Exploring my Path to Grad School: Math, Stats & Engineering

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In May I graduated from a small liberal arts college with a Bachelors in Math (3.6/4) and in Economics (3.8/4). In July I shipped off to Vietnam where I am currently teaching HS Math at a large private school in Hanoi. I took a last minute GRE before I left and scored reasonably well IMO (V 159, M 167).

My math background is heavily based in theory. I have completed coursework through Abstract Algebra, and Analysis: one semester of complex and a full year of baby Rudin's real. I also went through a summer program in BioStat, SIBS, at BU which included some exposure to SAS and R. My undergrad project was unoriginal (but did extend my experience in R), focusing on Model Selection with a bias (ha!) towards LASSO. I basically reproduced the results in http://www-stat.stanford.edu/~tibs/lasso/lasso.pdf

My physics and engineering background is also quite theoretical and only begins to scratch the surface. Thru Intro Quantum, E&M, General Relativity, Heat Transfer.

More relevant info: I honestly enjoy the challenge, structure, and beauty of higher mathematics. It's rigor does not intimidate me. That said, I (the young liberal idealist) find a lot of it purposeless and self satisfying. For these reasons I am drawn toward the applied side of mathematics. How can I put my analytical skill to use in this complex world of inequality and inter-dependence?

Statistics appears as a logical avenue. I was largely unimpressed with the biostats program at BU due to its dry, detatched approach to both the mathematics and the problem itself. We met hypotheses and applied the appropriate statistical tests... Over and again. Still, it's unfair of me to turn a cold shoulder on other opportunities in statistics. On the flipside I am hesitant to commit to a path without having a better idea of its destination.

Engineering attracts me but I feel somewhat behind pace when considering Master's programs in Environmental or Civil Engineering. Not even bothering with Mechanical...

My questions/concerns are broad and may be impossible for one person to address.
1. With my current CV what are my chances of getting into a decent Masters program in statistics (say Berkely, Davis, and/or CSU)? What about a Ph.D. track? What would I need to score to impress on the Math GRE ST?

2. What are some opportunities available to a M.A. in Stat? What do I eliminate by pursuing a M.A. in Stat versus a Ph.D. in Stat?

3. How much coursework would I need to make up to pursue a Masters in (fill in the blank) Engineering?

I am very open to any and all perspectives. At this point I am enjoying the struggles of teaching and don't plan to enroll in grad. school before fall '14. I'm just looking for a bit more clarity on the road that leads me there. Should I retake the GRE? Get more programming experience? Take some engineering courses?

Thanks guys.
 
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shameless bump.
 

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