QuoteOriginally posted by: quantstartQuoteOriginally posted by: DoubleTroubleAt the moment my main choice is Imperial College in London. I have good knowledge about some of the professors at Imperial, since I cited their work in my thesis, and read many of their articles. However, I realize that the competition is extremely high for a position there. My best chance is at my current university since I know every professor, and one of my teachers in functional analysis (i did very very well in that exam ) is the committee for choosing new ph.d. students. Also my thesis supervisor is very well-reputed professor and I hope he has good things to say about me. At least my grade was good, but he is very very reserved with praise (basically, everyone who is not Hörmander is bad. Even himself). Also, what is promising is that they are hiring a new professor in mathematical finance and numerical methods.Again, for full disclosure, I went to Imperial (although not for financial mathematics, for fluid dynamics) and had a great time there. If you can get a place there I would certainly take it. One of my friends is currently studying the MSc in Finance and Risk Management. He is having a great time, besides having to get back into the groove of being a student at 30...!Thank you very much for your answer. I really appreciate it. May I ask some more specific questions about how it is to take you Ph.d in London? How are the environment, working conditions, social benefits, salary etc.? The reason I ask is because I have discussed the idea of pursuing a Ph.d with 3 professors (whom I know well) at my school. Two of them took their Ph.d at Princeton and the other one from MIT. They all say that it was a really bad research environment for Ph.d students. You didn't get your own office, no respect or encouragement from senior researcher. You were basically just a student on scholarship. However, with that said there schools are brilliant in many other ways. They all said that Sweden, Denmark, or Germany is probably the best place in the world to take your Ph.d. from that perspective. It is more like a full time job, with decent salary (no need for scholarships), and all the social benefits that come with a job. I am very much aware that this was some time ago, and that things probably changed since then. I am really interested in hearing about your experience from London.Right now I am sitting here writing a body for my application letter. To my own university I don't need to be extremely formal (in fact, i think they can be putt off by it). Since there are many people that will read the letter I can't address it to a specific person. Usually I write "dead sir or madam" but I feel that it not appropriate to my own school. What is a more neutral way of starting off a application letter?Thank you in advance!