Applied vs Pure Math for an Engineering Student
Believe it or not, following the "pure" track might help you out more. 

I used to have an "applied concentration" to my math major, which meant I had to take mathematical modeling classes, graph theory, operations research I &amp; II, etc. on top of my core classes. When I decided to go the PhD route (applied), my advisor recommended I drop the applied concentration in favor of the pure, reason being that the pure classes will give me more breadth and better preparation for grad school.

Ultimately, this meant that I had to take abstract algebra, adv. Calc I &amp; II (also known as elem. real analysis), a proof writing class, etc. I did end up taking the modeling class as an elective. 

From the point of view of my advisor (who is on the grad. Admissions committee at my school) these aforementioned classes show capacity and mathematical maturity to a greater extent than the applied courses, which is what departments would like to see when considering your PhD application. Plus, they give you a foundation to build upon once in grad school.

So, I'd say take the pure classes and cherry pick (smartly) the applied ones as electives. This will ensure you're more prepared for the rigor you'll encounter wherever you decide to go. 

Best of luck!