ah25

Yes, it looks like a "real" complex analysis course, not engineering-focused! Real Analysis I is its pre-req. My first course was proof-based, actually! Barely any calculations at all.

Yeah, I will be aiming for the top programs--don't know which specifically yet. However, I don't think I will go for any school that would require the Math GRE--even with Abstract Algebra under my belt, I don't think I would do too hot--very tough to do well against the competition on this test!

Thanks for the additional suggestions on just taking/re-taking Real Analysis I! The grade I got before on this course was a B+, by the way. I realize to some it may seem like I'm making a mountain out of a molehill, but I really feel like I have very little margin for error, especially on this particular course.

Yes, Real Analysis II would be optimal over the summer, but that unfortunately is not available/offered.

Thanks, but Measure Theory isn't available! There is a calc-based probability course, but I already have that.

Thanks for your suggestion on Abstract Algebra. What caught my eye about Complex Analysis is that Berkeley and Chicago mentioned it by name, and as a successor of Real Analysis I course-sequence-wise, could perhaps help attest to my abilities there.

Since my first go at Real Analysis I yielded pedestrian results, my main goal for a summer course would be to just demonstrate to adcoms that I can handle advanced math, particularly proof-based. I presume Complex Analysis would be reasonably rigorous as an upper division course, especially since Complex Analysis's prerequisite is Real Analysis.

Thanks for bringing that up! Yes, that was my assessment, as well--that's what I was trying to get at by "sounds application-focused, involving calculations and approximations." The two "analyses" have essentially nothing in common, from what I understand. My Real Analysis I course covered the first four chapters or so of Rudin's Principles of Mathematical Analysis: Real and Complex Number Systems, Basic Topology, Sequences and Series, Continuity. The Complex Analysis textbook will be Brown and Churchill or Gamelin, from what I have seen from past syllabi--covering topics such as functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, the residue theorem, singularities, and more.

I got a lackluster (but not atrocious) grade in Real Analysis I, at an un-prestigious/low-ranked school. This could be a problem for my graduate school aspirations, since it is the most advanced math course I have so far. It could look like I am hitting my "math ceiling" to adcoms, and it is arguably the most important course for Statistics PhD admissions. Otherwise, my record is decent, with a GPA of about 3.8 between my mathematics and statistics courses, including the Calc Sequence, Linear Algebra, Math. Stats, and Probability. I have already graduated. I can use the summer to do post-bacc work at a well-regarded university that is highly ranked in statistics. I know, ideally, it would be to take Real Analysis II and do well. However, it does not appear to be offered during the summer (usually a spring course), and I would like to be ready to apply by the fall. Here are some of my options for the summer at this university: Real Analysis I - nominally the same course as I had before, but sounds more rigorous and expansive than my previous course Upper Division Linear Algebra - ditto; nominally the same course as I had before, but sounds more rigorous and expansive Abstract Algebra I - has lower division LA as a prereq Numerical Analysis - has lower division LA and Calc III as pre-reqs. Sounds application-focused, involving calculations and approximations. However, it's listed on Harvard Biostatistics and Berkeley Statistics sites as "encouraged to have" and potentially "useful" to have, respectively Complex Analysis - has Real Analysis I as a pre-requisite. Possibly could show that I can do well in something "beyond" Real Analysis? Mentioned by Berkeley Statistics as potentially "useful", and also by UChicago Statistics Any thoughts? I feel a bit torn... if I had to choose, I would pick Complex Analysis right now. Also, would I be shooting myself in the foot by doing any of the above 5 instead of just waiting a year and taking Real Analysis II?