Finding his own path

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I am a graduate student in major mathematics and now the time has come to choose a "specialization" (I have to choose 3 between 4 subjects).

I like algebra a lot and I am also interested in biomathematics. However I can't choose between these two directions. I like the way algebra is built, but I don't know what research looks like in this field. On the other hand, I do have a good idea of biomathematics research looks like.

I know that it is a very subjective question and that I should discuss of that with my teachers, but I would like to have your impressions and advices.

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You might want to look at Bernd Sturmfels' book Algebraic Statistics for Computational Biology. He applies algebraic geometry to a variety of statistical problems arising in biology.