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> At this point, either you know what all of those words mean or you don’t. If you do, great! You’re done. I'm not sure. I only have a rather rudimentary under
by Tainnor 3y ago
> At this point, either you know what all of those words mean or you don’t. If you do, great! You’re done.
I'm not sure. I only have a rather rudimentary understanding of topology, so I do understand the definition of a manifold on a technical level, but I don't know any interesting examples or theorems about them so it wouldn't be immediately clear to me why something being a submanifold is worth mentioning.
Similarly, I don't think that just reading the definition really gives you a good understanding of groups. You probably want to work through some examples of groups, and arguably, the importance of groups doesn't really become clear until you've encountered group actions.
- fpgamlirfanboy 3y agoYou skipped over the second sentence of what you're responding to: > Say you’re reading a paper or trying to implement some technology that uses a mathematical concept you aren’t familiar with In such a case you're not interested in either manifold or sub-manifold or group in and of itself. So a lack of familiarity with theorems isn't an impediment.
- Tainnor 3y agoI didn't "skip over" anything. If it's irrelevant to you that something is a submanifold or group, you also don't need to look up the definition. Reading mathematical definitions on their own just doesn't give you a whole lot of context about the objects they're describing.