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I have an engineering degree, a long time after graduation I started to fall in love with pure mathematics for its abstraction and beauty that I never experienced before when I was doing math courses.

The best choice I had is to apply to the engineering mathematics department as a master degree student.

My dream is to be some day a professional pure mathematician doing serious research in an abstract field, for now I like Analysis.

However, reasearch in our department is besed on applied mathematics, especially engineering problems. Nobody here believes in pure mathematics, most of the stuff is interested in numerical methods and really few of them are interested in the analytical methods to solve applied mathematics problems, such as perturbation methods and lie group methods to solve PDE.

My plan is to find a research area that is "close" to pure mathemtics in the master degree and try to find a "closer" area in the phd, I will try to find a phd program in pure mathematics, so I have two questions:

  • What do you think of my plan? will I be able to move smothly from applied mathematics in the master degree to pure mathemtics in the phd? Or do I have to change the plan?

  • What is the best research areas that fits my plan? Any recommendation?

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    $\begingroup$ It certainly not smooth but doable also you need to brush or gain lot of knowledge on Algebra ( Groups, Fields, Rings etc.), topology and some number theory also good. I suggest some part time study in pure maths to build good basics before you make the move. I am in exact situation as you but this is my plan just sharing with you $\endgroup$
    – Mr. Math
    Sep 7, 2013 at 21:33
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    $\begingroup$ Where do you live? Do you want to visit an university there or elsewhere? You should add information about the kind of Ph.D. programs you might take. (For example, as I understand it, in the U.S. you start your Ph.D. program after your bachelor’s degree instead of obtaining a master’s degree. This is different in Europe.) $\endgroup$
    – k.stm
    Sep 7, 2013 at 21:37
  • $\begingroup$ @K.Stm. I am from Egypt, hoping to do my phd in U.S or Euorope so i have a great educational experience. $\endgroup$
    – Akram Hassan
    Sep 7, 2013 at 21:39
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    $\begingroup$ @AkramHassan If you’re heading for Europe, it’s probably a good idea to try getting a master in mathematics first. This, too, could become very demanding if you don’t know the basics, i.e. Linear Algebra, Analysis and Algebra. If you do, I think you should still first do a Master to get to know mathematics a bit better before applying for a doctorate since a Ph.D. program in Europe only consists of your thesis as far as I know. Background: I’m mathematics student from Germany and I have no idea about this stuff except that I know some Ph.D. students here and their level in mathematics. $\endgroup$
    – k.stm
    Sep 7, 2013 at 21:45
  • $\begingroup$ @K.Stm. I think that, at least same places in Europe, there are a few courses in the PhD. $\endgroup$
    – Git Gud
    Sep 7, 2013 at 21:46

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You can make it easier on yourself by taking some more courses on pure mathematics to build your knowledge and also to re-insure that this is the field you would like to study

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    $\begingroup$ I sure will, is that considerable to admission committees? $\endgroup$
    – Akram Hassan
    Sep 9, 2013 at 18:11

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