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[Q] Should I take additional classes in mathematical analysis or in numerical analysis?

For my final year of undergrad, I’m debating between taking either a second sequence on mathematical analysis vs a graduate sequence in numerical analysis. Any suggestions on which I should choose?

I have already completed a two-course sequence on real analysis . Hence, I have a strong understanding of real analysis but not at the level of Rudin, which I hear is extremely helpful for graduate coursework in statistics.

On the other hand, I have also taken an undergrad course in numerical analysis . The first course in the graduate sequence of numerical analysis seems to have a lot of overlap with the undergrad course I took, although it goes in a bit more detail. The second course in the graduate sequence explores completely new topics and is much more advanced. This material would be very helpful in applied statistics, machine learning, and data science .

While it is possible for me to take both sequences in my final year, that would be *a lot* of work, seeing as the mathematical analysis class often demands 20+ hrs per week and the numerical analysis class is at the graduate level and thus moves really fast and has lots of assignments. Hence, I want to avoid taking them both together, if possible. One possibility is that I taken the first course from the mathematical analysis sequence in fall and then skip to the second course of the numerical analysis sequence in the spring seeing as the first course in the graduate numerical analysis sequence has a lot of overlap with the one I already took in undergrad. Although that would inevitably lead to some gaps in my knowledge as I skip to the second course. Plus, I would miss the second half of Rudin’s analysis which covers very valuable topics.

Any thoughts on this? I would appreciate any input.

P.s. I’m a math/stat and CS major aiming for a PhD in statistics focusing on applications .