Not sure what career path fits me best

[zonova]

Hello everyone, I'm facing a bit of confusion. I am currently in high school, taking a college level Calculus class and a college level Algrebra-Based Physics class. I am not sure whether it's because of the class, or if it's because of the math itself, but i seem to enjoy Calculus much more than my Applied Physics calculations.

Originally, i had been either wanting to go into Theoretical Physics or Mechanical/Electrical Engineering. I seem to like pure mathematics much more than applied mathematics, but at the same time i don't have enough experience in either to decide. Could any of you give me a description of what i would be looking at in both of these careers? Thank!

 

[Greg Bernhardt]

Pick ups some more mathematics books and see what interests you. Maybe you decide to go for pure mathematics?

 

[MarneMath]

I would be careful here. An introduction to Calculus usually does very little with what you actually end up studying in mathematics. To make this more clear, if you spend more time solving problems than proving problems, you haven't got to the crux of mathematics.

My advice is to read a more 'advance' type calculus book like Spivak, or Apostol and if that kind of thinking makes you excited and you actually enjoy trying to figure out the why in math instead just using techinques, then there is a good chance you'll love upper level mathematics.

If it helps though, I hated algebra based physics, heck, I hated calculus based physics, but I really enjoyed thermo. I personally ended up doing statistics because it was, for me, the right balance between theortical work and application. I just couldn't solve a problem for the sake of a problem being solved. No matter how interesting.

 

[zonova]

Thank you for the response, that makes sense. So, i'll find some books from spivak to get an idea of upper level mathematics. I'm guessing that's more pure math? Where/who would i look towards if i wanted to get an idea of what i'd be doing if i didn't get into pure math? Would the otherside of the spectrum simply be engineering/applied math? I'd like to get a taste of that too, i think that would help me ind deciding between the two.

Thanks

 

[MarneMath]

Pure math enough for someone learning calculus. Another book by an author who believed strongly in theortical knowledge and physical science is the great book on calculus by courant. If you want a calculus book that simply gives you some theory, but focuses on techniques, then basically any book out there will serve that purpose. I suggest the free one by Gilbert Strang on MIT website.

Also, let's not assume that applied math is mathematics that functions completely in the real world. I would say applied math is really focused on methods used in science/engineering, but the mathematical framework behind those methods can be quite 'pure', so I don't think there is a big as a disconnect as the name would allow some to believe. Think of as, 'applied math' is making the methods, and 'application' of mathematics as using the method.

You probably have encounted some making the method aspect, ie in Newton's method. While you may not be sure how Newton's method in optimization may tell us anything in the real world, but believe it or not, I used it my work with radars in the military :).

Then if you find that you enjoy designing things a bit more and using physics and math as tools to get projects completed, then you'll probably enjoy engineering. Does the idea of designing planes, circuits, machines, engines, etc get your motor going? If so, consider engineering.

However, if you like using math and learning more math, but get more interested in learning fundamental ways the world work, or then consider physics. I can't say more about that, since well, I did very little physics and it bore me.

:) I also encourage you to check out statistics. I can give you a link to my blog that can show you a couple of neat problems in probability that you may enjoy.

But remember, even though you start college soon, the good things is, you got plently of time to choose and even once you start, there is sill room to change things around.

 

[zonova]

Well, i guess there are two things that really get me going... academically speaking, anyways. I really love the feeling of looking at something extremely complex, like some proofs, equations or physics theories, and then completely understanding them. Like, being able to analyze things so complex seems really amazing to me. The second thing that i really enjoy would be more engineering related. I think I'm interested in mechanical, because i often find myself designing engines and gun parts and such. However, i also design a lot of robot-type things in my spare time, i don't know if that counts as mechanical engineering though.

Some college students i know describe applied math, like engineering, as a bit of a dumbed down version of pure math. But, i don't think this would happen with theoretical physics. So, i was thinking that i could... perhaps do a double major in math and engineering? And then go for a doctorate in physics, or something similar. This is another huge problem I'm having. There's so much i want to do, and i have no idea how to schedule it or fit it all in.I've actually done a college course on Stats, it was great. It didn't introduce Calculus concepts, however it went over a lot of other things such as regression models, normal curves, etc. I'm not sure if i'll further pursue statistics, though that's definitely a class that i'd be interested in trying in college. If you happen to have any more involved Stats problems, i'd love to look at them :)