I am currently applying to PhD programs in mathematics and need to complete a purpose statement as part of the application. There are several things I'd appreciate any advice you can give me on the following:
- What is a good way to end the letter in a strong way? I wanted to say something along the lines of "I greatly look forward to further understanding the intricate theory of XYZ" but this seems a bit cliché.
- I wanted to mention my specific interest in school XYZ/professor XYZ, but I don't know enough about his/her research to say something intelligent or insightful about it. What should I do? Is it better to have some indication I did my research for this school than to say nothing at all? To be clear, I am interested in the field of these professors but my knowledge is too shallow to fully understand the impact of their work. How can I add something substantive but not sound like I'm making things up to sound smart?
- For one of the schools I am applying to, a big reason I want to go there is due to their well funded program. Should I mention this or will it seem tacky?
- What is a "smooth" way of mentioning I want to work with a professor? It seems too abrupt to just say "I want to work with professor XYZ". What if this person doesn't have any current students (or at least doesn't have them listed in his/her Web page). Should I take it that this person is not currently taking students?
Any and all advice would be helpful. Thanks in advance!