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Typical math background for stats PhD

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I'm wondering if someone could shed some light on the math courses that you should take to be competitive for good stats PhD programs.

It seems like most universities' websites say 3 semester calculus, 1 semester linear algebra, math stats, sometimes real analysis. I've seen some people on here say you wont be competitive without measure theory or complex analysis, and I don't know if that's true or not.

What courses do you need to be competitive for good-great programs (like ranks 60-20)? And what about for amazing programs (like ranks 19 and better)?



If you don't mind: Here's my math background, and I'm wondering how competitive I'd be.

Calculus I-III, Linear Algebra, Real Analysis, Diff EQ, Probability, Mathematical Statistics, Econometrics (All A's)

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Some people get into top programs without a math degree or the recommended minimum math coursework, but this is usually because of the research that they already do, demonstrating an interest and facility with stat methods. In my opinion, you should focus on learning what is useful, not what is required, and as it turns out all math is useful if by learning it you become a more mature proof writer and more comfortable with reading proofs that involve analysis, linear algebra, and probability all together.

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