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I was very satisfied with being taught highly abstract mathematics. I think that the abstraction is both helpful and neccesarry. It allows you gain knowledge w
by constantcrying 4y ago
I was very satisfied with being taught highly abstract mathematics.
I think that the abstraction is both helpful and neccesarry. It allows you gain knowledge which can easily transfer between different area and problems. To me rigour and abstraction are the cornerstones of understanding mathematics.
I am very glad about my mathematical education, because it allows me to reduce even complex problems to special cases of things I already know.
Abstractness is not boring or uninspiring. What it gives you is a wider view, again and again you will run into applications see, that you already understand so much.
- mikrl 4y agoSomething like group/ring theory needs to be abstract. In fact, many practical applications of those things are themselves in applied math and physics. Something like differential equations or the calculus of variations is fun for examples but then you’re just teaching a physics class ;) Indeed, even the most practical applied mathematician needs to have put in hours learning the abstract things.
- ABeeSea 4y agoYea, Arnold’s ODE book is great, but it’s basically a physics textbook.
- ABeeSea 4y agoI agree with this. For example, teaching Lie groups / algebras from the historical perspective of the problem Lie was trying to solve would be a tedious exercise in multi variable calculus and PDEs. On the other hand, once you have a sense for the abstract and how it’s used, going back to read Lie’s original work (there’s a translation my Merker) gives interesting historical perspective, context, and new understanding. But I wouldn’t want to learn it from that perspective.