Not sure if I am up to a Maths degree

[rockstarlive]

Hi guys, I realize most of you are super smart, so don't laugh but I'm really struggling with Calc II and I'm thinking of giving up Maths. Is grasping the concepts and intuitively applying them a natural thing? How long did it take you to ace Maths in college?

 

[Bipolarity]

Do you mean proving theorems or just solving random problems and plugging in formulas?

BiP

 

[rockstarlive]

Like integrating, not too much proof so far..

 

[Bipolarity]

Like integrating, not too much proof so far..

Some integrals are very tricky, in fact my math professor once claimed that integration was more of an art and whether "you saw it" rather than instantly knowing how to solve the problem (as was the case in differentiation). Difficult integrals usually involve trying out different methods, and sometimes combining different methods. It gets better only with practice. It has little to do with talent or intelligence, just mainly practice. Practice helps in the sense that you know which methods not to try because you have seen them fail you in such situations before. That saves you a lot of time for tests.

Proofs are a different story. They require more than practice; a natural ability to visualize abstract concepts in a convenient and fast way is very essential, especially if your professor makes the tests very time constrained (like mine did).

BiP

 

[chiro]

Hey rockstarlive.

Math is something that can be learned with time and practice, and the right kind of teachers can make quite a bit of difference to not only how well you learn but also how not annoyed you get that can contribute to you leaving mathematics and math-related pursuits altogether.

It is a fallacy to say that all people are as good at each other: some do have advantages over others but that doesn't mean they are better.

If you want to become better yourself (and this is at anything, not just mathematics) then surround yourself with the right kinds of people.

Universities make this a lot easier since these kinds of people congregate in one place (like all social groups and interests do regardless of the interest itself), but nowadays with the internet, you can become part of communities that are free and have a much larger diversity than you ever could have had even twenty or more years ago.

So if you want to do something, surround yourself with people that can teach you and remember that you to as a student will also be a participant in this whole process.

If you want to do mathematics, then just keep doing it and do what any other person does that wants to become good at something: practice it, communicate it, participate in it, share it, and make it your craft slowly but surely.

Also one other thing that will help you is that if you become the teacher, you will learn quite a bit because you will be adding context to your existing knowledge base so helping out people in the situation you were in will also help make things "click" long after you slowly but surely forgot about them.

 

[MathWarrior]

I'm really struggling with Calc II. How long did it take you to ace Maths in college?

To be honest, I am willing to bet most people who are in upper division mathematics courses would have trouble with extremely complex integrals. Some of the are just exceedingly difficult to solve. Most people in the real world typically plug such equations into MATLAB.

I didn't feel comfortable with integrating until I took differential equations.

IMO, the main purposes of mathematics is largely understanding the mathematics, and the theory behind it is so that you understand what is going on and how to apply it in different ways.

Calculus 2 is hard for many people, doing integrals can become tedious and sometimes seem impossible without more insight. Do your best to chug through the class. I wouldn't be to worried about getting straight "A's" on everything. Aim high, do your best.

If your trying for a math major you will have some classes much harder then Calculus 2 that you just have to pretty much just do. If you get a bad grade at first who cares, attitude and persistence, beats out any mathematical aptitude in the long run.

 

[homeomorphic]

Proofs are a different story. They require more than practice; a natural ability to visualize abstract concepts in a convenient and fast way is very essential, especially if your professor makes the tests very time constrained (like mine did).

It's not necessarily an innate ability. People get used to doing proofs, too, and get better at visualization with practice. Being fast on a test just takes some rehearsal, for the most part, unless you are asked to be really original in a short time. Anything that can be prepared beforehand, though, can be made automatic by practice. If you can do it slow, you can do it fast. Just practice it until it goes from being slow to fast. I don't know, maybe it takes innate talent, but it also takes practice and isn't just something that you are born with, either.

To be honest, I am willing to bet most people who are in upper division mathematics courses would have trouble with extremely complex integrals. Some of the are just exceedingly difficult to solve. Most people in the real world typically plug such equations into MATLAB.

Well, that's true to some extent. I heard they gave a Fields Medalist some kind of trigonometric integral and it took him 3 hours to solve it. However, with practice, 99% of the integrals you find in a typical book like Stewart are pretty much trivial. There are a few exceptions. I got stuck on one while I was teaching, yesterday, but it's pretty rare for that to happen. One of the students knew how to do it, probably because he had spent some time on it. I could have done it, but in class, you don't have time to get stuck and think about it for too long. I would call very few integrals in a typical calculus class "difficult", maybe typically one or two in the whole class, though it is possible to come up with plenty that are more tricky, if you wanted more difficulty than is typical. It's not that easy when you first start learning calculus, though.