Taking a graduate version of a course I took in undergrad

Question

I am currently a second year masters student that will be applying to PhD programs in CS Theory. I have finished all of my required coursework for graduation, but my tuition is essentially free and I enjoy taking classes so I am looking for one to take this semester. The few that I am very interested in are full (with no chance of additional spots opening) but there is another that I can take.

My problem is this: It is a introductory graduate level combinatorics course. My undergraduate degree was heavily focused on discrete mathematics so I took two combinatorics courses (one that had a similar syllabus to this one until about halfway through the class). I did ok in the class as an undergrad but not as well as I would have liked in terms of grades.

My question is this: How would taking this course look to PhD admissions committees? Would they think I was sandbagging not taking serious coursework or simply retaking a class to boost my GPA (I would like to note that this is not the reason I want to take it. I am interested in the sections of the course that I did not have in my undergraduate class, but the difference between the classes will probably not be known to PhD admission committees. That is, they will just see Combinatorics for both.).

My undergraduate GPA was quite low, but I have good research experience. In this sense, my main goal is to minimize the impact of my undergrad GPA on my admission chances by taking graduate coursework and doing well (so far, my graduate GPA has been very high).

Thanks in advance.

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Edited to clarify "sandbagging".

Answer 1

You said your exact problem is solved, but I want to answer in a more general way.

PhD admissions are not uniform or even consistent year-to-year. Additionally, the at some departments, the professors who are on the admissions committee change year-to-year. Thus there is no magic bullet for admission into a PhD program.

In my opinion, someone like yourself who has undergraduate research experience, will be in a situation where the admissions committee won't care about your exact courses on your transcript. Your GPA may or may not matter, depending on the whims of the admissions committee.

Most likely your success with applying is a completely subjective decision made by people: and like all people they are biased and irrational. I am not trying to be insulting. All I am saying is that you cannot expect a process which is subjective to work like a deterministic computer program: where the same inputs result in the same outputs; where if you change your initial conditions slightly, but taking a graduate course, your outcome will be affected by it.

I will also add that some PhD program/departments may have objective thresholds. For example a GRE minimum score, and no matter how strong the result of your application is, if you scored lower that the threshold, your application is thrown out.

Answer 2

For an undergrad, taking graduate level coursework is generally(*) not going to look like "sandbagging". The very fact that it is a graduate course strongly implies that it is "serious coursework", and not just "taking easy classes"

It's pretty common for a university to have graduate and undergraduate courses with similar titles, e.g. "combinatorics". That does not imply that the courses have significant overlap, or that it's inappropriate to take both. Normally I would expect the graduate-level course to be substantially more advanced. The undergraduate course might be focused on elementary results and techniques; proofs might be omitted or handwaved. The graduate course would likely be aimed at preparing students for research in this area; careful and rigorous proofs would be a primary focus. An undergraduate course in combinatorics might be a prerequisite, or the corresponding material might be covered rapidly in just a few days of the graduate course.

So I certainly don't think that the graduate course would look like you were "retaking" the undergrad course.

(*) This assumes that the graduate course is one that's intended for students preparing for research in this field. So exceptions to this rule might include:

• Courses that are part of a professional masters program, intended to prepare students for careers in industry, K-12 teaching, etc. In such courses the actual material might not be significantly more advanced than in an undergrad course, though there might be extra attention paid to applications, pedagogical methods, and so on. But you might not learn much new mathematics in such a course.

• Courses intended for students from other fields. For instance, there could be a graduate-level statistics course intended for psychology grad students, who need to learn statistical methods to conduct psychology research. But the actual mathematical material might not be any more advanced than an upper-level undergraduate course.