Do you need some one considerably practical or do you wish to be much more independent? How many times would you like to satisfy the mentor in addition to remainder of pursuit group? Do you want a one-on-one feel or do you want to maintain a bigger party? Can you worry if you’ll mainly become employing a grad beginner or with a professor?
What exactly do you intend to escape the REU?
Would you like to see a preferences of what mathematics scientific studies are like? Want to become printed? Do you want to see plenty of latest math? Do you want to attend conferences?