Math Masters: Advice for UT Dallas Freshman

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I have just started my freshman year at the University of Texas at Dallas.
I had the opportunity to go to Northwestern but turned it down for financial reasons.
I am starting out in Pure Math. Currently, I hope to go into grad school to get a PhD, as I want to do research and tremendously enjoy rigorous mathematics. I have been spending a some time building my foundation in set theory, logic, and reading through Apostol's Calculus.

I have a substantial amount of AP credit and could graduate relatively quickly (in 2.5-3 years), with a BS in Math. From what I can see, UT Dallas doesn't have the best Math program out there. So I'm tempted to graduate in 4 years with a masters so that I can get some grad classes under my belt. Would top PhD programs look down on a masters for this reason?
I'd also like to stay for 4 years so that I have more time to get some research experience.
If I decide not to get the masters, I might go for a double major in computer science, but really nothing is as interesting to me as straight math, and I would prefer to take graduate courses.

Any advice from those experienced in the Math Track would be greatly appreciated.

Thanks.
 
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I think that will be a great boost when it comes time for you to apply. Getting a BS/MS in 4 years is great, you should definitely do it.