CS Student Wanting to Transfer, What School is Best for a Senior with Anxiety?

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BA vs. BS really does NOT matter, except in very specific circumstances. Unless you have a job offer that says you need a BS, these circumstances don't apply to you. What matters is the major, not BA vs. BS.

Looking at the courses you've completed, it looks like you might also be able to get both a BA Comp Sci and a BA Mathematics from TESU with very little additional effort. This would be arguably even better than "just" a BS Comp Sci. It opens up more job opportunities than just a standard Comp Sci degree.

The downside: you will need to take at least one Study.com class for TESU. Understandably, I don't see a Public Speaking class. There is a SDC course that is accepted at TESU as Public Speaking but it has ZERO presentations due. Just a final exam. Study.com uses a RECORDED proctor, not a live proctor. Probably 95+% of the time, nobody will even see the video and it'll get deleted without being watched.

You might also need to complete a few gen eds, like English Comp II. You've got Technical Writing, but TESU doesn't usually count that as English Comp II. If you're missing anything else, you can complete them on Sophia. Sophia is open-book and does not have traditional proctoring. They sometimes ask for ID verification, but they usually verify ID with a typing sample, if needed. Sophia's English Comp II isn't usually recommended, but it's not a bad option for students who want to avoid proctoring. If you're missing any other gen eds, you should be able to get what you need from Sophia.

No matter where you go, you'll get a new GPA. (WGU doesn't even do GPAs.) If you do ever continue to a Master's degree in the future, they'll either calculate your degree based on the last 30 credits you took OR your cumulative GPA based on all schools that you've attended. Some schools do one. Some schools do the other. A few might calculate your GPA solely based on whatever classes you took from the school where you graduated. But GPAs are weird and mysterious and don't really matter much outside of academia.

Can you explain the little additional effort further? CS requires at the minimum, Calc 1, Discrete Math, Stats.  Math degree requires those WITH Calc 2, 3 Linear Alg, then 15 math electives ?