Right now I’m a Junior in high school who (in my opinion) isn’t half bad at math. I compete in math competitions and like the subject as well. Naturally, I’ve been drawn to getting a Major in pure math. But, I’m not certain, and I have interests in other areas I might want to pursue (physics or game design.) So what I’d like to know is what is getting a math major actually like?
I’ve always looked at “pop math” which seems to suggest that college level math is mostly composed of proofs, abstract algebra, and analysis. And from what I’ve seen of these topics, they seem super interesting. But I’m worried I’ll get to college and I’ll be faced with more math like what we learn in high school (shoving formulas down our throats with no appreciation for the beauty and logic behind them.) I hate this style of teaching math and I don’t think I’d have the motivation to pursue math for four more years if it’s more like the incessant boredom of my current calculus class.
What classes would a typical pure math major cover? What can I expect to be doing in this classes? (I.e. creative proofs, repetitive exercises, or somewhere in between.) And to what extent would I have to do stuff I’ve already learned (I’m sure this last bit probably depends on the college, but in general would colleges make me re-take calculus or multi variable calculus?
