I have finished the first year of my Masters in Mathematics from a German university. The area that I intended to write my masters thesis in was in Differential Geometry. However, I have decided that I would not want to pursue a career in academia in the future, or at least not one in pure mathematics. I want to get a PhD in statistics from a top US university.

Is it a good decision for me to switch my major to Probability Theory and Stochastics? This would involve another year of coursework, thus making my masters 3 years instead of 2 years. Will this be reflected negatively on my grad school application? Will they think that if I couldn't complete my masters in 2 years, how can I complete my PhD in 4-5 years?

I have done well in a rigorous Stochastic Processes course in my first year of masters and I did well in 3 statistics courses and a couple of baby probability courses in my undergrad. I might also get to be a TA for the stochastic processes course next year.

The other alternative is that I start my thesis in Differential Geometry and then apply for a PhD in statistics. When doing so, I'm afraid that I won't be getting recommendation letters for a statistics program from my pure math professors. Are my fears valid?

  • It’s worth noting, if you don’t have it in mind, that a majority of US PhD students will not have any master’s degree at all, though a substantial proportion will have a statistics-focused bachelor’s degree. Sep 7 '20 at 18:18

There are a lot of issues here. Whether you get good letters from maths professors is up to them and your relationship with them. Only they can answer that, so you might pose the question to them. Not writing the thesis may impact on that, but only they can say.

As to whether a switch gives you any advantage in application to a US doctoral program, it also depends on that program. Every US university is different in that regard and you can, really, only learn the answer by making application. But I can guess, at least, that you can make it work either way. Math is a good foundation for statistics and the details may matter less than your insight.

But you can plan for both outcomes, at least, by applying now for doctoral programs based on your two year degree while still considering the three year switch. You have a year to figure it out and don't need to make a final decision at this point, I think.

And don't define "top" US universities too narrowly. If you do, you are likely to not get offers. Cast a wide net. There are lots of great US institutions that aren't in the top 10, or even 30, or ...

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