The AIM program is just one degree program in the Department of Mathematics. Some fraction of students entering the standard Mathematics Ph.D. program at the University of Michigan also choose to work on "applied" problems for their thesis research, but typically do not seek supervision outside of the Department of Mathematics. Whether you choose AIM or the Mathematics degree programs, you will have access to exactly the same faculty in the Department of Mathematics, and exactly the same mathematics courses and seminars. AIM graduate students share office space with, take many of the same courses as, and are advised by some of the same faculty as graduate students in the standard Mathematics graduate program. The degree requirements for the two programs are somewhat different, however.