What should I study after Calculus 3?

[Genericcoder]

Hey guys,

So I am a physics and math major so far I am took Calculus I,II,III linear algebra and statistics
I did really good in them almost acing all of them and aced vector calculus.

I am taking complex analysis and introduction to probability in fall. I have holiday in the winter break for about 1 month and I want to self study some high level material, so what would you suggest studying ?

I am planning to go into theortical physics PHD besides I really like math and started to like it even more than physics,so I want to improve myself even more than university so I need some suggestions.

I don't know if this is the right section to post this but it seems like it.

 

[micromass]

Was your calculus course very rigorous? If not, you might want to go through Spivak's calculus.

There's really a lot you can do now: real analysis, abstract algebra, differential geometry, discrete mathematics, etc. Pick something you're really interested in.

 

[Genericcoder]

Yeh it was very rigorous course but I might also check Spivak . Our Professor for vector calculus said that calculus is a subset of real analysis so I think should I go into real analysis ? What do you think ?

 

[HallsofIvy]

For a physics major, Linear Algebra and Differential Equations would be reasonable next courses. But why ask us? Your college catalog surely has a list of required courses and probably some "recommended" courses for physics majors. And your best possible source are your major professors.

 

[micromass]

Yeh it was very rigorous course but I might also check Spivak . Our Professor for vector calculus said that calculus is a subset of real analysis so I think should I go into real analysis ? What do you think ?

Yes, doing real analysis is a great thing to do next. Spivak actually is an intro to real analysis, so do take a look at that book.

Are you comfortable with proofs?

 

[Genericcoder]

Yes I am comfortable with proofs @ micromass. @hallsYeh I am already taking DE and also I am asking here because I want to get ahead of university and do more self study.

 

[WannabeNewton]

Differential topology/geometry and tensor calculus.

 

[chiro]

If you are really keen, you might want to look on Spivaks Calculus on Manifolds book (not the same as the other Spivak titles that may be referenced).