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Which courses (undergrad level but also master's level) in mathematics and statistics should be taken by a student aiming for a PhD in mathematical biology?

The basics I imagine are: Calculus courses, linear algebra and probability.

But then I would guess other important courses would be: ODE, PDE, Complex analysis(?), Fourier analysis(?), Markov chains(?) (the ones with (?) I am unsure about).

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I think a student should consult with math and/or biology faculty at his/her university. If they don't know, they probably know someone who does. – Gerry Myerson Feb 22 '12 at 23:11
@Desmond Your question is probably appropriate for the nearly-in-beta-SE…. Check out the proposal and commit to it if you're interested. Then we can get it off the ground and get the site in beta! – Xoque55 Mar 3 '14 at 4:51
@Xoque55: The site is now in beta (and has been for 416 days at the time of writing this comment). It's been renamed "Mathematics Educators" - Beta Q&A site for those involved in the field of teaching mathematics. – J W May 3 '15 at 20:04

As Gerry Myerson points out in a comment to your question, you should ask the appropriate people at your university. Since this is a late answer to your question, I hope you have already done so, but perhaps this answer will benefit others.

Searching online for applied mathematics programs in biology reveals many courses (e.g. Brown University's Applied Mathematics - Biology degree.) Some others can be found on The Society for Mathematical Biology's Degree Programmes in Mathematical Biology page.

Certainly, calculus, linear algebra and probability are fundamental subjects. Statistics and differential equations are also important. For computational biology, discrete mathematics, especially graph theory and combinatorics can be valuable (see, for instance, Lior Pachter's courses).

At an advanced level you may run into various subjects from partial differential equations to nonlinear dynamical systems to stochastic processes to computational topology to algebraic statistics. What to choose will depend on degree requirements, what is available at your university and the advice of experts in the area. I would also recommend asking about taking suitable biology courses and other subjects, such as programming, algorithms, chemistry and physics.

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