PhD in pure mathematics

[chaosintegral]

Hello,

I am wondering my chances for getting admitted into a Math PhD program for the schools listed below.

Stats:

Undergrad Institution: large prestigious university

Undergrad Major: Chemical Engineering

Undergrad GPA: 3.3

GRE: 780Q/500V/4.0WR

I am going for a second bachelors degree in mathematics at a state school this upcoming fall. I plan on getting a 4.0 in all courses and at the same time do directed research with professors. I also plan on taking the Putnam Math Competition this fall, and I'm currently scoring around a 30 on practice tests. Im also going to be taking the math GRE, and hope to score atleast above an 800.

Area interested in doing research: Low Dimensional Topology

What are my chances for the schools below (given that i accomplish everything that i plan on doing)?

UCLA

UC Berkeley

University of Notre Dame

Purdue University

University of Maryland

University of Virginia

University of Wisconsin, Madison

Ohio State University

Also, would my undergrad gpa in chemical engineering really matter if i do well at a state school in pure mathematics? And how much does the Putnam Math Competition matter?

[kuz]

Don't get ahead of yourself.