Hello everyone,
I will be beginning biostat grad program at Harvard in the fall. I ultimately plan to apply to statistics/OR PhD programs next year (I will be completing my MS next fall).
I am aware of the fact that many graduate schools prefer students to have completed two semesters of real analysis, and I have been definitely planning to take graduate-level real analysis courses at Harvard graduate school. However, I come from a non-mathematics background (my degree is in chemical engineering from one of the ivies, and I have not taken proof-based math classes in undergrad), and my advisor suggests that I take proof-based probability classes that are designed for biostat PhD students in lieu of real analysis.
Descriptions of probability I and probability II are as shown below:
1) Probability I
Axiomatic foundations of probability, independence, conditional probability, joint distributions, transformations, moment generating functions, characteristic functions, moment inequalities, sampling distributions, modes of convergence and their interrelationships, laws of large numbers, central limit theorem, and stochastic processes.
2) Probability II
A foundational course in measure theoretic probability. Topics include measure theory, Lebesgue integration, product measure and Fubini's Theorem, Radon-Nikodym derivatives, conditional probability, conditional expectation, limit theorems on sequences of random stochastic processes, and weak convergence.
Would it be sufficient to take these probability classes in replacement of two semesters of real analysis? I plan to take one elective stochastic course as well in addition to two probability classes.
Thank you.