> It seems that this is written out of a perspective of some missing knowledge.
Well, the author talks about what "we learned in school", not university, so that checks out but only because you two have different audiences in mind.
Well, the author talks about what "we learned in school", not university, so that checks out but only because you two have different audiences in mind.
This is not uncommon in the UK – but it is also not common either, and depends on exactly what A-level modules you did. My understanding is that it's quite rare to do exactly this in high school in the united states – but there, I think limits are taught much more heavily. I think having a clear, short statement of having "assumed knowledge" somewhere probably helps avoid these issues.
(I thought the article was excellent, and beautifully illustrated!)
It is unexceptional (indeed, expected) to get through an American undergraduate science or engineering degree without ever taking an abstract algebra course (much less the 2+ apparently expected of German pure math students).
But in any event, the top post here by Garlef is barking up the wrong tree. Division algebras, field extensions, and galois theory (per se) are not the tools to use for studying arbitrary-dimensional geometry. What you want is Clifford algebra (which Clifford himself, and later Hestenes, call “geometric algebra”) and then geometric calculus, which can be used on arbitrary manifolds, in non-metrical contexts, etc.
Basic geometric algebra should be taught to advanced high school students and all undergraduates studying any technical subject.
Math students looking for a math-style introduction to geometric algebra should try Chisolm (2012) https://arxiv.org/abs/1205.5935