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I am planning on doing a tripos III this year in order to explore my interests and improve on a few bad grades in my undergraduate coursework. I would like to aim for a top 5 Math PhD program.

I have heard that the tripos exams are after most of the admission period in the US. Given this, how much of a factor does simply attending the tripos play in getting an offer for a PhD?

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If you are aiming for attending a top five mathematics department in the U.S. immediately afterwards, Part III of the Tripos plays almost no role. It's not uncommon for students to do Part III, but often after already being admitted to the U.S. department and deferring for a year. Occasionally someone who was turned down the previous year applies again while doing Part III and is admitted, either because their application looks stronger or because they have better luck. However, attending Part III plays little role in this. The bar for Part III admission is lower than for top five U.S. Ph.D. programs in mathematics, so merely being admitted is not in itself a factor. The Cambridge academic year doesn't even start until October, so there's generally no useful way to get letters of recommendation from Cambridge faculty based on Part III: they simply don't have enough to say at the point at which letters are needed. The net effect is that you are applying with letter writers based on the previous year, and the only function of Part III is demonstrating that you are doing something productive with your time (it certainly looks better than taking a year off, for example).

  • That is a bit disappointing. Are people with a distinction in the tripos guaranteed PhD admission at Cambridge? If this is not the case, then there seems very little point to my taking it and it seems like a bad idea in general anyway. – Epicurus Feb 23 '15 at 9:02
  • I don't know the Cambridge admission policies regarding the Tripos. In general I think it's a very worthwhile program and a wonderful learning experience, just not ideally suited to building credentials for US graduate admissions (because of the timing issue). By the way, your application might still look stronger even if you can't get letters from Cambridge faculty, because it will include your senior year accomplishments as an undergraduate (and any bad grades from earlier will be further in the past). – Anonymous Mathematician Feb 23 '15 at 17:07
  • Most current (pure maths) Part III students applying for continuation get an offer conditional on being top third of the people getting a distinction. With this kind of offer, it is hard to get any funding. It is also difficult to plan with this condition, as a top third distinction cannot be predicted reliably. – Zahlendreher Aug 27 '15 at 18:25

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