Hey Veeky Forums, any math/physics major around?
I've successfully finished my first Calc and Algebra courses (math degree) but I don't feel that I have a good learning method yet. Any advice?
Please don't say "practice, practice and practice", I know this is a somewhat necessary condition but it's definitely not sufficient.
>I've successfully finished my first Calc and Algebra courses (math degree) but I don't feel that I have a good learning method yet. Any advice?
practice, practice and practice
of course
Read the book. Don't focus too much on the excercises (especially if they are tedious). Just get the big picture.
When you don't understand something, google it. math.stackexchange.com usually has the answer.
After you are finished, check the class notes a bit and solve older exams.
You are going to be scoring 90-100% this way.
x=4.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
They are tedious indeed.
Will get more into Stack exchange.
Thx for the legit advice
Thx too
For physics, the biggest thing is not taking anything for granted. If you just remember a list of formulas, you’ll have no actual idea of what’s going on. You should convince yourself of every forumula you use by deriving it yourself. If you can’t derive it, then you probably can’t use it effectively.
This is especially true for when you approach things like accelerating frames and tensors for the first time. It can be super tedious, but they’re simply not concepts that you can just look at and understand intuitively like you can with 2d kinematics. At least, they weren’t for me or any of my classmates.
When taking notes, don’t write everything the teacher writes down. Write down the important shit, and fill in the rest by yourself. If you’re being taught a theorem, that means you should be able to prove it by yourself. You really won’t learn anything by scribbling down whatever your professors write on the board. Understand what they are doing and why they are doing it.
Learning math and physics is a tedious task unless you’re some type of child prodigy. When you get to the higher levels, if you’re not willing to put some effort in, it will reflect in your grades. The idea of “practice, practice, practice” might sound more annoying than it is useful, but it’s really the most effective way to do things.
A good baseline standard you should hold yourself to when you’ve studied through multivariable calculus is that you should be able to look at any integral and recognize how you would go about solving it.
I would also recommend going further in your rigorous maths than what is required by most physics programs. At least take a class on proofs and one on abstract algebra. Maybe some real analysis and complex analysis if you can fit it in. You cant possibly use the language of mathematics effectively if you don’t understand the language in the first place.
Not OP, but thx. This is legit advice.
Are you a physicist? How do you deal with problems that requires more tricks to solve than actual physics?
In my final year of undergrad, doing a double in Applied Math and Physics.
In my experience, many problems in Physics require some level of cleverness as well as mathematics. While it seems like a case by case scenerio, what your typical motivation in pulling out “tricks” is to make a hard problem into an easy problem. It’s like when you transform your boundaries for a tricky integral or the boundary conditions for an ugly PDE. The entire point of doing that is to write the solution of the hard problem as it relates to the solution of the easier problem.
In some cases, yes it takes just pure intuition, but for the most part when you use a “trick” it’s actually based in a methodical thought process, rather than pulling something out of a hat.
Like, when you solve ODE’s, half the time you’re guessing the answer because you know what it should look like. So my best advice when it comes to getting comfortable with clever solutions is to understand what solutions to problems should look like first and foremost. Once you do that, you can build an understanding of how a hard problem can be solved using the solution of an easier problem.
Take adderall and cram like it was finals week. Works every time senpai.
In addition to what was said by , be selective about how to spend your time. There are a lot of different things to do in college, and at least in my experience it was easy to not have the necessary time required to really dive into understanding the material.
On the other side of things, if you're tempted to only study, think about finding at least one non-math/physics thing to get involved in. You don't want to forget how to interact with other humans.
Thank you. Do you select a few problems to work or you try to do all the problems from your textbook?
Well, definitely do all the problems your professor either assigns or recommends you do, because those problems will most likely reflect the concepts they will be testing you on, and you want to assure yourself of a good grade.
After deriving everything and doing all the problems your professors recommend, I would read through your text books. Many times a text book will skip through a derivation or will leave part of a solution as an exercise for the reader, and those are typically pretty instrumental.
Doing all of the problems is very time consuming and with an intensive major like Physics, you do reach a point where free time becomes scarce. If you have the ability to, sure, but I don’t think doing all of the exercises in a textbook will be that much better than nailing down the core concepts. If you do have extra time, try to locate the problems that aren’t super mechanical and rather force you to be clever and actually think critically about what you’re doing.
OP Here
That's a well elaborated reply, thanks for your time.
>Learning math and physics is a tedious task unless you’re some type of child prodigy. When you get to the higher levels, if you’re not willing to put some effort in, it will reflect in your grades. The idea of “practice, practice, practice” might sound more annoying than it is useful, but it’s really the most effective way to do things.
Well, I'm pursuing an Applied Math degree and I'm not a prodigy, I just understand through hard work.
I just hate the idea of using "tricks" to solve problems, so I try to understand everything I can and by doing so I may not get to the final exams having comfortably studied all the subjects.
>A good baseline standard you should hold yourself to when you’ve studied through multivariable calculus is that you should be able to look at any integral and recognize how you would go about solving it.
I think that's a good guideline, I think of solving integrals as doing push ups or some basic skill/tool so I can later be comfortable in higher levels of maths.
I have received another good advice: learn until you can explain it to a newbie.
I have never tried it, it may be an interesting expermient I guess...
OP Here
I actually struggle a lot to find time, I'm taking strong measures to only have 1 or 2 activities in my life (besides some socializing).
If you have any particular advice from your experience on this it will be very welcomed.
BTW
Do everyone study along the professor classes or some of you study via self learning?
Brainlet with somewhat related question:
I know that math is cumulative, new concepts build on the previous ones in order to proceed forward.
However the more I'm going through the various arguments the more I feel that it takes me more and more time in order to properly get it than the previous one; somewhat as if the learning curve isn't linear.
Am I overthinking it or is this something relatable?
It's probably because you are not properly understanding the previous stuff. Read them again.
yes it is boob
Do you write notes when reading a book? I mean besides proofs
I feel like I'm wasting time when I take notes.
Last year I started uni and I was lazy unwilling guy - mostly because I still had the high school mentality; I took notes but it was just what the professor was writing onto the board, filled with occasional fillers.
Once I come back home I left the notes there; needless to say these notes were as useful as wastepaper later on. I had to study everything again from scratch, since I wasted all that time.
This year I tried, instead of brainlessly follow the professor, to write down the links between the arguments: I was more busy trying to connect what he said rather than playing catch-up with his speech.
Afterwards instead of jerking off, I looked up the notes and - unlike what many do - I didn't just copy&paste what I wrote, I actively try to make everything said in lesson as clear as it can possibly be,
even if that required 3-4 reviews and total rewrites, each time acquiring more and more proficiency about the topic.
Point is professor > self learning, always. He knows what he's talking about, he can point out the links to make everything work, you don't. You'll just waste weeks of time for something often subtle and pointless.