Improve Your Math Study Techniques

[Noxide]

I need some tips on how to improve my study techniques.

Normally, I:

work through all the examples in a section and make my own notes
do the questions in the section and refine my notes again
write out a final copy of my notes and memorize them

Although this works well, it's just not efficient.

I need some tips to improve the efficiency of this studying system.

 

[n!kofeyn]

Please see the posts https://www.physicsforums.com/showthread.php?t=351178".

Do you mean inefficient in that it takes up too much time? You may be spending too much time memorizing and getting everything out of the section and not spending enough time applying that knowledge by working enough problems. Working as many problems as possible is what allows you to detect your weaknesses.

Also, maybe spend less time completely rewriting your notes. Does this really improve your retention or ability to apply the material?

If you find yourself having to write up complete notes, then maybe learn LaTeX if you are planning to do pure math. It's good to learn this eventually. Plus, once you get decently proficient at it, it will allow you to quickly edit your notes rather than completely rewriting them. I would only recommend this if you are doing upper level math and not the more computation based courses.

 

[Noxide]

Thanks. I read your posts and found them very helpful.

I often find that I overwhelm myself in trying to focus on 1 section and it's contents until I have completely mastered it, meanwhile neglecting most of the other sections.
How do you get out of setting unrealistic goals like trying to do every single question in a section?

I'm going to try "mixing it up" in the section before I've memorized the concepts of the section. I think I may indeed be spending too much time memorizing rather than trying.

 

[n!kofeyn]

The thing you want to achieve is balance plus repetition. It isn't reasonable to understand one section absolutely and then move on to the next. In fact, it's rare that will happen anyway. Do one section until you feel you've covered it sufficiently and then move on. Once you've finished the sections you've set out to review, then rinse and repeat. Don't set there spinning your tires on just a single idea or concept.

 

[Noxide]

Will do!

heh, one more question...

How do you overcome arrogance? ie after learning a subject or a class really well, i feel as though every other class should come just as easily but without the toil. Do you have any tips on... deflating one's own academic ego?

 

[n!kofeyn]

Well for one, I just refuse the idea of arrogance, and don't entertain it at all. I also try to avoid certain mathematical lingo and fancy-talk to avoid the higher than thou attitude. Also, mathematics has a way of naturally checking one's arrogance and brings humility to even the strongest of minds. I don't know what level of courses you are taking, but as you move up the abstraction ladder of mathematics, things become much more difficult. Math students are put through the calculus, linear algebra, and differential equations sequence, but then things change direction completely and they are faced with analysis and abstract algebra. This change of pace basically says that you know nothing and now we'll build up everything from scratch. This is humbling in itself.