Number Theory vs Differential Equations

Pre-College Issues High School Life
1

I’m currently taking Calculus III (basically Multivariable) through a dual enrollment distance learning program with a college. Next year (I’ll be a senior), I’ll be able to take a) Differential Equations (at my school), b) Number Theory (at my school), or c) Number Theory (through the college).

I’m really, really interested in math. Besides being my favorite subject, I kinda find pleasure in doing it. But due to scheduling, I won’t be able to do both Diff EQ and Number Theory.

Diff EQ: It’s really versatile, especially with engineering, which is what I want to study in college. I really enjoyed my calculus courses, so I figured I’d enjoy this too. The applications seem amazing xD.

Number Theory (at my school): I’m in math team, and I never realized I loved numbers so much. Studying number theory would be a great addition to all of the umm applied-ish classes that I’ve done. The courses that I’ve done so far with math seems kinda mechanical, and I think the cool abstract part of number theory could shake things up (if that makes sense). Plus this course gives me a good intro into proof-making, which is something that I have not studied.

Number Theory (through the college): This is much more proof-based. It assumes that I have a background on doing proofs, which I really don’t. I can learn, of course, during the summer, but I’m not sure how prepared it would be. I think that doing this course would give more content than the one at my school. Also, this course would require that I learn how to use math programs like Sage and LaTeX. The other course requires this too, but this would be taught as part of the course. Also, I’m worried about college apps / other hard classes that I’ll be taking. However, I think that using this credit towards college would be easier though, which seems nice.

I’m at an impasse xD. Can anyone offer any advice? Thank you!

2

ODEs are really fun. I can’t opine on number theory.

3

@bandicoot12 Number theory is a pretty fun subject since it has some pretty neat applications. Knowing how to properly write a proof is very useful when studying mathematics, so taking number theory might not be a bad idea.

I don’t know anything about Sage, but I’m quite familiar with the LaTeX typesetting language, and it’s not hard to get the basics down if you’ve done any amount of coding before. I type nearly all my papers and homework in LaTeX nowadays.

Differential equations is also a fun subject, but for me at least, I didn’t get the same amount of “enjoyment” (most of the problems involved simply applying a set of rules or methods) as I did when I took number theory or combinatorics.

4

I’d take number theory at your high school.

5

If you don’t already have plans for this summer, you might be interested in applying to the [Ross Mathematics Program](http://u.osu.edu/rossmath/) at Ohio State, or [url=<a href=“http://www.promys.org/%5DPROMYS%5B/url”>http://www.promys.org/]PROMYS[/url] at Boston University. These are summer programs that focus on number theory.

You probably don’t need to know Sage or LaTeX for the college number theory class, unless the description specifically says otherwise. I took around ten proof-based classes before I ever learned LaTeX. The class might use Sage, but I don’t think they’ll expect you to know it at the beginning. If you want, you can email the professor and ask whether they think your background is sufficient.

With a class like number theory, though, you would probably have a better experience in a classroom than online.