Need Help with Undergraduate Math Courses for Statistics PhD Programs

[COMonteCristo]

So I'm in my senior year of a physics major at my university and am looking to apply to some statistics PhD programs this fall. I was wondering how important it is to take a Real Analysis course before/during the semester I'm applying. I signed up for a course in Real Analysis at my university, but was advised to take a course in proofs first which would push back my Real Analysis course to my second semester (after applications are due). The other course I'm taking this semester to prepare for applications is a Mathematical Statistics course. Would it be better to take something like Advanced Linear Algebra in place of the Math Stats to have another math-heavy course on my transcript for applications? At this point should I even be looking to apply to PhD programs anymore? Thanks for any help!

[bayessays]

Depends on a lot of things. First off, I'd say math stats in general will help you slightly more than more linear for admissions, though both are good courses.  The importance of real analysis is going to depend a lot on the type of program you're applying to.  If you don't have any proof based math courses, you're probably not going to a top 10 PhD program. But it gets less important the further down in the rankings you go. Also, it depends a lot on your profile.  If you are a physics major at Harvard who has As in a bunch of thermo/quantum classes, nobody is going to be worried about you handling the math.

If you don't feel confident in your ability to succeed in real analysis before the proof course, you can always take the proofs course, submit your applications and try again next year if you're not happy with your results.  Rushing into classes you're not comfortable with and doing poorly could have more lasting negative effects.