Real Analysis or Complex Analysis

[tropian1]

I'm about to start scheduling my courses for next year, and I have the option of taking either Real Analysis or Complex Analysis. I'm double majoring in Math and Physics, and I want to go to grad school to study either Applied Mathematics or Physics. I haven't taken any higher level math courses yet, (excluding calculus), so my knowledge of both these courses is pretty limited. Which one will benefit me more going into grad school?

 

[Xiuh]

Can't you take both courses?
I think Real and Complex analysis are both pretty much essential to any math degree.

 

[tropian1]

I'm actually required to take a semester of a course called "Intro to Analysis" and then I have the option of either Real Analysis or Complex for another semester. I could definitely take both, however I'm already taking a ton of courses as it is. The course description for Real Analysis says it's a continuation of Intro to Analysis, whereas Complex Analysis just has Intro to Analysis as a prerequisite.

 

[Hercuflea]

This is kind of a tough decision. On the one hand, complex analysis will be much more applicable to the career track you are looking for. On the other hand, Real Analysis will definitely be a solid preparation for complex analysis. Real isn't required for complex, but a lot of the same ideas apply, for example uniform convergence of a series. If you can, take both but take Real first. If for some reason your university only offers complex once every few years or something, you should probably go ahead and take it.

 

[tropian1]

Assuming I take Real Analysis, would it be out of the question to try taking grad level complex analysis later on?

 

[Xiuh]

Assuming I take Real Analysis, would it be out of the question to try taking grad level complex analysis later on?

It's perfectly doable, but it certainly won't be very easy.

 

[Robert1986]

Assuming I take Real Analysis, would it be out of the question to try taking grad level complex analysis later on?

Not knowing anything about you personally, I would assume this would be very difficult. I would imagine most grad complex analysis classed already assume you know a lot of stuff (like what is an analytic function, Cauchy's theorems, maximum modulus stuff, etc) and these topics are quickly introduced and these theorems quickly explained (to get to more advanced stuff).

 

[tropian1]

Right, it just sounds like trying the other way around would be a terrible idea. I'll try fitting both in, that seems to be my best bet. Anyways, thanks for the advice.