Jim VK

You sum up your argument in the last line, but the grammar makes it difficult to understand your point. The supporting paragraphs show benefits to both collaboration and competition, with a little more strength on the collaboration side. If you're saying you agree that collaboration offers more value than competition, I'd recommend refining your response.

The site was hacked, but it's being addressed now. Thanks for your patience!

Congratulations BeccaFL!

Seems like you already have your analytic philosopher recommendations covered. It seems unlikely that your third recommendation would be held against you in this situation.

I'd use their work address. If they're a professor, I'd list the school where they receive correspondence.

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Yes, it's worth going to your university's employment page (and reaching out within your department). Many jobs get cross-posted, but you can sometimes get more attention coming directly from the university.

Undergrad GPA may be challenging for U-M and UIC. Maybe reach out to alums to get their recommendations.