A warning: Math 525 may turn out to be not much different than 425, depending on who you're taking with. Nowadays, I believe that most sections have no touch on Measure-theory related stuff. If you want that, go for Econometrics. The end should be either Markov Process (Intro to 526) or Monte-Carlo Methods.

That said, the biggest difference is only for the "rigorous" introduction to concepts for convergence (a.s, in Probability and etc), which should be taught in STATS 426 but at lease mine did not do that. Most schools will do convergence stuff in the second Mathematical Stats class (i.e our STATS 426 version).

Thus, once again, I highly recommend Math 526 over 525, based on who are teaching the class. You would be able to suceed in 526 without 525.

Some other info: In the past, Math 490 was easier than 525, but it seems to change recently because of instructors.

Good luck on your choices!

Quote Originally Posted by shinnyu View Post
Cauchycomplete, thank you so much! Nice to see a Michigan peer here.

1. Yup, now I am certain that retaking RA isn't a good strategy at all.

2. Actually, I am on the waitlist for MATH 525 (also 526). I was a bit worried that since I've taken 425, 525 won't add too much value. But it does seem like those two are quite different, especially that 525 touches upon measure theory at the end. Also taking tutonic's advice into consideration, taking 525 next semester sounds like a great idea. As for 490 and 663, well, tbh I am a bit worried that it will take me a lot of time and effort to excel in those classes. Since next semester I will be working on my applications, I'm trying to keep the course workload manageable...

3. Thanks for bringing up the phd econometrics class! I did not know about that somehow... I checked the syllabus and it certainly looks very useful and relevant.