<p>The general classes need for a math REU vary, but very little. ~99% of the time they require linear algebra and at least one class in advanced proofs, which is typically either Abstract Algebra and/or Real Analysis. It seems to be that it is to make sure you know what pure “math” truly is. Then, of course, depending on the program it can vary. An algebraic program may require algebra, while a more applied one will require diff eq.</p>