Maximizing Math Success: Tips for Improving Study Habits and Skills

[stgermaine]

Hi. I just came back from the registrar and dropped the complex analysis course I was failing.

I don't think I slacked off. True, it's the summer and I had a few kickbacks with my friends that I wouldn't have had during the academic year, but I really wasn't doing much else besides complex analysis. It wasn't my first upper level course, as I've taken abstract algebra and linear algebra, where I got A- and B+, respectively.

I am concerned since I'll be taking more upper level math courses, and the unsatisfactory performance on complex analysis may translate to future classes.

How do you know if you really did your best but couldn't do it OR if you really could have worked even harder?

Another thing is working smarter. A frustrating thing about math is that the amount you learn isn't directly proportional to how much time you put into it. For example, I took intro psych course last semester and how much reading I got done was proportional to how much time I put into it. For math, if you don't understand something, then it doesn't matter if you spent one hour or the whole day. It's like there's an activation energy for each concept and unless you break that threshold, you might as well have put zero hours into it. So I guess I should really develop study habits and skills that allow me to math learn better.

Anyway, any feedback for a starting math major on study habits/skills would be great

Thank you

 

[Theorem.]

Learning math is not like learning psych. It is not, and should not be, rote memorisation. These courses teach you to be a creative thinker and to put concepts together. Accordingly, sometimes you will get frustrated, but you have to keep at it and use the resources available to you. If you really want to understand it you have to work past the point where you aren't sure if you slacked off or not- much past that point. Mathematics requires REAL thinking, which is one reason why it is so beautiful. You really get to learn things as opposed to just drilling them in your head.

That being said I don't think anyone here is in a position to tell you whether or not you are stupid. I do think you need to try harder- and perhaps you have to try in different ways. You can't treat these math classes the same as you would a psych course because they aren't the same. You have to go into them prepared to be engaged, creative, and active. You can do it. Hopefully you get some good tips on here.

 

[Choppy]

There's no easy answer for knowing whether you've reached your own intellectual limits. Although, I would encourage you to avoid the dicotomous paradigm of "if I can't do X, I must be stupid."

One thing to consider in your specific situation is that it's the summer. Maybe you just needed a break from studying and your less than satisfactory performance is your way of telling yourself you need some time off.

In more general terms I would say that learning how to assess your own performance abilities is part of your education. So now that you've had an unsatisfactory experience, you may want to avoid thinking about it for a while and then look back after you've had a few weeks and assess the experience from a more distant perspective. Do you feel like you really did your best? Or was it a case of not having enough gas in the tank? Are you really interested in this stuff to begin with?

With respect to study habits, one thing that I have found helps is that you have to get to a point where you're applying the concepts you've learned to problems of your own creation. Finishing the homework is one thing. But can you take it to the next level and apply it independently? I know it's hard to find time for this king of thing, but that is where, I think, the real learning starts. If this is really tedious, or you don't care to be doing it, then you might ask whether you're really all that passionate about this stuff on not.

 

[Mandelbroth]

Hi. I just came back from the registrar and dropped the complex analysis course I was failing.

I don't think I slacked off. True, it's the summer and I had a few kickbacks with my friends that I wouldn't have had during the academic year, but I really wasn't doing much else besides complex analysis. It wasn't my first upper level course, as I've taken abstract algebra and linear algebra, where I got A- and B+, respectively.

I am concerned since I'll be taking more upper level math courses, and the unsatisfactory performance on complex analysis may translate to future classes.

How do you know if you really did your best but couldn't do it OR if you really could have worked even harder?

Another thing is working smarter. A frustrating thing about math is that the amount you learn isn't directly proportional to how much time you put into it. For example, I took intro psych course last semester and how much reading I got done was proportional to how much time I put into it. For math, if you don't understand something, then it doesn't matter if you spent one hour or the whole day. It's like there's an activation energy for each concept and unless you break that threshold, you might as well have put zero hours into it. So I guess I should really develop study habits and skills that allow me to math learn better.

Anyway, any feedback for a starting math major on study habits/skills would be great

Thank you

Math is merciless. It really doesn't care if you do well or not. It is beautiful in that it requires you to think in the purest way imaginable. That is why it is, arguably, the best area of academics. It's also, just as arguably, the hardest.

I think the problem you're having isn't from not putting in enough effort. You refer to doing mathematics as "working." In my opinion, you won't get very far with this. You should think of it as something fun. Often, I will refer to what I do outside of my normal studies as "playing" math when people ask, because that's kind of what it is: it's my way of having fun.

I would say that this situation only says that you've found a part of math that is difficult for you. That's good! More fun for you! If you still have the textbook for the class, read through it by yourself and do problems in your free time. If you get stuck, come back to PF. I know I'd be happy to answer your questions (as would many of the other people here) because it's fun for me. Don't let yourself get discouraged because something in math is difficult. You are not "stupid" just because you did poorly in complex analysis.