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I want to improve my competitiveness for grad school admissions. My intended area of study is AI/Machine Learning and possibly other math and statistics heavy fields of Computer Science.

My undergrad math grades were terrible, mostly C's and a few B's. Although my mathematical maturity improved tremendously after years passed, as you will guess I have no proof for this. So I decided to take a math class to show my skills to adcoms.

Now I have to choose exactly one from the two options available:

  • an undergrad MATH level mathematical analysis class following through walter rudin's PMA book or
  • a graduate EE level Random Processes class about stochastic processes following through Ross.

So from an admissions comittee member perspective, which class do you value more for judging a students mathematical maturity?

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I'd go with the graduate-level class. But just taking one class is not likely to make much difference.

What you really need is for your recommendation letters to specifically address this point. Nobody will believe your claim that your grades do not accurately reflect your true level of mathematical maturity (although you can certainly demonstrate your mathematical maturity in your research statement). But people will generally believe your references if they make the same claim, especially if they back up their claim with specific and credible evidence of your mathematical maturity, and more generally of your potential for research excellence.

This will only happen if you develop a closer collaborate relationship with your professors. Don't just sit in the back of the random-processes class and get an A. Talk with the instructor; ask cogent questions; ask about research opportunities, or at least directions for further study. Impress them. Give them proof.

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