This document gives some very brief advice for students interested in applying to graduate school. Much other information is available, for example:
Top-tier schools such as UW are flooded with applications from candidates with excellent qualifications, and have to make hard decisions among these, selecting just a few to admit.
The process is inherently subjective. It includes:
I don't think that tailoring your application toward a single faculty member is necessary or good. You don't know whether that person is still actively working on the same projects you found on their website, or is interested in new students this year. However, the advice to tailor your application by mentioning specific faculty members is very common, and some faculty at some schools may be swayed by it.
Just as with an academic job, you shouldn't be depressed nor angry if you don't get in your first choice. There may or may not have been anything you could do about it, and you don't understand the reasons behind the decision. Getting mad is immature and unprofessional, and it won't do you any good.
You are likely to have to make a decision among different schools with differing advantages. If the decision is easy, lucky you! This advice is for people who are having a hard time deciding.
Choosing a graduate school is in part a rational decision, but in part an emotional one. You may just know which place is best for you. Many people find it helpful to make a table of pros and cons of each choice. If at some point you start fiddling with the weights of each factor, then you know that you have already made your mind (though you might not yet consciously know your choice) and are now just trying to justify it.
Don't choose the school with the one professor you are dying to work with. Instead, choose a school that has at least two faculty members you can imagine working with. You never know when a faculty member will be denied tenure, will form a start-up company, or will be hit by a bus. These are all the same event from the student's point of view, because the student has lost the advisor. (The different events do feel different to the faculty member.) Occasionally, well-meaning people have different styles and just don't click or have good chemistry. For all these reasons, it's important to have a backup advisor in case things go poorly.
Your resume (known in academic circles as a CV or curriculum vitae) should include a list of your publications. This is concrete evidence of your ability to do research, which is one of the most important criteria for admission to a research-oriented graduate program. Don't make the admissions committee work to discover your papers, for instance in your statment or buried within descriptions of your work. If you include submitted papers that have not yet been accepted, then you must list those in a different section. If you intersperse them with the rest of your publications, then you will give the impression of dishonestly trying to pad your resume, which will hurt rather than help your chances.
Don't bother to include descriptions of your class projects. It doesn't add anything, because readers know you have done projects in your classes but also know these are probably small in scope and not indicative of your true abilities. Do discuss projects that you undertook outside class, including for research or internships.
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