College selection for Pure and Applied math Phd programs

[mathbee]

Hi , I'm applying to Phd programs for math - both pure and applied - specifically for differential equations and numerical analysis - ni fall 2015. 

 

Please advise me as to the choice of colleges, especially for the field of PDE and numerical methods. Also, which program - pure or applied - should I apply to for PDE and numerical methods? It is quite confusing as a lot of the faculty members working in these fields are listed in both sections.

 

My profile :

 

Undergrad Institution: International School(among best undergrad institutes within country)
Major(s):Mathematics
Minor(s):
GPA:7.1/10 (Batch average is about 6/10)
Type of Student: International Female

GRE Revised General Test:
Q: 165 
V: 154 
W: 3.0 
GRE Subject Test in Mathematics:
M: 660 (51%) 

TOEFL Score: 109/120

Program Applying: Some Pure Math/Applied Math - Differential Equations and Numerical Analysis

Research Experience: 3 research projects at home university - each about 5 months long,- related to numerical methods and evaluation of differential equations and integro-differential equations and PDEs. 
Presentations for each project done at college. 
One paper submitted to arXiv and submitting to an student journal . Another paper submitted to arXiv.
Upcoming thesis project at NUS in the same field. 
Summer research project with fellowship at a nationally reputed institution.

Any Miscellaneous Points that Might Help: Did all available (about 8-10) grad-level courses - including PDE, Functional Analysis, Numerical Analysis of ODEs
Any Other Info That Shows Up On Your App and Might Matter: All Recos should be strong and all my recommenders know me from very long projects.

Applying to Where: (Color use here is welcome)
Almost final list:open to suggestion based on possibility
Upper Reach/Dream:
UCLA
NYU/Texas Austin(Unsure)

Reach:
University of Minnesota 
Georgia Tech
Purdue
Texas A&M (Unsure)

Match:
University of Southern California
Arizona State University
UIUC

Safety:
University of Florida
University of Iowa

 

Please give me some advise as to my selection on universities as I've started to apply, and need to fix on the colleges immediately!
All the best to everyone!