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I’d argue that people need to be taught basic group theory and abstract algebra first, preferably in the form of puzzles to get familiar with more abstract thin
by PartiallyTyped 4y ago
I’d argue that people need to be taught basic group theory and abstract algebra first, preferably in the form of puzzles to get familiar with more abstract thinking, and to see things in terms of composition of objects instead a of mixing numeracy in the mix.
I think that numbers create all sorts of problems because people focus on them as they are familiar and miss the bigger picture.
- qsort 4y agoI don't think it really works, at least not for most people. Abstract algebra (i.e. actual algebra, as opposed to doing useless stuff to poor polynomials) requires one to have developed the mathematical maturity to iron out informal thinking. Good luck explaining "prime" and "irreducible" are not the same. I think a path that would work better is through problem solving, like olympiad problems. But even that definitely isn't for everyone.
- yellowcake0 4y agoThis reminds me a bit of the New Math pedagogy, popular in the US during the 1950s-1970s. Without the proper context, group theory and abstract algebra are deeply uninteresting subjects. It would be like trying to read Bertrand Russell before you learned your ABCs, ridiculous. It's important to start with numbers because they are familiar.