General 'how to study math'-type help request?

[MissSilvy]

I know this may sound silly, but right now I'm a physics major just starting the calculus sequence and I just have a question or two about how everyone else studies math. Obviously, math is important for later on, so I want to learn it correctly and not just study enough to pass the tests.

For me, math is doable but I always seem to get stuck on problems and I want to run to the TA. Tech subjects seem like there's no way to learn it yourself without someone standing over you and checking your work. I know that other people seem to manage just fine without spending outrageous amounts of time in the TA's office so is there any way I can wean myself off of this tendency?

And a final question about how you go about studying math. Currently what I do is go to the lecture, take notes, and then later rewrite and reread the notes, and finally attempt homework. Does anyone do it differently or have any suggestions?

Sorry for the rambling and I appreciate all the advice I get, truly. Thank you!

 

[mrb]

I'm a math major and only a couple years ahead of you, but FWIW:

You may be giving up too quickly on problems. Sometimes the best way to learn is to slog through it yourself for hours.

Personally I don't find lectures especially useful. In fact if they're not on a simple topic sometimes I can't even follow them. If the prof introduces concept X, and that's a concept you would have to think about and play with for an hour to really get a grasp on, you are going to be sitting listening to the rest of the lecture and not really understanding what's going on. Instead, I do this (at least, I try to): I stay ahead of the class. I come to each lecture already having read the textbook section the lecture will be on, played with the concepts, and worked some problems. This way the lecture reinforces the material and possibly adds new insight, and I'm not struggling to keep up with an hour long talk about concepts I don't understand. I take minimal notes, only writing if there is some real insight I didn't get from working on my own. Sitting while someone talks at you is just not a good way to learn this stuff.

Also, you say you rewrite and reread the notes. That can help, but do you also play with the material? Try to find boundary cases or what have you? Or even just make up your own examples that help you see how things work?

 

[yojoe]

mrb is right, you need to work through problems over and over. Preferably before the classes. This might not work for you but here is how I do it:

(1) I gather as many of examples of a problem as possible (this is also useful for in the future when you can't work something out, you can go back and look at your encyclopedia of examples).

(2) I work out how each example was done. I take notes of each step.

(3) I then try and make those steps as succinct as possible. A simple example would be converting complex numbers to radians, which I would break down into three steps (i) draw a diagram (2) find |z| (3) use trig ratios to find answer in radians. You might find a different way to do it, hence the need to work it out by yourself and come up with your own patterns (that lectures will either sharpen or correct).

(4) I then memorize the 'how' and practice it over and over. Combine it with other left-field problems etc.

 

[PowerIso]

Copying examples is fine for lower division math classes, but as you move up to more abstract classes, then it becomes little use. It's more helpful in the long run to learn definitions, learn theorems and see why they are true, and then apply those theorems and definition to problems. The quicker you learn how to do this, the better you'll be in the long run.

Since you just started calculus, then doing many problems will still be helpful, but if you also work on learning definitions and theorems, you'll find that you'll know more than most of your peers.

Lastly, if you find that you do get stuck on a question, move on and then come back to it. If you can't solve it then ask for help, but before asking for help, try to think of some ideas that may work and ask if it will and if it won't find out why it won't.

 

[Vid]

The obstacle is getting used to the idea that there is no algorithm so doing homework in math classes at the college level. In high school algebra or calculus, you were given something like the quadratic formula and a list of second degree polynomials and told to do the mind numbing task of using it over and over again. This will not be the case in college level classes. Knowing every method used in a particular section is certainly necessary, but not sufficient to do the homework. The homework will require you to use your own problem solving skills to be able to get the right answer. In my experience as a calculus tutor, I can't tell you the number of students who've said to me, "I'm following the example exactly, but I can't get the right answer."

 

[zoner7]

Copying examples is fine for lower division math classes, but as you move up to more abstract classes, then it becomes little use. It's more helpful in the long run to learn definitions, learn theorems and see why they are true, and then apply those theorems and definition to problems. The quicker you learn how to do this, the better you'll be in the long run.

I am struggling with this so much right now. I've never gotten below an A in my life at a damn tough college, but in my discrete mathematics class, I can barley keep up. I currently have the equivalent of a C, possibly lower. it's all because I'm struggling to apply the theorems about prime numbers, GCDs and others. How do you do it!?

