Tips for a freshman mathematics university student

[member 587159]

Next year, I will study mathematics at university. I think I'm well prepared, I already did some linear algebra (I got some books from my brother who studies physics and the mathematicians and physicists share some courses in the first year) and with effort it seems to work out. But, are there any tips you can give me for the following year? How I will have to study? What I should focus on? I know these are mainly personal things/opinions but I still think it's interesting for me to know.

Thanks a lot in advance :)

 

[FactChecker]

It sounds like you have already looked at calculus and linear algebra. I have 3 suggestions:
1) Probability and statistics has many applications and takes a while to get used to. You may not need it in your first year, but there is an Insight thread here where many people are suggesting that it should be taught as one of the first math subjects.
2) Complex analysis has many applications. The consequences of a function being "analytic" (having a derivative as a complex function) are very different from what you would expect with from real functions.
3) Abstract algebra may be the first introduction you get to rigorous mathematical proofs. The abstraction is something that takes some getting used to before you can appreciate it.