For those of you who are great at maths, how do you study? (For those of you who don't need to study, while that is great, your perspective won't be of much help to me.)
I want to get into maths, but I don't know any efficient way to approach learning it. I end up just getting very bored, desu.
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If it's boring to you, why bother learning it? ; - )
As for me, I study by reading the textbook and doing the practice questions, nothing else needed 9/10 times.
>I end up just getting very bored
try studying other subjects of math. you might get hooked on with other types, otherwise
self discipline is your only way to get great at math
It isn't math itself which bores me, but the rote memorization of method and repetitive executions of practice (it is a bit difficult to define what interests and doesn't interest me about it). What math is capable of, and what it is, interests me very much - more even than women. I'm not poor at it either, but I want to become much better and I need to draw on the wisdom of you patient, diligent anons to whip my lardly cognitions into shape.
I may be a pseud, but with any luck today will be a step towards a cure.
>self discipline
What regimens do you implement? How often and/or long do you study for? Any mental exercises you employ for applying the mathematics to its uses?
>rote memorization of method
you're doing it wrong
unless you're going for a math phd, there is nothing wrong with rote memorization
>how do you study
I don't, I'm just naturally good at maths. Never picked up a textbook. I usually learn shit by solving tasks in exams. If you need to study math you've failed already.
nothing wrong at all, except that it's the most boring and ineffective way to learn it.
How do you study it user?
As I said (or at least implied), that is wonderful, I'm happy for you, but your point of view isn't useful for me.
Don't study math, retard. You will never make it. You don't deserve to make it. You will never see the light for you have not been granted a soul to appreciate it.
>comes to the thread bc I feel super identified with your problem and wants study tips too
>anons refuse to help bc apparently we are condemned to be retarded forever
Ah, this page never disappoints me
Helping you would be like trying to teach a worm to sing. It doesn't matter what you do, the worm simply lacks the capacity to succeed.
Not him, but one of the best students on my shitty third world college here.
When I study, I try my best to understand the concept by visualizing, connecting it to the previously leaned mathematical framework and mere intuition. For example, when I studies Analysis I, I had a lot of issues with convergent series and convergence theorems for series and such, so I spent a lot of time trying to draw a lot of graphs for examples of convergent sequences and try to understand what exactly does the definition of limit mean in all those cases, why does for every epsilon exist a delta that ONLY depends on epsilon; why is uniform continuity different from ordinary continuity; what exactly does the Mean Value Theorem mean and so on. Those might be trivial examples, but that approach has served me well over the years.
It has proves especially useful in my first differential equations class - what seemed mostly like memorization of techniques to others, appeared kinda natural to me because I have already had developed intuition for differentiation and integration and all of the underlying processes.
TL;DR:
Learn the basics and understand all the previous concepts before learning a subject.
Not him
I think about the issue at hand. Then I think about how the discoverer of the math discovered the math necessary for the problem. For instance, newton (or whoever it was) needed a way to calculate the change of a property over time so he came up with the idea to check the surrounding points and compare it to the point of the property. As the surroundings get smaller, the property become more clear. And thus limits were born.
OP here, I am a physics major with a maths minor, but I had considered pursuing higher degrees in both fields.
Unless you're at the top of a field, the most interesting questions will always remain closed to you, and that is a frightening, depressing thought - rife with anxiety for me, in fact.
I'm not sure why, but it is truly fearful for me to imagine only ever possessing second-hand knowledge of the fascinating problems man faces in the sciences.
I have friends who study in humanities, some who are even accomplished already, and these fields, while interesting, seem like mere pastimes for men, so although I could excel in fields like classics or linguistics (and still intend to, as a hobby), I would rather learn the way you all think about math, so I may continue my pursuit of a more adult intellectual life.
This is self-refuting, as this thread's existence implies an appreciation for mathematics already.
Do you do more than the assigned homework usually?
Thank you both for excellent posts. This is a kind of information I'm very interested in. Your thoughts are helpful.
