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Chances for Stanford/MIT ChemE PhD?

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I'm applying to grad schools next year and I'm going to be the first in my family to pursue a PhD so this is honestly kind of nerve wracking. The reason why I am posting here is because I have good academics but mediocre research and recs.

Here's my stats:

  • Major: ChemE (top 4 of ~25 students)
  • GPA: 4.1/4.3
  • Rank: Top ~12 out of ~240 students
  • GRE: 167V/170Q/4.5W
  • Research
    • No peer-reviewed publications in refereed journals.
    • Freshman year research published in school journal
    • Sophomore year research in new lab wasn't very good or productive
    • Junior year research in same lab presented at an AIChE conference
    • Working towards a publication in same lab (but I don't know whether I will be done by grad school applications)
    • Did work study in a psychology lab sophomore year as a work-study student, nothing really came of it
  • Recs
    • Probably will not be great. Not sure what to do about this.
    • Freshman year research adviser expects us to write our own recs, it usually never works out for undergrads because we don't know how to write recs
    • Sophomore + Junior research adviser barely knows me, other than the research I've produced (which only recently started working out)
    • Most profs only know me from class
  • Awards
    • Large institutional scholarships (financial aid)
    • Two summer research grants at university
    • Speaking prize at AIChE conference
  • Orgs
    • AIChE 
    • Tau Beta Pi
  • Teaching
    • Teaching assistant for two undergrad courses and one grad level course

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I can only say rec letters matter A LOT so you probably want to talk with your sophomore+junior research advisor about that. It's not hard to write your own recs, just brag (no don't do that), maybe ask your freshman year advisor for a template or a previous sample rec letter? Other than that I think your profile is really strong, but there's no telling about someone's chance to schools like Stanford or MIT. Sometimes you need more than a strong profile, such as luck (PI in your area happens to need a new PhD student or something). If you are a domestic student, also try NSF GRFP. 

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I was curious about your home institution...

Small ChemE class (25), very small overall class (240 students). High ChemE to overall ratio; sounds like a tech/engineering school. Your test scores are stellar. And your school has a research journal...

Is it Caltech?

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