Hello friends, I am currently a senior, trying to get a reasonable list of schools for me to apply...

Any insight will be appreciated, and if you could tell me rough chances of getting in (I know, I know, you are not ad coms, but it is my strong feeling that you guys know more than my advisor on this topic for some reason...) I will be especially grateful.

So here is the breakdown of my academic profile...

I attended Nation's top 5 liberal arts college for 1 1/2 years, with a total math gpa of 3.9. I have taken 5 classes there: Lin. Alg., Multivar. Calc., Diff. Eqs., Real & Complex Analysis. I got A- on RA, and A on the other four. Yes, I used to be a physics/chem. major, that is why I've taken so few courses...

I transferred to an Ivy school, well-regarded for its strong math program, and obtained a total math gpa of 3.8. The classes were:

Honors Lin. Alg., Honors Analysis II, Honors Abstract Algebra

Diff. Eqs., Probability, Statistics, Geometry, PDE.

This year I am taking 3 graduate math courses (Real analysis, Algebra, Probability). I expect to have a math gpa of around 3.8 by the time I apply for grad schools.

I have NO RESEARCH EXPERIENCE WHAT SO EVER. (And my advisor insists that it is of little importance in math, but many of you guys seem to think otherwise?)

My recommendations are not going to be super terrific, but my professors seem to know me well enough, and it will be better than average.

As far as GRE goes, haven't taken the general kind, but on the subject one, my percentile is 93%.

I want to apply for applied & pure math(analysis).

So... what chances do I have...?

Thanks in advance!

BTW, below is a list of few schools that I want to apply (and wish to get in):

TOP: UCLA(app. math), UC Berkeley(analysis), NYU(app. math)

Wish-to, but I think I have no chance of getting in: Harvard, Princeton, Stanford, MIT, Caltech