One more thing - do your proofs. Spend as much time with them as you can and try to learn them with rigor, try to understand why each step happens and how is it related to the rest of the proof and to the theorem. Proofs are where most of the "underlying knowledge" lies - if you truly understand the proof of the theorem, it is easy to understand the meaning of the theorem. Do your proofs, even outside of the classes. Do them for fun.
Think of it like reading. When you see a word you don't understand, do you look up its definition? How do you remember that definition?
I get the feeling most people approach math like they are reading a foreign language. They have to frequently look up translations instead of walking around with a working knowledge. The problem comes from not remembering translations after the initial look up.
If im struggling with the concept I do, If not than usually only if Im bored
Read theorem.
Apply example to understand how the theorem works.
Write proof based on insight from example.
If unable, do more examples.
Then write proof.
Once you do this enough, you gain an intuition on how to proceed. You'll know what techniques to apply in your proof and you can test lemmas and corollaries.
You can also find counter examples to theorems by changing the qualifiers of the theorem if you don't understand a particular aspect of it.
Where did you learn your proving methods? A course? A book?
>How do you remember that definition?
Force of will and associations, generally, but, most of all, frequent use. I suspect you are right - point taken, friend.
This sounds fantastic, and although I can imagine your meaning quite well, could you provide an example? Alternatively, could you provide a link to a video which shows this kind of methodological approach, or, even, a text recommendation?
I don't know of any books, but here's a hw problem that I had in number theory.
Theorem: if a,b are positive integers both not 0, then a = qb + r for some integer q and 0
I made a mistake. b > 0
*tips*
Where are you from user?
Literally the only real way to study math is doing a little bit of reading from the textbook and doing a shit ton of practice problems
OP if you're still in this thread just do practice problems a couple nights in advance before a test. If there is a practice test, take that and then practice where you struggle. If you are just trying to get into math, start with popmath. That will get you interested then work your way to more practical math.
Balkans. Why you ask?
Thought I knew you from somewhere. Is all.
Try the lecture to a wall technique
I learned about it from a book called OVERNIGHT STUDENT
Also depressing: if you dont make a major contribution by 30 you wont ever
Well, do you?
Describe the person you had on your mind. What exactly did you recognize in my post?
>dont study at all
>day before exam
>panic
>take a fuckton of ritalin and caffeine
>study 36 hours in a row
other than developing high blood pressure in my 20s, its all good
>I usually learn shit by solving tasks in exams.
this is unfortunately how to get good grades (in the current system) but I am not so sure it is how to learn
what year are you on user
>read
>do problems
>rinse and repeat
literally nothing else to it
First teehee
You could try "How to Prove It" by Velleman or "Book of Proof" by Hammack. I've done some of the former, and, as a possible brainlet hoping to get good enough to get a doctorate in maths, I feel the intro to logic and generic proof methods Velleman went over helped my reasoning. Seeing the thought processes behind other people's work is easier now.
If anyone is around to give a non meme answer then, I'd love to learn your method.
So far I've just been doing problems until they make sense. To give a basic example, 1 + 1 is 2 because you're moving down the number line.
Literally this. FPBP and anything else is just mental masturbation. All you need to get good at math is practice until you get it. If you're a brainlet, it's harder but you'll still make it. If you're moderately smart it won't be hard, just tedious I guess. I don't really like math but I'm 4 years in Electrical Engineering anyway. I just take doing math as a job, if you enjoy it you'll have a way easier time with it just because time flies when you're doing something you like.
You won't make it
...
Forgot to add, just read the "A mind for numbers" book and global.oup.com
also, the tl;dr of it is:
1) use pomodoro thingy
2) don't study more than 3-4 subjects at the same time, and with this I'm not talking about learning japanese and QFT in the same moment, but only focus your daily attention to that amount of subjects at most.
I write a lecture about what I'm studying, then I do the exercises.