Courses

There is a myth that the more graduate classes you take, the better your applications for grad school will appear. While it is valuable to have a taste of grad courses and advanced topics as an undergrad, we are very confident that your chances of getting into a good program is not in direct correlation with the number of graduate classes (or A pluses) on your transcript. In fact, a transcript filled with graduate classes may become a red flag for the professors on the admissions committee, as it may send a signal that the student is in a hurry and hasn't built a solid foundation.

Therefore, you should not feel pressured to rush yourself in terms of taking classes. This might sound cliche, but it is YOUR math journey after all, and you do have the freedom to choose the pace and the directions you are going. Some students may come in with more background and experiences in advanced math, but that doesn't mean that you are "behind".

So, how does one decide what courses to take? As a rule of thumb, it is crucial to expose yourself to a wide range of fields early on, both for your general math education and grad applications. Furthermore, mathematics is interconnected, and you might find your knowledge of complex analysis handy when you are doing research in algebraic topology. Once you have a general (and maybe still vague) idea of the overall landscape of math, you may want to pick a few directions that appeal to you and take more advanced undergrad classes or grad classes in those directions.

It is always a good idea to talk to others (your advisor, upperclassmen, previous instructors, grad students) when plotting your course load, both for suggestions and sanity checks. In general, people are very willing to share their experiences and journeys in math.