So I'm currently an undergrad at a top math university with ~3.6-7 GPA (probably all A's this semester). Here's my full coursework by the end of this year: Lower Division: Multivariable Calculus Linear Alg. & Diff. Eq. Discrete Math Upper Division: Linear Alg. Abstract Algebra Real Analysis Numerical Analysis Complex Analysis Graduate-Level: Ordinary Diff Eq. Functional Analysis & General Topology I and II Multivariable Complex Analysis Algebraic Topology I and II Differential Topology Symplectic Geometry Kaehler Geometry Research for 1 year [in Geometric/LD Topology] Also, I know that LORs make the most difference for admission and while they are highly variable, I think I should have a pretty good one from my research advisor and another from one of my graduate professors who I have a good relationship with. Does this put me ahead of most REU-acceptees? And what's the criteria for a very solid application? I appreciate any response, even if it be obvious. Thanks.