What are some tips for understanding and applying higher level math concepts?

[Deimantas]

Hello all,
I'm a guy who's bad at maths. I intended to study something easy - like law, history and the like. But I made a last second decision and chose to study something more useful - applied maths in my case. What I'd like to know, is what math subjects should I improve at (if I don't want to get kicked out)? I've spent last two months studying math individually 4-8 hours a day, now I'm rather good at the basics, I've even mastered basic trigonometry and logarithms. I understand the concepts of calculus well. But when I open one of those math books that universities issue, I go like "huh?". I can hardly understand a thing, it's all on a whole new level. I'd like to hear some tips on what should I improve in order to handle math at university level (any help is welcome).

 

[qspeechc]

Well, firstly, law and history are not easy subjects, lol And I suppose Law is a useful thing, but you could easily argue agianst that...

Anyway, are you going to enroll at some university or college? Because if you do they will guide you through what you need to know.

Well, the first thing is to make sure you understand your school mathematics, that is, algebra (logarithms are a part of algebra), trigonometry, geometry (co-ordinate and Euclidean), and pre-calculus. It is important you understand these things thoroughly before moving on to calculus. Don't worry if you are taking a long time, because it is really important you understand these topics well.

If you are studying on your own try to get books with answers or solutions at the back, or else ask here in the forums for help.

After that you can think about studying calculus, and maybe some physics (Halliday, Resnik & Walker; Young & Freedman; Sears & Zemansky; etc.). But, once you've covered pre-calculus you are ready to enter university.

Have you considered studying engineering? Also very useful, in some respects like applied maths, but maybe a bit less mathematical.

 

[chiro]

Hello all,
I'm a guy who's bad at maths. I intended to study something easy - like law, history and the like. But I made a last second decision and chose to study something more useful - applied maths in my case. What I'd like to know, is what math subjects should I improve at (if I don't want to get kicked out)? I've spent last two months studying math individually 4-8 hours a day, now I'm rather good at the basics, I've even mastered basic trigonometry and logarithms. I understand the concepts of calculus well. But when I open one of those math books that universities issue, I go like "huh?". I can hardly understand a thing, it's all on a whole new level. I'd like to hear some tips on what should I improve in order to handle math at university level (any help is welcome).

Hey Deimantas and welcome to the forums.

My suggestion for you is to understand the why behind the math you learn.

Typically what happens is that you build up a toolbox of mathematical tools like calculus and then what happens is that you solve a problem by using the results you have already developed along with constraints that are specific to a problem, and maybe a few more developments that you need to work out for that specific problem.

So with calculus, you should by the end realize how to construct a variety of measures like length, area, and volume as well as combinations of units like density, flows of various sorts, and other physical units. What you should be able to do, is to realize what the differentials are so that you can intuitively derive the expressions for your problem. You will need this kind of "intuition" when you work on new problems.

A lot of the prerequisites to working on applied problems require a lot of symbol manipulation where the exercise is basically transforming one problem into another one and eventually to something that you can work with. This is an important path of math, but in my opinion, it is more important to really understand the assumptions that including things like what a specific DE actually "means" or what the assumptions of a statistical distribution are actually implying about the nuts and bolts of a particular process.

It will make your life a lot easier if you do this especially for higher level courses. You won't really look at the symbols per se, but rather what they really represent.

So yeah to wrap up, find out the assumptions for every opening statement and what that means, and I think you'll be a lot better off: chances are if you know what's really going on and you forget a step in some transformation of a result, it will be a lot more trivial to understand the "trick" used to go from line 3 to line 4, in comparison to say trying to learn how to apply your knowledge to a new situation when you have no idea what you're really doing.