Chance me for graduate school please

[cytochrome]

Chance me for graduate school please!

Stats:
Junior at a SMALL liberal arts school

Math/chemistry double major

4.0 GPA

2 years of research (thesis at home school) + 2 summers of REUs in biophysics at Princeton and the Czech Republic (hopefully 3 coming up) = lots of presentation and mathematical modeling experience
-Chemistry thesis - synthesis of a antimicrobial compound
-Mathematics thesis - existence and uniqueness of nonlinear relativistic wave equations and Schrödinger equations

Track and field team - decathlete

Honors program - various community service projects

Resident director (RD)

Math 101 teacher

Calculus lab assistant

Chemistry lab assistant

Calculus tutor

Water quality analysis - full time job, lots of experience with statistics and ExcelCourses:
Math - Calc I-III
vector/tensory analysis
linear algebra
abstract algebra
ODE
PDE
probability theory
complex variables
Mathematica programming

Physics -
intro I&II
Classical mechanics
Quantum mechanics I & II
Physical chemistry I (thermo) & II (quantum)

Chemistry-
general chemistry I&II
organic chemistry I&II
inorganic chemistry
analytical chemistry
biochemistry

GRE - not taken yet! Assume an average score

I want to apply to chemical physics PhD programs to study quantum mechanics/chemistry or applied mathematics to study chaos theory and/or PDEs.

Would I have a shot at good research universities? I know I'm lacking in the physics courses, my school doesn't offer a physics major and I have to commute. I also haven't taken any grad level math courses, which I know is important (again, school does not offer them) :(
Is there hope for top tier research schools? I'm looking at Harvard chemical physics (dream) and University of Maryland chemical physics, as well as applied math at various schools.

 

[TheKracken]

What school do you go to (just curious??)

 

[cytochrome]

It's such a small school that no one I know who doesn't go there has ever heard about it. It's so small that I'm uncomfortable saying because it will show up on google or something and I'm definitely the only person at my school that wants to do a PhD program like that

 

[TheKracken]

Well, its seems like you have a very good application.

 

[chill_factor]

You have a shot at Harvard or MIT. But just a shot. There's literally nothing you can do to make your application better unless your mom or dad donates MIT 1 million dollars, so apply to all the good schools you can.

 

[cytochrome]

I'm wondering if it's worth it to not do an REU this summer and take some graduate level courses in topology, analysis, and mathematical physics at a university near home... Are these kinds of courses necessary for top programs in applied math?