Hello everyone!

I am having some difficulty deciding on whether or not I should pursue graduate school applications this fall or next fall. Here is a little bit of my academic bio:

Undergrad Institution: Small Liberal Arts

Major(s): Mathematics, Economics

Minor(s): Philosophy, Physics

GPA: 3.74

Type of Student: Female Minority

GRE Revised General Test:

Q: 170

V: 165

W: 6.0

GRE Subject Test in Mathematics:

M: (Taking in September and October)

Program Applying: Pure Math

Research Experience: Undergraduate research project in Economics (two of them), research project in Galois theory, research internship currently (no publications), two conferences

Awards/Honors/Recognitions: Dean's list 3 years, other misc. awards that are not helpful imo

Pertinent Activities or Jobs: Tutor for 3 years, TA for 2 years, PLUS group facilitator for Biostats class

Any Miscellaneous Points that Might Help: Independent projects with professors, taken an introductory algebraic topology

Any Other Info That Shows Up On Your App and Might Matter: McNair Scholar (not sure if this matters)

My research interests are in representation theory (lie groups/lie algebras) and their relation to mathematical physics and algebraic topology. I have recently visited the University of Washington and talked to the entire math department. I got great advice and met with nearly every professor and about 10 graduate students currently attending. University of Washington was always my top choice. After learning more about UC Berkeley and reading about the research there, I would really like to attend UC Berkeley. That being said, I want to be competitive.

The issue I'm having right now is that I feel as though I'm balancing too many things at once (research, applications, studying for GRE, work, etc). I would like to do well on the subject test (above 80% percentile) but have not had sufficient time to study for the test. On top of that, I have all of these applications, researching into schools and speaking to professors... I feel that it is a bit overwhelming. I would like to make my application as strong as possible and currently I think if I worked on the GRE this year instead of hurrying and taking it this fall that I would have more time to study. I would also like to publish and work harder on my research. If I postpone the application process I can still TA, take a few geometry classes and relieve some of the pressure I'm feeling. My question: is it advisable to wait and strengthen my application? I would still ask for my letters of recommendation right now (and probably still apply for NSF right now) but was wondering if anyone had success doing this and/or should I do this myself?

EDIT: Math courses I have taken:

- Real Analysis or Advanced Calculus (1 year - 3 courses)

- Abstract Algebra (1 year - 3 courses)

- Galois theory (1 quarter)

- Linear Algebra (1 quarter), Advanced Linear Algebra (1 quarter)

- Foundations of Mathematics (Proof-writing course some call it)

- Single/Multivariable Calculus (4 courses)

- Differential Equations (1 year - 2 courses)

- Numerical Analysis or Numerical Methods (1 quarter)

- Probability and Statistics (1 year - 3 courses)

- Probability Theory and Mathematical Statistics (1 quarter)

- Complex Analysis (1 quarter)

- Algebraic Topology (1 quarter)

Note: 4.0 in almost all of them

Would take (if I stay)

- Survey of Geometries (1 quarter)

- Foundations of Geometry (1 quarter)

- Partial Differential Equations