<p>You’re actually allowed to enroll in virtually any math course. The placement test is “advisory”, so you can actually enroll in pretty much whatever you want at this point. You could take Linear then Vector if you really want to retake both of those courses. Vector usually comes after Linear, so starting with Vector would also be reasonable. But most people don’t like Vector very much. I would personally recommend forgetting those courses you’ve already taken and going for Combinatorics with Shahriar, if you think you’re up to it. I know a freshman who did that last semester with a similar background and it went well.</p>
<p>As for CS, you’d have to ask a professor first, but you will be allowed to skip 51 and choose between taking 52 and 62 next. 62 then 52 is probably the best idea.</p>