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> I still don't know why something is "efficient with" (a coefficient). That's just a name. You don't need to know the etymology to understand the topic at ha
by bonoboTP 7y ago
> I still don't know why something is "efficient with" (a coefficient).
That's just a name. You don't need to know the etymology to understand the topic at hand. But if you want to know, you can think of co-efficient as "together-effector". In 3x, 3 is a coefficient of x, as it's something that "acts together" with x. There isn't really much more to it. You don't understand concepts by studying their names in much detail.
Another thing to get used to is that the same word may be used for different concepts in different contexts (or different words for the same thing). Often there is very little connection between them. You have to accept this as a fact of history. You can of course try to look for connections, but don't get frustrated because of not finding any. And some concepts are just badly named. Naming things is hard. Don't try to deduce things based on the names of things. Learning to understand names as just labels is an important step in acquiring good abstraction skills necessary for math.
I think this may be an issue for certain people that they approach math from just the wrong angle. The jargon and terminology is of course important for understanding of the content, but the prerequisites are not really lingo-understanding, but concept-understanding. Unlike in other fields, you don't learn math by pouring over the text and reading page after page. You read something and try to understand it. You play with it, you stand up, take a walk and try to work out why something is the way it is, think of examples, try to clear up what you don't quite get. You cannot use the same learning tactics that you'd use for, say, accounting or humanities. The pages read per hour is pretty low in math.
- ColinWright 7y ago> you don't learn math by pouring over the text and reading page after page. You read something and try to understand it. You play with it, you stand up, take a walk and try to work out why something is the way it is, think of examples, try to clear up what you don't quite get. Absolutely this. Math is a not a spectator sport, you can't acquire the skill and knowledge by reading. You must engage with it, fence with it, wrestle with it, make it your friend and spend time with it. I remember not so long ago playing with some equations and accidentally proving Pythagoras' Theorem. It wasn't new, it wasn't deep, but it was satisfying, in much the same way as getting code to perform as you want, accomplishing some task in an elegant way. But if you don't spend the time, you'll never get the insight(s).
- bonoboTP 7y agoYes, I think some people falsely learn early on that stumbling upon something they don't quite understand is a sign that they are failing. I sometimes even think (though I'm not so sure) that having too good textbooks can be an impediment for above-average students as they have less to wrestle with and things are laid out and pre-disgested too much. I may be wrong though, because you can then just get to the next levels until you hit the wall. But I feel like anecdotally I got good value from deriving some basic things and reorganizing the somewhat badly presented materials in some of my classes. Later on I found very good American textbooks (although widely out of the reach of my wallet at the time), from MIT etc. which were crystal clear in some of the intuition that I had to sweat out for myself. Maybe I could have spent that energy at higher levels, though.
- mygo 7y agoA good textbook is indispensable. The difficulty of a student is knowing which book is good, and which could be doing a better job at teaching. Is it a difficult subject or do you need a better book?
- bonoboTP 7y agoIn my country (Hungary, but I saw similar attitude in Germany as well) its not unusual to learn entirely from the lecture material (own notes or provided script and assignments) without any textbook. Some people do get a book from the library, but it's not really expected from you.
- mygo 7y agomy original comment before editing said book/teacher. I use them interchangeably, but I hope the message is still there. Namely: Is it a difficult subject or do you need a better teacher?
- nkrisc 7y agoMore people should play with math like they play with new programming languages or tools. I've learned a lot by just trying to describe in geometric terms the relationships among shapes I see around me or use in my design work. I learned more about trig working out what angle I needed to input in some design software to make a line cross two exact points than I ever did in high school. I'm very much a visual learner so I find geometry in particular very satisfying since I work out relationships visually (and then mathematically to prove it).