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Before the PhD · Build your foundation
Taking graduate and PhD courses early
Few things on an application signal readiness as clearly as doing well in a course above your level.
Taking a course above your level sends one of the strongest signals an application can carry: an undergraduate in a graduate course, or a master’s student in a PhD course. It shows serious commitment and real ability, and it answers the question every committee is asking, “can this student handle our first year?”, with direct evidence instead of a guess.
What it takes
You will need the right prerequisites and the instructor’s approval. Do not treat this as a formality. Talk to the instructor before the semester starts, explain what you have already taken and why you want the course, and ask honestly whether they think you are ready. Instructors are usually generous with students who approach them this way.
An example
Suppose you have completed real analysis, mathematical statistics and undergraduate or master’s econometrics. The natural next step is to ask whether you can take the first-year PhD econometrics course. If the instructor agrees and you do well, it is exceptionally strong evidence on your application, for PhD admissions and for predoc positions alike. It also gives you a professor who has watched you do PhD-level work, which is exactly the kind of person who writes a strong letter.
The same logic applies to graduate courses in real analysis, probability or statistical theory in the mathematics or statistics department.
Be honest about readiness
The signal works because the course is hard. A weak grade in a graduate course can hurt more than not taking it at all. Take one only when your preparation is solid and your semester has room for it. Graduate students often work in study groups, and you may need to make an effort to join one or to work with the teaching assistant. Plan for the course to take substantially more time than an undergraduate one.