You only need to do Big-O proofs at work if your job is thinking up entirely new algorithms. But that *is* your CS theory professor's other job (besides teaching), so they think it's really important to know.https://twitter.com/EmilyKager/status/967165799071809536 …
That's a pretty good indication that you should need to learn it for a PhD, and be able to ignore it for a BA/BS.
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Generally BA/BS should prepare you to locate & make practical use of results in your field of study, PhD should prepare you to develop new results.
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