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I have nothing against Princeton, just surprised to see its place (#13) in the 1990-2004 placement ranking posted by ResearchFrontier. Maybe its recent placements are indeed "significantly better than Stanford", I honestly don't know, but anyone interested in that can easily compare their post-2004 records.

^ In the placement ranking by Schmidt and Chingos, Princeton is only #13. Not saying it's not a fantastic program, but is Princeton really on par with Harvard and Stanford for political science? Yes it has the Ivy name, but so do Yale and Columbia.

I agree with puddle. You should only consider going to the program of lower tier (i.e. top10 to top20 constitutes a difference in tier, imho) if it offers you much more financial support (free money, not TA/RA) so that you will have significantly more time for your own research and coursework. When I was an applicant two years ago, I made quite a few friends during campus visits, and in the end most of us chose the highest ranked programs that admitted us, and it turned out that all programs make empty promises during recruitment. I'm not saying "fit" is less important. It's just that at this stage, there is no way you can know how that part of your grad school will work out, so pivot on indicators with less uncertainty. And congrats!

OP, the short answer to your question is, do well in calculus 1 and the gre quant section, that's something you can definitely do in one year to strengthen your application. The long answer... 1. Saying trig is not useful for polisi phd is wrong. Yes you won't write your dissertation on that, but you need basic stuff like that all the time for college level math, as well as polisci method courses if you enter a phd program with serious training. 2. Calculus 1 is more useful for you than linear algebra at this moment. Also don't waste your time on stats courses now. You need the full calculus sequence and one linear algebra to take probability theory, after that you will be in a good position to learn stats. 3. People who got into top programs typically have very high gre quant scores, but most of them don't have much math background. So relax, focus on what you can do now. 4. Be cautious about information you get from gradcafe and PSR, where people who think anything with number and greek letter is "math" intimidate you with stuff they don't really understand.