To be fair, some of us learned about quaternions over finite fields before anything about 3D graphics. The first time I heard about this application of them, I was gobsmacked. Saying this because my professor for that course was quite excellent.
Nice! For undergrad, I was 2 courses shy of a math major || CS major, but then I saw neither was ABET accredited. Wat? Not to worry, because the CS & Eng major was accredited but required physics and chemistry for engineers series, interfacing, computer architecture, and a load and store (or was it compare and swap?) more electives approximating an EE major. It was really an EE/CS program but they couldn't call it that for historical and intercampus political reasons.
I think most of the difference in mastery of a given topic in an academic setting comes down to the skill and interactivity with a competent and expert lecturer who also has expertise in the additional domains of public speaking and teaching. Ken Joy and Sean Davis were the virtuosos of teaching at UC Davis: massive and accessible brains. Intellectual curiosity and an semi-extroverted personality help too.
Or over the reals. I have studied quaternions a number of times but never studied 3d graphics. They are interesting algebraically as part of the sequence of divison algebras reals, complex numbers, quaternions, octonions, nothing. https://en.m.wikipedia.org/wiki/Hurwitz%27s_theorem_(composi...
