How competative is this scholarship? What is the level of knowledge needed for undergrad research for math. For example, if I wanted to do abstract algebra, would the dummit and foote book be enough to start looking at research or is a much deeper knowledge required? (masters level). Are there some topics like logic and number theory easier to do research in than say analysis? My Profile: Finished first year undergrad, 84% avg with standard calc, lin alg, cs, and probability courses. Was not in the advanced level theoretical lower level math classes at waterloo, but switching into them next semester. Thank you very much, I tried to find this online for a long time, but did not get anywhere, as the USRA applies to all sciences, and research in math is different than say chem or physics (experimental).