Undergrad Institution: Midwest liberal arts state school

Major(s): Mathematics - Actuarial Science for 3.5 years, recently switched to Mathematics - Statistics

Minor(s): Music

GPA: 3.60 cumulative, 3.47 in the major (however, I have As in all of my "pure math" courses)

Type of Student: Asian minority (not Chinese or Japanese)

Coursework: Two semesters of analysis, one (maybe two? - probably not - will self-teach if necessary) of algebra, two semesters of linear algebra (second semester indep. study using Axler), and probability with measure theory (indep. study using Resnick).

GRE & TOEFL: N/A (at the moment). I want to use the gap year to get a good score on the MGRE and GRE. Need to learn topology, discrete mathematics, differential equations, and complex analysis. After this, I would like to through Spivak (calculus text, not used at the uni. I attend) and Rudin (not used at the uni. I attend).

Program Applying: either Pure Math (Analysis) or Statistics

Research Experience: Paid projects in knot theory and homology, time scale calculus, and musical geometry. Unpaid projects (started up on my own and presented in math retreats through the uni.) on musical set theory and (measure-theoretic) probability theory.

Awards/Honors/Recognitions: Outstanding senior award from math department.

Pertinent Activities or Jobs: Tutored for 7 semesters for everything from calc. I to real analysis and abstract algebra, in addition to music theory, economics, Spanish, and actuarial science courses. TA for an elementary stats class and calc. I class (with excellent feedback - can quote students and professors). Grader for calc. I, III, mathematical modeling, statistics, actuarial science courses - and soon, abstract algebra.

Any Miscellaneous Points that Might Help: Passed three actuarial exams, have had 2 years' experience with LaTeX.

Any Other Info That Shows Up On Your App and Might Matter: Have had a position where I am paid to create study materials, and another position in which I had to chair a committee (run meetings and create a project for use in housing at the uni I attend).

Questions:

1) What kinds of schools should I look into when I apply for grad school? Right now, I'm considering MN, UW-Madison, and U of Iowa.

2) What should I spend my gap year doing? My plan right now is to learn all of the math that was not covered in the courses I took.

Thanks!