Type of Student: International (Indian), Male

Undergrad Institution: Foreign (Indian), well-known

Major(s): Chemical Engineering

GPA: 8.53 / 10

Grad Institution: Foreign (Italian), not well-known

Major(s): Mathematical Modelling

GPA: 3.5 / 4

Marks in the Italian system: 110 / 110 with honours

GRE Revised General Test:

Q: 170 (98%)

V: 160 (85%)

W: 4.5 (80%)

GRE Subject Test in Mathematics:

M: 740 (68%) (How bad is this really? Should I send it when I have the option not to?)

TOEFL Score: (116 = R30/L30/S27/W29)

Program Applying: PhD in Pure Math/Applied Math/Statistics/Financial Math

Research Experience: Master's thesis: On a pre-published numerical method in Mathematical Finance. 6 month research; decent, nothing great, no significant new results.

Awards/Honors/Recognitions: Scholarship for Master's studies from a well-known research school near the university.

Pertinent Activities or Jobs: Took some classes on Linear Algebra and Big Data in the company I was working in. (I'm not sure if I should mention this. I have no official records except for my employment letter.)

Any Miscellaneous Points that Might Help: I'm basically trying to shift to (pure) Math. I hope the lack of UG math classes and poor GRE Math scores will not hurt me too much. Also, my grad classes were more applied than pure.

Any Other Info That Shows Up On Your App and Might Matter: Work experience of 1.5 years, implementing machine learning algorithms for big data.

Recommendations: Two strong, one weak

Applying to Where: (Tentative (have to significantly shorten this), not mentioned implies Math)

Super ambitious:

Princeton - ORFE

Brown - Applied Math

Columbia

U Illinois Urbana Champaign

Ambitious:

U Texas @ Austin

U Washington

UC San Diego

Purdue U

Ohio S

Georgia Tech

Carnegie Mellon U - Financial Math

Reach(?):

Boston U

UC Santa Barbara - Stat

Michigan S - Stat

Texas A&M U

U Southern California

Safe(?):

Iowa S

North Carolina S

Louisiana S

Florida S - Financial Math

Questions:

1. I have no clue where I stand. I am not sure if the universities I have denoted 'Reach' and 'Safe' are really so for my profile. Also, am I being too optimistic or pessimistic?

2. I do not have a very strong math background on paper (all UG math courses missing). In light of this, should I send my not-so-good GRE Math score when I have the option not to?

3. Should I also apply to lower universities?

4. Please suggest any other university I should look at.

Thank you for any suggestions.