Write about coursework/background or research first in letter of intent? (and misc. question) I am graduating next spring with a Math and Statistics BSc, and am currently applying to graduate math and statistics programs. There is program in particular that has caught my attention. It's essentially a pure and applied stochastics Ph.D. program in the UK. The program description mentions that coursework constitutes an important part of the program in the first few years, and that relevant math background is important in the admissions criteria. However, in the latter few years research becomes a critical aspect of the program, and consequently research potential is also important in admissions.

Thankfully I have a strong coursework and research background that is relevant to this program, and will describe both of these aspects in my letter of intent. What I'm not sure is which I should discuss first. My impression is that since selection committees are viewing hundreds of applications, it is necessary to get the most important information written early on in the letter. I'm unsure if I should mention my related advanced coursework or my related research first. I would guess that research should come first since research potential is less common than a strong coursework background. Any thoughts on this is appreciated.

Another question I have is: should I mention the names of some of the faculty I've worked with in my letter? From what I've been told my previous and current research supervisors are respected and well known for their work in numerical methods and stochastics (respectively). I'm also currently taking an advanced graduate course in stochastics with one of my referees who is apparently very well known as an expert in stochastics. Something like "in my current research supervised by Professor X... (etc)"?

Thank you!
Put aside the details for a moment and think about the larger picture. You want your application to support your suitability for the program and your likelihood of success. Everything should support that and you have limited space to express it. For a doctoral program research is primary, so research experience, especially if guided by well seasoned and respected professors is a key message. Naming them is easy and may help and can't hurt. 

As to already being grounded in the required coursework, that is not trivial, but less important. There is time after you begin to decide which courses you need and which you don't, but having a solid background is positive. Your CV or transcripts will already speak to these, of course. 

So, the message is, I'm a great candidate, my background coursework and research has well prepared me, my interests and work habits will propel me and others can attest to my dedication and good results. Fit everything else around that message.