I am currently doing MS in Mathematics. As far as I know there are two approaches which anyone can take to do Mathematics- Analysis and Algebra. Choosing which area to work on seems difficult to me. Currently I like both but I have to decide which area to pursue.

I wanted to know if we can switch our fields later in our career? For example, if I do my MS thesis in Algebra how feasible will it be for me to switch to Analysis in my PhD?

  • 2
    $\begingroup$ This site is concerned with the teaching of mathematics. In its present form this question is off topic. $\endgroup$
    – Karl
    Oct 6, 2015 at 18:28
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    $\begingroup$ I'm voting to close this question as off-topic because it is not really on-topic here, as it is not about teaching mathematics, and in addition is based on a false premise. A revised version might be on-topic on Academia; moreover if the question could be turned into one about teaching, it could be on-topic here too. You can edit the question. $\endgroup$
    – quid
    Oct 6, 2015 at 19:00
  • $\begingroup$ @quid One might change the question to: A student came to his advisor, whether he could choose different subjects for the MS and PhD theses. What should the advisor advice? $\endgroup$
    – wythagoras
    Oct 6, 2015 at 19:21
  • $\begingroup$ @wythagoras this could be a possibility. In this case I prefer to let OP decide what they do. It might be preferable for them to move to another site. $\endgroup$
    – quid
    Oct 6, 2015 at 21:48
  • $\begingroup$ Perhaps this question is germane at academia.stackexchange.com $\endgroup$
    – vonbrand
    Oct 7, 2015 at 14:49

1 Answer 1


First, there are many more fields in mathematics than just Abstract Algebra and Analysis. For example, Number Theory is also very suitable for an MS thesis or PhD. There are several other fields, but they are somewhat less common.

Your PhD thesis is not really meant to be a follow up on the MS thesis. In both theses you are using the things you've learned in Algebra and Analysis class to go into the depth and investigate something. Since should have had plenty of courses in both fields, so you know the basics of each fields, you can switch form fields. However, since the Master thesis doesn't have to be original research, but the PhD has to be, you can use the MS thesis to review and expand your knowledge on one of the subjects so that if you write the PhD thesis about the same subject, you have a better ground to stand on. This might save time in you PhD thesis. In short, you can switch, but it might cost you some time and effort when you're writing your PhD thesis.


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