Would you rather have taken graduate analysis i/ii or honors...

[LeatherBoundBook]

I am leaning towards taking courses during the coming school year, my senior year, as follows (with other courses from my second major):

Fall: graduate real analysis i, modern algebra

Spring: graduate real analysis ii, applied linear algebra, upper level theory of statistics course

But instead of the modern algebra and applied linear algebra in the fall and spring, respectively, I could take honors abstract algebra i and ii as long as I substitute the graduate real analysis i and ii with any two of the following (two-course sequences count as two courses)

graduate probability theory (i and ii)

mathematical modeling

complex analysis

honors introduction to topology

introduction to ordinary differential equations (I took a combined differential equations/linear algebra course)

partial differential equations (i and ii)

I am unable to take the honors abstract algebra sequence concurrently with the graduate real analysis sequence due to a schedule conflict. The modern algebra course is primarily an introduction to groups, rings, and fields. The honors abstract algebra course would cover much of Artin, 2nd edition. My question is "which of the courses would you rather have taken," not "which do you think I should take," so that I can avoid answers that imply strong dependence on my future plans. I am unsure of whether I will be going into academia or industry; it is true that I am considering going into engineering research and development or into a masters or PhD program in math. I would love to someday have a very highly developed knowledge of probability and statistics (to the graduate level). My second major is in engineering.

I would also be interested in hearing responses to the sub question: do you think the honors abstract algebra two-course sequence would be noticeably superior than the course in modern algebra with regard to prep for the math GRE or for graduate school in math? I could follow up the modern algebra course with the one on complex analysis, thus killing two birds because they are both covered in the GRE.

Thoughts appreciated.

Edited July 27, 2016 by LeatherBoundBook

[LeatherBoundBook]

Still looking for replies! Any opinions?

[twilightgalaxy]

Since you're not getting much traction from any actual math majors, I guess I'll throw in my two cents ;P Between abstract algebra and real analysis I would've taken graduate real analysis hands down. I find in the types of math papers I have to read (optimization, engineering and statistics) familiarity with basic concepts in analysis (especially measure theory for anything probabilistic) helps while despite taking 2 semesters of abstract algebra I can't say that I've ever used it. 

I know you didn't want answers that depended on future plans, but I'm going to take a crack at it anyway. For grad school in Math, at least in Pure Math, my impression is that algebra and analysis are both super core topics, so I'm not sure how to swing on that. For probability/stats and I would guess engineering, real analysis is much much more useful. 

[cyberwulf]

You might get better feedback at http://mathematicsgre.com

For various reasons, this board has become quite stat/biostat focused.