Don't like my calculus class, but want to be a math major....

[CaptainAmerica17]

I am currently a junior in high school and recently, my guidance counselor has been asking me a lot of questions about what I want to major in. Within the last 6-8 months, I have been leaning heavily towards a math major. That was until I started my calc class this year...

I'm in AP Calc BC right now and I'm bored to tears with my class. A majority of the problems are stuff like this:

"A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(3t). Find the acceleration of the particle when the velocity is first zero."

and I hate it.

I've caught myself straight-up falling asleep while trying to do my homework assignments. I self-study in my free time (currently Analysis and Abstract Algebra) and I really enjoy those subjects - as in I spend most of my free time writing proofs. I really want to be a math major, but I don't how much of the degree is taken up by classes like my calc one. It feels hypocritical to say I want to do math as a career but almost literally hate my math class. I guess I prefer theoretical stuff, but I don't know if that's something I would have to wait to get to a graduate level to really enjoy. Has anyone else experienced something like this? What is a math major really like?

 

[Mark44]

Have you considered something like the Running Start programs that exist in many states? Instead of taking a high school calculus class, you can take college-level classes in Calculus. These typically go much faster than high school classes, and you get college credit for them.

 

[FactChecker]

Please be more specific about what you hate in that example. Is it too easy or just not interesting? If it is trivial to you (I mean really easy to do it correctly, not just in theory.), then you can think about other math problems or help other students who are having trouble. The class time is really short. It should not make that much difference. If the homework time is a problem, maybe you can talk to your teacher and satisfy him that you can spend your time on harder material. But you better make sure that you really can do the standard class examples without errors.

 

[CaptainAmerica17]

@Mark44 It's an AP class, so if I pass the exam, I'll get college credit for calc 1 and 2 - if that's what you mean.

@FactChecker
The more I think about it, the more I'm pretty sure I just don't like calculation. I find it tedious and I stop paying attention after awhile. That's why I'm thinking it might be a bad idea to go for a degree.

 

[gmax137]

what answer did you get for your example problem? I'm curious to find out how rusty I am at this kind of thing.

We must be opposites; where you hate this sort of problem I find them to be irresistible little puzzles. As pointless as a crossword, I know, but I can't help myself.

 

[Infrared]

No, you definitely don't have to wait until graduate school to do theoretical math. Most of the coursework for a good math major should be proof-based (analysis, algebra, topology, number theory, etc.). Still though, being able to do calculations well is an important skill, and you won't be immune from having to calculate just because you're doing proofs-based math. Proofs can have calculations in them, and sometimes it's good to see how mathematical theorems can make a computation feasible.

(For what it's worth, in your example problem $s(0)$ is undefined, so your domain shouldn't include $0$)

 

[FactChecker]

@Mark44 It's an AP class, so if I pass the exam, I'll get college credit for calc 1 and 2 - if that's what you mean.

@FactChecker
The more I think about it, the more I'm pretty sure I just don't like calculation. I find it tedious and I stop paying attention after awhile. That's why I'm thinking it might be a bad idea to go for a degree.

I think there is an important question -- can you do the calculations? If not, then IMHO math is probably not for you.

 

[CaptainAmerica17]

I think there is an important question -- can you do the calculations? If not, then IMHO math is probably not for you.

Yes, I can do the calculations, and I them all incredibly repetitive and dull - which judging from these answers may be more a characteristic of my class, rather than of calculus itself. Over the summer, I may just restudy it by myself to get a better perspective. Thanks for answering, this was kind of a stupid question.

 

[CaptainAmerica17]

what answer did you get for your example problem? I'm curious to find out how rusty I am at this kind of thing.

We must be opposites; where you hate this sort of problem I find them to be irresistible little puzzles. As pointless as a crossword, I know, but I can't help myself.

I'll try to get back to you with the answer after I finish my homework.

 

[Mark44]

@Mark44 It's an AP class, so if I pass the exam, I'll get college credit for calc 1 and 2 - if that's what you mean.

You may get college credit for it, but the consensus here at this forum seems to be that the actual college classes are more rigorous.

 

[symbolipoint]

Some people are at risk of believing that course credit means not needing to re-study the course or, not needing to re-enroll in the course for a second time. Credit is one thing - but competence or proficiency is another thing.

 

[Crush1986]

No, you definitely don't have to wait until graduate school to do theoretical math. Most of the coursework for a good math major should be proof-based (analysis, algebra, topology, number theory, etc.). Still though, being able to do calculations well is an important skill, and you won't be immune from having to calculate just because you're doing proofs-based math. Proofs can have calculations in them, and sometimes it's good to see how mathematical theorems can make a computation feasible.

(For what it's worth, in your example problem $s(0)$ is undefined, so your domain shouldn't include $0$)

The limit does exist, doesn't it? t goes to 0 much faster than the log goes to infinity. I’d expect the limit to be 0.

