2026-08-21 20:57 UTC
I was wondering how the order of the courses you have to take as a math major can influence your way of perceiving mathematics.
As far as I know, some systems tend to leave more abstract courses (like algebra) for the second year of university and concentrate the more "applied" ones (like physics, informatics) in the first year. This is the case, for example, at ETH Zurich. However, in other places like Italy, algebra I is taught at the early stages.
What is your opinion on this: should math majors be immediately educated to abstraction with such courses? Or has this any influence at all, other than making it easier for first year physics and math students to switch between the two degrees?
Replies (1)
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@caten@mathstodon.xyz 2026-08-21 21:12
@eudaemon@mathstodon.xyz People will say that our modern approach is unnatural because people originally studied things like the ring of smooth functions on a torus without having defined rings, manifolds, or even the real numbers properly. The issue is that if you do all the historical development first you'll take forever to get to the modern perspective, but the modern treatment frequently risks feeling piecemeal and undermotivated. I do think the order you learn things matters, but I also think what you get out of a math curriculum varies a lot from one student to the next.