Advice on writing a Ph.D. statement of purpose for CMU

Tell me your personal story, but don't overdo it. I'd like to know what makes to tick, and I'd also like to know why you are committed to doing a Ph.D.  But also keep in mind that not every story is going to stand out.

• Students in unusual situations might want to say more.  Often these situations entail more risk (will the Ph.D. work out for you?) but perhaps more upside as well (your special experience brings something novel that you can leverage, or shows your unique character/drive).  Are you coming back to a Ph.D. after 20 years in industry?  Did you switch fields?  Did you overcome some tremendous adversity?  Why and how?  If you can explain in a compelling way, it can work in your favor.
• Conversely, if you are in a "typical" situation it's OK.  Tell me a little bit about  you so I know where you are coming from and can get an idea of why you want to do a Ph.D. and what kind of student you would be.  However, spend most of your energy and space on other aspects of the application.
  

Tell me about the research you have done, if any.  I want to know that you can describe the problem you confronted, argue that it is important and was challenging to solve, compare (briefly) to prior work, and explain your technical solution and how you validated it at a high-level.  Doing this in a short essay is hard, but if you can do so effectively it's a very good sign for research.

Tell me about some problem you are interested in.  It doesn't have to be the only problem you want to work on, but it should be a good scientific problem.  You should explain what is the scientific question, why it is important, why it is hard, and why it is open.  You might give some ideas for an approach to solving it, though characterizing the problem well is often critical.  This gives me an idea of what you might do in graduate school and gives me additional insight into your readiness for research.

Tell me the general areas you are interested in.  This is your opportunity to show you are interested in more than just the problem above, if you are.

Mention my name if you want to work with me.  This helps to ensure I'll participate in reading and evaluating your application.  It's OK to mention more than one name, but naming the whole department is superfluous.

Finally, good luck with your application! CMU is very competitive and unfortunately we do not have the capability to accept all applicants who might succeed here. But professors like myself are excited to see your application, and (in the best case) to have you come here and join us...the best part of our job is working with creative and talented students like you!