 

[Infrared]

The limit does exist, doesn't it? t goes to 0 much faster than the log goes to infinity. I’d expect the limit to be 0.

Yes, the limit exists (and is zero). That does not mean that $0$ is in the domain.

 

[FactChecker]

Going for a degree in pure mathematics will be nothing like doing calculus homework. Judging from the subjects that you like, you should definitely continue. If you talk with your teacher, I wouldn't be surprised if he allowed you to self-study more advanced material and reduce the calculus homework. I would.

 

[jtbell]

There are two aspects to math.

The part that academic mathematicians (and apparently you) are interested in is the formal structure: logic, theorems and proofs. To put it another way, the "theoretical" part of math.

The part that most STEM students are interested in is how to use math to solve whatever problems they're dealing with in physics, engineering, etc.: the calculational techniques, with just enough understanding of the underlying structure that they can apply those techniques appropriately. To put it another way, the "applications" part of math.

High school math courses focus mostly on the applications. Even in college/university, many introductory courses in calculus and linear algebra, even differential equations, focus on applications; these are targeted for non-math majors. However, many universities also have introductory courses that focus more on proofs and theorems, targeted at math majors. Above the introductory level, courses for math majors are mostly proof-based: abstract algebra (groups, rings, etc.), number theory, etc.

So if it's the "proofy" stuff that you're interested in, rest assured you'll get plenty of it when you're in university.

 

[FactChecker]

Keep in mind that the examples of your class are ones that can be done easily by hand. There are much more challenging problems that occur in practice and take most of one's time. You may start to get interested in the numerical methods that are often used on harder problems.

 

[pasmith]

Yes, the limit exists (and is zero). That does not mean that $0$ is in the domain.

In a more rigorous course the implicit $s(0) = 0$ would be explicitly stated.

A bigger issue is that what are allegedly the velocity and acceleration of a particle are also not defined at 0 and and their limits don't exist.

 

[MarneMath]

If you can solve those problems, and interested in theory then Math major will probably be ok. Keep in mind that you should expect a few courses similar to plug and chug even if you study math, but as you progress the level of abstraction should increase.

As a side note, whenever I was bored in classes I would relate the topics to a skill I was learning. For example, in high school, I wrote a various functions in C++ to solve most of my calculus homework (or give me a close approximation). Doing this, I learned a lot of approximation methods, some of which still end up in my code today :).

 

[CaptainAmerica17]

Just wanted to say thank you for all of the answers everyone gave, it was all really helpful. It took me so long to respond because of school. After some long thought, I realized that I'm just not really a fan of physics - in the way it's presented in my class. I'm going to take the time to re-study calculus on my own this summer with a much more theoretical approach. We've started integrals and it's been fun again because we're not doing applications - I don't like applications.

 

[symbolipoint]

Just wanted to say thank you for all of the answers everyone gave, it was all really helpful. It took me so long to respond because of school. After some long thought, I realized that I'm just not really a fan of physics - in the way it's presented in my class. I'm going to take the time to re-study calculus on my own this summer with a much more theoretical approach. We've started integrals and it's been fun again because we're not doing applications - I don't like applications.

Restudying on your own will be good. You'll learn that stuff better. Don't neglect applications! Later, you will know what your Math (and Calculus) will be good for, and you may very well be solving real-world problems (applications) in the future.

 

[CaptainAmerica17]

what answer did you get for your example problem? I'm curious to find out how rusty I am at this kind of thing.

We must be opposites; where you hate this sort of problem I find them to be irresistible little puzzles. As pointless as a crossword, I know, but I can't help myself.

Here's what I got:

"A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(3t). Find the acceleration of the particle when the velocity is first zero."

velocity = s'(t)

s'(t) = ln(3t) + 1

ln(3t) + 1 = 0
t = 1/3e

acceleration = s''(t)

s''(t) = 1/t

s''(1/3e) = 1/(1/3e) = 3e <--- answer

 

[Mark44]

t = 1/3e

Use parentheses!
Here's what you wrote, in LaTeX: $t = \frac 1 3 e$. Obviously, what you meant was $t = \frac 1 {3e}$.
If you're not using LaTeX, your equation should be written as t = 1/(3e).

s''(1/3e)

Same comment as above.

BTW, this is "sort of" an application of derivatives, but not one that is very motivational. As you get further along in your studies, the applications are likely to be more realistic, and possibly more interesting.

 

[CaptainAmerica17]

Use parentheses!
Here's what you wrote, in LaTeX: $t = \frac 1 3 e$. Obviously, what you meant was $t = \frac 1 {3e}$.
If you're not using LaTeX, your equation should be written as t = 1/(3e).

Same comment as above.

BTW, this is "sort of" an application of derivatives, but not one that is very motivational. As you get further along in your studies, the applications are likely to be more realistic, and possibly more interesting.

Thanks for the heads-up, I forgot you could do latex in PF. Also, you're not the first person to say that the applications should get more interesting. I guess I'll just wait and see.