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)"?