Help me figure out what range of schools to apply to

[rules42]

Hi Everyone,

I'm interested in applying to PHD programs in applied math but am having problems figuring out the range of schools I should apply to. I've spoken to my professors about it but everyone seems to have a very different opinion. Some have suggested I might be better going for a masters or spend another year in undergrad, while others have encouraged me to apply to mid to high tier programs. I figure getting the perspective of people looking from the outside in may help me figure out what I should do.

Undergraduate Institution: Large mid ranking public school

Majors: B.S. Mathematics

GPA: 3.5ish, Math Gpa: 3.5ish (sorta)

Type of student: White male

GRE Scores:

Q: 168

V: 150

W: 4.0

Math: haven't taken yet probably somewhere between 50% and 60%

Courses and Grades

Business Calc: B

Calc 1: B

Calc 2: D (mono that semester =/) retook and got a B

Calc 3: A-

Introduction to real analysis I: A-

Introduction to real analysis II: A

Honors Linear Algebra: B

Differential Equations: B+

Complex Analysis: A

Numerical Linear Algebra: A-

Introduction to Abstract Algebra: A

What I'm taking this semester

Graduate Numerical Analysis

Real analysis I (Rudin level)

Modelling in applied math

Research Experience: I've been working with one my professors for about a year and will be submitting a paper for publication with him in roughly a month or so

Letters of recommendation: I should have one awesome letter, and two okay letters.

Other random stuff: President of math club, tutor for about 6 month

So ya I didn't do so well my first year and a half of college, but have picked it up since then. I'm kind of hoping that an admissions committee would ignore my grades in lower division courses and possibly lowish subject GRE. A short list of some of the schools I'm thinking of applying to are

Penn State

UT Austin

Arizona State

Claremont

NC State

Do you guys think I'm aiming to high? I know that Austin and Penn State might be a bit of stretch, but would a school like Arizona State be within reason?