 

[Nick M]

I read the material that will be covered in the next lecture. I then go to lectures and listen. I then read the text again. If I don't understand the topic, I will look up the topic in another text that explains it a different way (try your campus library). Then I attempt the problem sets. For a one hour lecture, I expect a half hour of prep-reading, an hour of re-reading after the lecture, and a couple hours for the problem sets and to re-cap everything. Get all this done ASAP, so if you do have trouble you can go get help.

I find reading and understanding the text/examples to be the most important part. The problems for me then seem fairly straight forward (for the most part).

 

[PowerIso]

I am struggling with this so much right now. I've never gotten below an A in my life at a damn tough college, but in my discrete mathematics class, I can barley keep up. I currently have the equivalent of a C, possibly lower. it's all because I'm struggling to apply the theorems about prime numbers, GCDs and others. How do you do it!?

Really, it's just about reading the book, asking questions in lecture, and doing the homework. When you learn these theorems, you need to sit there and think about what it means and if you really want to get ahead think about what more theorems the the theory or definition implies. It's difficult at first, but it's a skill that needs to be worked on.

Prior to this point, you probably were given a theorem and shown how to apply it and then you followed some simple method to solve all problems and probably forgot the theorem. It doesn't work that way anymore.

You now need to take the theorem, read what it says, know what it means, and then look at your problem and see what you are given that will allow you to use theorems you know and work your way to the end result. At first you will make a lot of mistakes and take long ways to the answer or just hit a roadblock. it then becomes important to step back and see where you are going in circles and find out if there is a better way. If you can't find one, ask a friend for a hint or a professor. Sometimes just talking the problem out helps solve it.

 

[zoner7]

yea, it seems like the majority of students in my class struggled with the last homework that was proof based. it was our first assignment that was almost all theory and that we had absolutely so problems that we could simply imitate to obtain the correct answer. I guess I'll just keep reading the theorems until it makes sense.

 

[quasar_4]

I used the books "How to Ace Calculus" and "How to Ace the Rest of Calculus" and they really helped me to transition from my middle school mentality of "find and copy examples of problems" to "what's really going on?". So, I'd suggest finding some good books that make it clear to you.

In my upper level courses, if I don't understand straight off the bat, then I reread...then reread, if necessary. Even weird and difficult concepts seem to make more sense when you've read about them so much, and eventually you figure it out. Struggling with problems is really the best ever. If you figure them out instantly, later on you'll probably forget how you did them. If you struggle for hours and find it difficult, it will stick with you and you'll actually learn the material better.

 

[Troponin]

I don't know that I've taken a single useful note in a Math course. lol

That might be a bit of an exaggeration, but in my opinion, it's more beneficial in math than any other subject to treat the lecture as "reassurance" for what you've already worked through.

The only way I can get anything out of a lecture is to prepare notes ahead of time from the book or syllabus, worth through problems as best I can, and then "listen" to the lecture while trying to see the professor's steps before he makes them.

I see so many students copying directly from the blackboard, barely keeping up with the pace of the professor. Perhaps that works for them, but I get nothing out of that. I'd be better off spending that time working problems on my own.

 

[tim_lou]

yea, it seems like the majority of students in my class struggled with the last homework that was proof based. it was our first assignment that was almost all theory and that we had absolutely so problems that we could simply imitate to obtain the correct answer. I guess I'll just keep reading the theorems until it makes sense.

In my experience, it is pretty useless to try to "read" a math book in the sense that you described.
To really read a math book (for me), I look at a theorem, then ask myself, why is it useful? why does it seem to be true (to gain intuitions)? it helps to look at some examples to see certain patterns. then I try to have some idea of how the proof may go and then read the proof. Afterward, you should try to prove that theorem without looking at the book at all. This part is hard, because sometimes somethings may seem so trivial that it seems silly to do it. However, there may be a lot of neglected technical difficulties and subtleties one wouldn't realize without running through the proof. This is how to truly learn a result. To gain more intuitions, try looking at different examples and counterexamples (when some conditions are neglected). As other people mentioned, there really is no way around this to really learn math.

 

[2ltben]

Do the homework and all of the unassigned problems you have the answers to. All of them, up to the point where it becomes busy work and you stop actually learning new concepts. Also, faculty has office hours for a reason. Use them. Lower division students usually don't unless it's right before a test.

Proof-based mathematics is a different beast entirely.