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Math Coursework Recommendations

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Thanks in advance for any thoughts or help!

I am currently a masters student at a fairly prominent MS program in statistics. As an undergraduate, I had an unconventional background (business school), but I had a strong academic performance (3.99 GPA), took a fair bit of quantitative courses (Calc 1-3, linear algebra, 3 stats courses in the math department, and several upper division quantitative economic courses) and had relevant internship experiences that thankfully led to a surprisingly successful run of applications.

I have gone back and forth between whether I want to continue on to a PhD in statistics. Because of external circumstances, the earliest I could apply to programs would be around 2 years after finishing my masters program, so I will be applying for jobs for when I graduate next fall. However, I am giving serious thought to going a PhD, and I want to make sure I keep that door as open as possible should I ultimately make that choice.

I have recently started doing research with a professor in the department, and during my first year in the MS I took intro to real analysis 1. Comparing my background to some of the other ones I have seen on the site, it seems like mine is most lacking in terms of mathematics courses so I hope to take some this upcoming year.

In the fall, I could take one of: Stochastic Processes (applied non measure theoretic, graduate level course), Abstract Algebra 1, or an upper undergraduate level math course in data analysis (this is my preference strictly from an interest perspective and because the professor and course are supposed to be very good and it would be very applicable should I stay in industry).

In the spring, I could take two of the following: Numerical Analysis (graduate level, not a typical applied numerical methods class, extra emphasis on optimization), Intro to Real Analysis 2 (grad level, typical multivariate analysis course), and Advanced Linear Algebra (upper level undergraduate, but relatively advanced class compared to a typical second linear algebra class, going into topics like banach spaces, Bauer-Fike theorem, Gerschgorin theory, etc...). 

From a pure "this looks interesting" perspective, I think I would take the data analysis class class in the fall and Numerical Analysis and Advanced Linear Algebra in the spring. However, I would love to hear feedback! There are lots of resources out there that stress piling up on as many math classes as possible, but I think its hard to know what specifically to take outside of the standard calc 1-3, linear algebra, and real analysis.

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If those classes are what interest you most, then I say go with them. If you decide to apply to PhD programs, you will have your Masters in Statistics (from a reputable department which will also work in your favor), so that signals to adcoms that you can perform well in Casella & Berger mathematical statistics and graduate-level Theory of Linear Models. Nobody will question your ability to handle more advanced mathematics if you have those plus a semester of real analysis. Having Advanced Linear Algebra and Numerical Analysis on your transcript will look great as well. In your statement of purpose, you can emphasize the mathematical nature of these classes to stress that you studied the underlying theory, not just how to apply numerical algorithms and linear algebra tools.

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