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I am a new Master's seeking student in Mathematics, and I'm trying to get a jump on my research focus/concentration for eventually writing my Master's Thesis. My interest is primarily prime, perfect, and Mersenne numbers. When I try to formulate a plan though, my ideas are always too broad and vague, or are way too specific. Does anybody have advice on how to decide on a topic? How long is the average such thesis? Perhaps what I thought was too vague and expansive would be a perfect length and I was just second-guessing myself too much.

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    Talk to your advisor. If you don't have an advisor, find one now. Only your advisor can tell you the right answer. – scaaahu Sep 18 '13 at 4:37
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To expand on scaaahu's very valid comment, consider the following:

  • what specific topic(s) interest you the most.

  • which of these do you have some level of confidence in pursuing at a Master's level.

  • Who has the expertise to be able to advise you, are the willing to do so (they may be overloaded).

  • Are their enough resources available to start research in the chosen field.

  • Finally, what is the 'end-game', where do you hope to go with this qualification?

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