For this list, I'm basically assuming that I'm interviewing a candidate for a Ph.D. level (or equivalent) numerical analyst R&D type position. If they don't feel comfortable discussing the basics of these items, then they probably can't do too much more for us than algorithm plug&chug. Which has its value, but not what I had in mind.
That said, I also wouldn't expect someone to write out implementations on a whiteboard under pressure (I'm not a Google recruiter). I'd be more interested in prodding their brain to gauge their general level of understanding, which is (I'm pretty sure) how hiring committees for mathematicians in academia operate. If they have a good foundation, I think it's less important that they've rote memorized implementation details.
That said, I also wouldn't expect someone to write out implementations on a whiteboard under pressure (I'm not a Google recruiter). I'd be more interested in prodding their brain to gauge their general level of understanding, which is (I'm pretty sure) how hiring committees for mathematicians in academia operate. If they have a good foundation, I think it's less important that they've rote memorized implementation details.