<p>Hi! I'm currently in the process of deciding which PhD programs I should apply to for the Fall 2015 semester and was wondering how high I should be shooting. I'm currently a senior in chemical engineering at Clemson University, with a 4.0 GPA (I'm expecting to graduate with at the least a 3.95), co-op experience, and 3 semesters of undergraduate research in computational work through the honors college. I don't have any papers published as of yet, but my research adviser is currently in the process of drafting one in which I will be listed as a coauthor. I'll also be taking the GRE later this week, but I've scored in the 160-170 range (verbal and quantitative) on practice tests (I'm a little more concerned with the writing section - I'm expecting to score anywhere between 4-5). Would PhD programs at schools like MIT, Stanford, and Northwestern be unrealistic for me? I'm mostly concerned that I won't be able to compete with similar students coming from more prestigious undergraduate programs.</p>
<p>Any input would be greatly appreciated. Thanks!</p>