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I'm about to start my MSc in Computer Science studying "Combinatorial Optimization", which was already the theme of my undergraduation thesis. I like the field and the research, but I'd rather prefer working with numerical methods and techniques. The problem is my current university has a very weak research on that, and it is located in the maths departament.

My two questions are:

1) Is it possible for a CS student to work with numerical methods in MSc and PhD level?

2) If I complete my MSc in CS (optimization), is there a chance of me being able to apply for a PhD (on other universities) to study numerical methods (usually located under maths)? I have heard some people talking about the importance of "breeding" in academic research;

I know it usually depends on the university, but the questions are more on a "is it likely" fashion.