Hmm, a good question. I think the smartest path to take here is to speak to Columbia, specifically the Career office, telling them your concerns about the JTerm program given the lack of official internship. Honestly, Columbia is a great program with a great name, and can likely get you where you want to be. Haas is a great school too of course, and perhaps a bit better located given your goals, but prestige-wise it's about the same level as Columbia (meaning its not Stanford
), so if you DO decide to reapply, you are taking a big risk, even with your very strong profile.
Hope this helps, and if you have any further follow-up questions, I'll be happy to answer.
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