Hello, all. I am an undergrad at a large state university in the US studying math. I’m 19, have senior standing, and am taking graduate and advanced undergrad courses. To date I’ve taken linear algebra, introductory real analysis (Abbott), & a course in set theory/logic/proofs (Velleman). I’ve also self-studied general topology (Munkres) & a bit of group theory (Pinter).
Currently I am taking group theory (Dummit & Foote), intermediate real analysis 1 (Lindstrøm + baby Rudin), advanced linear algebra (Friedberg et al), and (grad) algebraic topology (Hatcher).
In these next three semesters, I plan to take undergrad number theory, ring&field theory, intermediate real analysis 2. I’m also planning on more grad courses: real analysis (1&2), algebra (1&2), differential geometry, (maybe combinatorics,) & algebraic number theory. Plus I’d like to do some independent studies and an REU.
cum. GPA: 3.8. Math GPA: 3.7. Deans list. President of math club.
Given all of this, do I have a good change of getting into a top-25 grad school for pure math, presuming I have solid letters of rec & do decently well on the general and subject GRE’s?