UCLA Undergrad -> PhD at Columbia/MIT?

They are not. You can go to Columbia or MIT with an undergrad from anywhere - definitely from UCLA.

Right now, focus on getting good grades and exploring what topics in computer science and math most fascinate you. Talk to your professors about opportunities to do research in one of their labs/research groups in the area you’re interested in. In the fall of your sophomore year, you’ll want to look for summer research internships, but most of them don’t take rising sophomores (mostly rising juniors and seniors).

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