Hi. I apologize if this is too long. I want to get a feel for my plan of action. I want to aim for a top 10 mathematics graduate program (Edit: I am interested in UC Berkeley). For the record, I am a junior double major in mathematics and computer science at a lowly ranked liberal arts school. I am wondering if I have a good shot if I follow this transcript/profile:

Calculus 1, 2, 3

Linear algebra 1

Discrete mathematics

Ordinary differential equations

Introduction to proofs

Abstract algebra 1

Probability and statistics 1

Advanced calculus 1

Partial differential equations

Elliptic curves (Algebraic; an undergraduate independent study. However, upon request, the professor can teach turn it into a graduate level course but it will still be marked as an undergrad course on my transcript)

Cryptography and cryptanalysis

Foundations of geometry

Abstract algebra 2

Functions of a complex variable

Introduction to topology (point set)

Theory of numbers

Linear algebra 2

Probability theory

Theoretical computer science

Advanced calculus 2

Introduction to modern algebra 1 (grad course)

Introduction to modern algebra 2 (grad course)

Differential geometry (grad course)

Algebraic geometry (grad course)

Algebraic topology (grad course)

Real Variables 1 (grad course)

Real Variables 2 (grad course)

**Perhaps I will take for fun: Stochastic Ordinary Differential Equations (grad level)

I do not want to say that I have research experience in mathematics. I worked in a small group on an algebra research project as an "REU" and I am not proud of myself, so I will leave it off.

And as part of my profile, assume I can obtain 3 good letters of recommendation. Also, suppose I do very well on the mathematics GRE and the Putnam exam (I am planning on taking it next year). Also, suppose I get an A or A+ in all of the above courses with the exception of 1 B+ in Calculus 1 and a B in Linear Algebra 1and an A- in probability and statistics 1.

Do I have a realistic shot?