Does having qualifying exam subjects on my transcript help? (Math)

Question

For context, I am a international (undergrad) student in mathematics willing to apply to a pure math PhD program in the U.S. this year. Recently I've been interested in commutative algebra and algebraic geometry, and I'm planning to take graduate courses in algebra/commutative algebra and intersection theory this upcoming semester. On top of this, I was initially planning to take a course on smooth manifolds, but recently I felt that first of all I might not have enough time to prepare for all the midterms/final exams, and more importantly I have learned the subject material by myself and I do not want to spend more time going through exercises again to prepare for the exam. Instead, I want to focus on practicing commutative algebra/homological algebra.

The reason I'm hesitating is that a graduate student friend of mine currently in a U.S. institute told me that having qual courses on my transcript (in this case smooth manifolds) would really help in the whole application process. When it comes to PhD applications I know that there are no definite answers, but I want to know if this is true from a committee point of view, heuristically speaking. Any information would really help.

Answer 1

Doing well in any advanced courses, whether intended as preparation for qualifying exams or not, is a plus. But you need to do well in them, not just have them on your transcript.

Note, also, that in the US, admissions is broad based, not just GPA based. In particular, good letters of recommendation are important. The writers who are best are probably those you have worked more closely with than just having taken some advanced course with. "Mr. Lee did well in my manifolds course." isn't enough.

If you are as advanced as this question suggests, consider doing a research project with some professor. Their letter would hold more weight if you do well, even if it doesn't result in publication.

Also note that qualifiers will differ somewhat between institutions and among subfields, though probably less in math than in some other fields.