that's also a good idea. it's also much more engaging and creative than passively writing things down. another thing that makes learning more active is trying to come up with examples for the definitions
3. exercises
many textbooks give exercises between definitions and theorem, doing them right away is generally a good idea, that's another way to make studying more active. I also like to take a look at the exercises at the end of the chapter (if that's the case) once in a while to see which ones I could do with what I already learned and try to do them. sometimes it's really hard to solve problems freshly after studying the theory and that's what worked out examples are for, it helps. mamy textbooks offer solutions of exercises, I like to compare the "official" ones with mine. it's obviously better than reading the solution before solving the problem on my own, but when I'm stuck for a long time I check if my idea for the solution at least makes sense. if it's similar to the solution from the book then I know I should just keep going
4. textbooks and other sources
finding the right book is so important. I don't even want to think about all the time I wasted trying to work with a book that just wasn't it. when I need a textbook for something I google "best textbooks for [topic]" and usually there is already a discussion on MSE where people recommend sources and explain why they think that source is a good one, which also gives the idea of how it's written and what to expect. a lot of professors share their lecture/class notes online, which contain user-friendly explenations, examples, exercises chosen by experienced teachers to do in their class, sometimes you can even find exercises with solutions. using the internet is such an important skill
5. studying for exams
do not study the material in a linear order, instead do it by layers. skim everything to get the general idea of which topics need the most work, which can be skipped, then study by priority. other than that it's usually better to know the sketch of every proof than to know a half of them in great detail and the rest not at all. it's similar when it comes to practice problems, do not spend half of your time on easy stuff that could easily be skipped, it's better to practice a bit of everything than to be an expert in half of the topics and unable to solve easy problems from the rest. if the past papers are available they can be a good tool to take a "mock exam" after studying for some time, it gives an opoortunity to see, again, which topics need the most work
6. examples and counterexamples
there are those theorems with statements that take up half of the page because there are just so many assumptions. finding counterexamples for each assumption usually helps with that. when I have a lot of definitions to learn, thinking of examples for them makes everything more specific therefore easier to remember
7. motivation
and by that I mean motivation of concepts. learning something new is much easier if it's motivated with an interesting example, a question, or application. it's easier to learn something when I know that it will be useful later, it's worth it to try to make things more interesting
8. studying for exams vs studying longterm
oftentimes it is the case that the exam itself requires learning some specific types of problems, which do not really matter in the long run. of course, preparing for exams is important, but keep in mind that what really matters is learning things that will be useful in the future especially when they are relevant to the field of choice. just because "this will not be on the test" doesn't always mean it can be skipped
ok I think that's all I have for now. I hope someone will find these helpful and feel free to share yours
" 'They' isn't singular!" Oh yeah? Show me its multiplicative inverse matrix then.
DO YOU KNOW WHAT I JUST REALIZED
YOU KNOW THE HAIKU BOT???
OFC YOU DO
YOU KNOW THAT MESSAGE HE PUTS AT THE END OF EVERY POST????
"Beep boop! I look for accidental haiku posts. Sometimes I mess up."
YEAH???????
WELL THATS A HAIKU TOO
Beep boop! I look for
accidental haiku posts.
Sometimes I mess up.
NOW YOU LOOK ME IN THE EYE AND TELL ME THATS NOT THE CUTEST THNIG YOUVE EVER HEARD
have you ever wished for an interactive phase plot of polynomials in the complex plane?
one that you could use even from your phone?
then good news!
[neocities]
can someone please get these hoes under control i'm BUSY
Thank you, /r/ProgrammerHumor, I love you endlessly.
Redditors competing to make the worst volume sliders possible...
