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I can tell from personal experience that I only properly understood simpler mathematics when I started learning more complicated one. For instance, in linear al
by js8 10y ago
I can tell from personal experience that I only properly understood simpler mathematics when I started learning more complicated one. For instance, in linear algebra, finite dimensional (euclidean) vector spaces became a cakewalk once we started talking about functional analysis.
So, I think, even if you don't need that particular stuff in your work, it's still a good training.
Also, there has been a pushback against "rote learning" in the past couple decades. I believe that our minds need repetition in order to learn patterns and understand abstractions properly. Yes, you forget most of it, but without it, you won't learn it properly. I don't think you can be any good in any field without lot of time spent on boring and repetitive things (AKA "work").
- Davidp00 10y ago>I can tell from personal experience that I only properly understood simpler mathematics when I started learning more complicated one. That's interesting, I have similar experience. Maybe that just means we didn't learn the original material well enough?
- alejohausner 10y agoOne of the commenters to the original article talks about this phenomenon specifically. Each math course you took taught you some ideas or techniques, but those techniques weren't really learned until you used them in the next course. For example, you didn't learn algebra well until you used it in calc 1; calc 1 skills are really cemented in difeq. https://micromath.wordpress.com/2011/05/17/time-lag-in-learning-mathematics/ https://micromath.wordpress.com/2011/05/17/time-lag-in-learn...
- randcraw 10y agoBut the only way to maaster new material is to apply it to something more advanced, rather than just practice it. Rote takes you only so far; you can solve only problems you understand already. But learning new kinds of problems expands your understanding of the limits of the concepts and techniques you already know.
- deleted 10y ago[deleted]