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

Tell us why doing research in your chosen field is important to you. We'd like to know what makes you tick, why you are committed to doing a Ph.D., and what you hope to do with it (if you've thought about that yet). If your background is unusual, tell us about it and how it bears on your Ph.D. plans. This section can provide useful context, but keep it relatively short; spend most of your time on the research you've done and what you hope to do in the future.

Tell us about the research you have done, if any. We 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 us 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 us an idea of what you might do in graduate school and gives us additional insight into your readiness for research.

Tell us 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 the names of specific faculty if you know you want to work with them. This helps to ensure the right faculty will read and evaluate 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!

- Jonathan Aldrich