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I am going to apply for a programme of mathematical and theoretical physics for graduate studies and I'm currently studying maths. What is a good area to do a thesis (that is to say, considerable extra work and research) in? Here "good" means useful for my following studies and possibly making a good impression in the selection process for graduate studies.

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closed as primarily opinion-based by Qmechanic Jul 7 at 14:11

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.If this question can be reworded to fit the rules in the help center, please edit the question.

    
What does good mean here? –  BMS Jul 7 at 14:10
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"number of applications of a certain math area in physics, usefulness in the following studies" –  user10024 Jul 7 at 14:16
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Since this has been closed here you might want to ask the same question at the academia stack. –  boyfarrell Jul 7 at 14:28
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You should find out what mathematical and theoretical physics research is done at the departments of the universities you want to apply to. If you give a list of theoretical physics areas, we can give you a meaningful list of particular advanced mathematics applied in them. For almost any theoretical physics, you however need elements of the following: differential geometry, ordinary and partial differential equations, infinite-dimensional linear algebra, group representation theory, variational calculus, and numerical mathematics. But I think you'll impress best by great work in any field. –  Void Jul 7 at 14:40
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@user10024: You should really sit down and think what part of mathematics you like the best. Is it solving specific equations? Finding answers to questions about mathematical objects? Proving theorems with formal proofs? What kind of mathematics you have enjoyed the most so far? How much of a physicist would you like to be rather than a mathematician? Write this specifically down, go through the universities' departments, find overlaps in research and write them also down. Then you can write all this in your question. But we can't read your mind or do the research instead of you. –  Void Jul 7 at 15:03