Tips For Studying Math

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

More Posts from Bsdndprplplld and Others

bsdndprplplld

3 years ago

i ended up not doing topo yesterday and made an animation of a lipschitz function instead:

i'm kinda proud of it even though it's messy. had so much fun with it. maybe i'll do some more today

but i want to do that topo content i planned to do so we'll see. i also need to do some coding and finish an art comission

Tags

studyblr mathblr

3 notes View Post

bsdndprplplld

1 year ago

people using a matrix as just a bunch of numbers in a grid or a way to summarize some elaborate calculation instead of a way of notating a linear transformation (or at least a set of points) feels kind of genuinely profane to me. like its one of the only times i feel like i "get" the concept of the profane. how could you do that to her

90 notes View Post

bsdndprplplld

3 years ago

i gotta say i don't buy all them planning strategies and tips that require more effort than just sitting and doing the work

i mean that might help some people but i find that when i am doing something important to me i need no plans nor do i need motivation, i also don't procrastinate, everything falls into its right place

and if achieving something takes so much effort in preparation, is this even supposed to be a thing? idk, maybe that's the reason why i have no external proof of my work lol

1 note View Post

bsdndprplplld

2 years ago

Hello, dear! 🌻

I saw your post wanting book recommendations. I'm sorry for your previous struggles, but I hope this list may help you find something you love!

-"The Housekeeper and the Professor" by Yōko Ogawa (The professor is a mathematician!)

-if you like Vonnegut, you may like Haruki Murakami, specifically his older titles like "Wind-Up Bird Chronicle" and "Norwegian Wood" (I feel these books do a good job of expanding on people's motivations and moods.)

-"The Elegance of the Hedgehog" by Muriel Barbery (Again, excellent at conveying emotions.)

-"Hunting and Gathering" by Anna Gavalda (This one is technically a romance - a genre which I personally would normally HATE - but it portrays such realistic characters, their struggles and their natural dialogue during fights that it actually felt more like I was reading about a collection of lives that I had the pleasure of spying on from above. I really love this book!)

-for WWI and WWII-themed titles, I'd recommend the Battlefield comics by Garth Ennis (He's SO good at writing believable characters and realistic dialogues.)

-if you don't mind high fantasy, any of the books in Terry Praychett's Discworld series about the wizards might be up your alley (You can read them independently without issue, or start from the beginning of any of the wizard titles. You can find a reading guide online! The wizards of his world are very regimented about how magic works - somewhat like mathematicians - and it's very funny.)

-the "Cemetery of Forgotten Books" series by Carlos Ruiz Zafón (I'd skip the 4th one - the main character/POV changed and I wasn't as impressed with the writing in that one - but the first 3 books are an absolute dream to read. The characters are so charming, lovable or completely horrifying, it feels like a wonderful foreign mystery series that takes place in 1940s Spain. It was really interesting to try to keep track of such a unique mystery amidst the second world war.)

I hope those help! Please enjoy your reading journey. ♡

hi, and thank you so much for the recommendations! I appreciate it a lot, those books sound really good

Tags

books

5 notes View Post

bsdndprplplld

1 year ago

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).

28K notes View Post

bsdndprplplld

1 year ago

thinking about the time a prof told us that in real research mathematics it's fine to be slow, speed itself is not essential, as long as you can find it within yourself to make consistent unyielding inexorable forward progress, like the time some guy stole an M60A3 tank and terrorized a suburban neighborhood with it, said guy wasn't going that fast but plowed through cars and telephone poles and shit no problem. i'm not kidding that's what he said, that's the metaphor he used, he told us that the act of mathematics is like the 1995 san diego tank rampage

26K notes View Post

bsdndprplplld

2 years ago

Quatrefoil Knot

1K notes View Post

bsdndprplplld

1 year ago

Tags

category theory of course although tough choice between this and algebra we should include piccirillo with knot theory

1K notes View Post

bsdndprplplld

1 year ago

omg that sounds so cool

one of my friends found radiooooo which is a site that streams music from any country from any decade (well, most countries/decade combos work) and we’ve been digging going on a quest to find what is rad

so far the following is good

50s/60s/70s/80s russia

70s cambodia

20s japan

80s ethiopia

80s india

178K notes View Post

bsdndprplplld

1 year ago

saving this for self-care and for anyone who might need this

also, I can add: squint your eyes hard and then looking at something far away. it's supposed to help your eyes relax and a bonus simple grounding exercise!

from my personal experience, once you start paying attention to how different it feels on your eyes to look at something far away as opposed to something close, you can relax your eyes without needing an object to look at. now when I'm going to bed I imagine a tree far away and I feel my eyes relaxing, it helps with me fall alseep faster. it might be a placebo ofc, I know nothing about eyes, but it is still a good trick for falling asleep regardless of the supposed effect of it on the eyes

We need like “unclench your jaw” posts but for eye strain. Like

Go look at something 20ft away for 20 seconds.

Tags

selfcare

196K notes View Post