i am a freshman physics student and naturally my curriculum includes math-classes. The thing is, that -at least for the time being- teachers cover only the surface of topics so as to have only a practical knowledge of math. However i understand the philosophy behind that strategy, i find mathematics too beautiful to confront them as only a box of tools for my physics. More over i believe that the deeper in understand mathematics the better theoretical physicist i will become.
So, to be more explicit this semester i studied linear algebra. Since my book covered as i said only the basics i naturally researched the internet. However, the deeper i got the more unknown topics and definitions poped up like tensors, permutation group,metric spaces etc some of them i later got an idea of .
So what i would really like to ask is, if there is a right sequence of topics to start learning deep mathematics that will eventually help me with physics as well.
For example: I know that calculus is like the bible to a physicist...so i would like to study for example the principia at some point because i would like to know the very basics of calculus as well.
Another Example:I really liked linear algebra and i know that a physicists makes use of it a lot as well. Should i have studied something else before linear algebra to make more sense to me? for example group theory etc?
Hope i am making some sense. Thanks in advance.