Hahaha, your experience is just the opposite of mine. Nevertheless, yes, mathematics is very beautiful. In fact, I too would argue it is probably the most beautiful subject to pursue in college (note: there is heavy bias in this response).
Having said that, I would like to warn Calculus I, II, III, ODE does not give the “correct” picture of what mathematics actually is. In fact, unless you are going for economics, differential equations, or engineering, I would like to argue that those math courses give a very… uhmm… wrong (?) view of what higher math at college looks like. In fact, I would argue even Applied Math seems a bit more theoretical than your standard Calculus series.
Before you chose the route of mathematics, I really advise you to speak to your advisor. Yes, advisors rarely help out and seem pointless but it never hurts. You never know whether changing to be a math major means staying an additional semester or what not.
That said, do note by pursuing as a math major this late especially with your sequence, do not expect to land in some top math graduate school after graduation. It is actually pretty atypical for top math undergraduates to start from Calculus I.
Having said that, if the professor life is not for you, then no needs to worry! Mathematics is a fascinating degree with lots of fun and challenge on the way. However, I feel that many people do not know what higher math is before dedicating themselves to the degree.
in fact, unlike what many science and engineering majors think, math majors rarely touch numbers (even if you are in the applied side) and do not touch integrals as much either (unless you are in applied in which you will see lots of differentials and integrals).
After the typical Calculus sequence comes Ordinary Differential Equation, Linear Algebra, Analysis, Modern Algebra, Topology, Differential Equations, etc. etc. (not true for applied math majors but then again, I am not as informed in the applied as before switching to computer science, I pursued only pure math quite heavily).
I think you should be warned math changes A LOT once you hit Real Analysis or Modern Abstract Algebra. In fact, it is actually what turned me off from a math degree.
If you have the chance, just “scan” through Rudin’s Real Analysis in your local college library or the Internet. Even just flipping through the pages quick should inform you what higher math looks more than the current Calculus sequence you are in.
In fact, if you have the time (since it is the summer), go lookout and try Tom Apostol’s Calculus book. That should give you a more correct view of what higher math looks like.
If it’s too theoretical for you, you should perhaps go the more applied math route.
If it is too hard for you, well… don’t worry. Analysis is known to be the hardest undergraduate math course and Apostol’s Calculus is Analysis lite. Of course, there are those who claim modern algebra is harder but I honestly before switching to Computer Science found Modern Algebra much more do-able and intuitive. Analysis was where I was … -_- …
If you enjoy it, well, good luck. Maybe Analysis branch is right for you!
If you still love math but not “that field”, then maybe Algebra or Cryptology or Number Theory or Topology or what not is for you. Who knows. I found out that I’m an Algebra guy. Algebra for the win! Too bad Analysis and Topology are more or less requirements. They make me throw up…
All that said, ya, that’s all I can say. Before majoring in mathematics, please know difficulty of a math major before taking it. Calculus, Linear Algebra, ODE I feel gives a very bad picture of the difficulty of college math. If I knew all that before, maybe I would have not tried to do physics and computer science together in the beginning of my college years and devoted all to just mathematics. That said, I’m quite confident had I never tried to do too much things together, I too would have pursued as a mathematics major.
So, try it out! The subject is fascinating
Just don’t be surprised if you realize you will be studying and reading quite a lot. In fact, I would claim it is probably the most time intensive major in undergrad if you are motivated. BUT the time spent is totally worth it. You learn so much and it’s just… i don’t know, fantastic beyond imagination.
In higher math, you will feel like you are in the edge of (in)sanity. What I mean by that is that many times, you will stare at the same 1 sentence for hours or days or weeks to ponder what that 1 sentence in the theorem is saying. It sounds truly like someone who is in paranoia but trust me on this, it’s worth it and is some of the best experiences I had in college … to sit down in a desk or outside and stare at the same sentence all day to figure out the definition.
Plus, here’s some cool math video to motivate you to be a math major. If it wasn’t for my intense curiosity for computer science (as I realized I can self-study the rest of math concepts with my current mathematical maturity), I would definitely have given the major a thought.
https://www.youtube.com/watch?v=knFlmhgJfRY
Ahh, do note though, with a mathematics undergrad degree, your prospect is quite limited if you are stubborn in using your mathematics skills right out of college.
Though this is for physics, it is quite relate-able with a math degree as well…
https://www.youtube.com/watch?v=Bu3pYKKqRS8
Yes, you don’t go to college to get a job. In fact, I also believe in that. However, if you are devoting that many hours as you would with a mathematics degree, it would help to know what your prospects are… right? Research before doing anything. That said, do note that mathematicians are usually ranked as some of the happiest people in the world. And actuaries too apparently. So ya, math majors apparently have extremely good life in terms of happiness.
If mathematics is calling you, then mathematics you do. Ya, that’s my 1 chip.