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Still sounds suspect. No explicit examples worked out all semester?
I was a math major, and I don't find this suspect at all. Beyond 100-level courses, college math is primarily about logic, often applied to numbers, but also often applied to non-numbers. It would be entirely reasonable for a full semester of a class not to involve any engagement with numbers beyond the kind of basic everyday stuff, and explicit examples would be irrelevant, because those examples wouldn't involve numbers anyway. A majority of college-level math is writing essays.
However, on that note, I would say that I disagree with the notion that this would make math, or certain types of math, a verbal field. The fact that it's primarily about writing essays doesn't make it verbal, because the essays are based around rigorous rules of logic, which is what makes it a quant field, rather than a verbal field where such rules just don't matter.
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Probably the class that stood out to me the most as having basically zero concrete examples that cash out on the level of actual numerals was differentiable manifolds. Who the hell wants to actually describe any concrete examples of those objects all the way down to the level of numerals?! That just sounds painful. I mean, maybe there was like one simple example of a problem on a torus way back in the introduction part of the course, just to give a nod to the idea that one could go get at real problems, but I actually don't remember anything other than like, "Oh, here is an example of how the state space of a dynamical system could be represented as a torus or a cylinder, or..." but stopping short of actually solving any particular problem on them.
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I believe him. For tertiary math education the actual numbers are mostly irrelevant. Consequently the undergrads/profs don't bother and just use "some constant C" or in the rare occasions numbers mostly < 10 or 100.
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There were, but I don't remember numbers being used, Just stuff like Z to represent the integers with x,y elements of z, never explicitly saying x = 12, z = 25 or whatever.
Replying here only to avoid unnecessary duplication.
I'm a doctoral student in pure math. The reason I have a hard time believing it is that there was computation in the same courses described. A few that come to mind:
Ring theory: primary decomposition of ideals. Of course it's defined abstractly, but pretty much any concrete exercise would involve ideals of finitely generated polynomial rings and required computation.
Differentiable manifolds: Early on, we worked out a formula for stereographic projection and its inverse. Lots of other examples in low-dimensional spaces.
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