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 matheods 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?
Thanks in advance