What's math beyond calculus?

Question

As a high school student I have already completed the equivalent of Calculus 2, covering advanced material such as differential equations and L'hopital's rule, so I have seen a lot of math already. I am also going to take Calculus 3 in college. It seems that the hardest thing in math is integrating complicated integrals. I suppose what I really want to ask is, how much math is there left to learn beyond calculus? And are they on the same level of difficulty as Calculus 3 or harder?

Answer 1

Disclaimer- I am not familiar with the content of the courses mentioned, but the answer should stand by itself.

For the sake of clarity, I shall answer your question in two parts- 1. How much math is there beyond differential equations ?

Simply put, more than anyone can ever hope to learn in a lifetime. Even ignoring all other branches of Mathematics, there is way more to Calculus, then you can possibly be taught in the mentioned courses - partial differential equations, vector calculus, rigorous foundations using set theory and sequences, various definitions and types of integrability and so on. Of course all that is before you encounter other branches of math like linear algebra, linear programming, advanced statistics, Kolmogorov probability ... and of course, abstract algebra. There are several advanced topics in each of these fields, and you can find our more about them at mathstackexxhange here, mit ocw and a ton of other places. Mathematicians like Archimedes, Aryabhat,Newton ,Leibnitz,Euler ,Ramanujan, etc spent years studying and developing those.

Tip- Try googling 'Math'.( Also check out the wikipedia page) ( No offence, but you need to do that)

2. How hard is it? That depends on where you stop learning. Everything after that would be impossibly hard, everything before it will be child's play. On a more serious note, you will find trouble once you reach the rigorous theories and abstract algebra taught starting from college courses.

PS- Just don't give up :D.