Originally posted by Palynkaanother useful 'revelation' is to realize that basic math up to university level is not hard and anyone will learn all of it if he just wants to. you just need to build up some routine. it's exactly like training tactics.
Math is a language. If you realize this (or what this means), then your level of math will improve dramatically.
it's all very mechanical, and after you've done it for a while you start wondering why on earth you used to think it was hard.
Originally posted by wormwoodSo true!
it's all very mechanical, and after you've done it for a while you start wondering why on earth you used to think it was hard.
Some people might get it much faster than others but below uni level I really think everybody with normal conditions can do it.
I don't math much as a language but I think this is a fairly adequate description of it. Math for me is ideas and the relationships between ideas. Once you get this you're on your road to math dorado.
Originally posted by wormwoodI think that although routine is important, you'll be able to understand much more if you 'understand' why you4're doing what you're doing.
another useful 'revelation' is to realize that basic math up to university level is not hard and anyone will learn all of it if he just wants to. you just need to build up some routine. it's exactly like training tactics.
it's all very mechanical, and after you've done it for a while you start wondering why on earth you used to think it was hard.
My point that math is a language is that mathematical operations and expressions can be 'read' and understood. Think of it this way, you can memorize the rules of grammar and without understanding a word of it, for example, know which words are synonyms of one another. But if you know what the words mean, you'll find it much easier to both learn the rules and the synonyms, etc...
Math is the same. You can train and train until you get the routines in your head, but if you understand why the routines are such, then with a fraction of that work you'll be not only able to do those routines, but apply those techniques elsewhere.
Originally posted by Palynkawhat I meant was that it's not enough to simply understand a mathematical concept or a tool, but you have to actually use it until it becomes routine. only then can you spot it in more complex constructs and apply the same idea elsewhere without tripping over.
I think that although routine is important, you'll be able to understand much more if you 'understand' why you4're doing what you're doing.
My point that math is a language is that mathematical operations and expressions can be 'read' and understood. Think of it this way, you can memorize the rules of grammar and without understanding a word of it, for ex ork you'll be not only able to do those routines, but apply those techniques elsewhere.
I think we actually mean the same thing, but you include the routine in understanding and I used a more narrow definition of understanding?
Originally posted by mlpriorI think saying that you don't have to use your imagination in maths is...well...wrong...
I agree, match is a breeze compared with English or any other subject where you have to use your imagination!
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For starters, being able to "imagine" certain mathematical structures, for instance groups, is pretty essential to their study. And being able to conjour up a bizarre step in a proof that there is, at first glace, no reason for you to even consider requires imagination. It is, perhaps, hard to explain, but it is using your imagination, if a bit different from the parts of your imagination that you use in English etc.
Originally posted by geniusi entirely agree, trying to get mathematics into the real world takes a lot of imagination. People do not realise how important maths is. It is a foundation block for so many occupations. Business solutions rely on maths (optimal feasible regions to maximise profit given marketing constraints). Carpentry requires trigonmetry whilst engineering relies on differentiational equations. Also science requires maths as well.
I think saying that you don't have to use your imagination in maths is...well...wrong...
For starters, being able to "imagine" certain mathematical structures, for instance groups, is pretty essential to their study. And being able to conjour up a bizarre step in a proof that there is, at first glace, no reason for you to even consider requires imagination ...[text shortened]... agination, if a bit different from the parts of your imagination that you use in English etc.
Originally posted by geniusI was always taught you should shy away from any kind of visualisation of mathematical concepts, as it will only work in specific situations and thus restrict the ability to apply the abstract concept.
I think saying that you don't have to use your imagination in maths is...well...wrong...
For starters, being able to "imagine" certain mathematical structures, for instance groups, is pretty essential to their study. And being able to conjour up a bizarre step in a proof that there is, at first glace, no reason for you to even consider requires imagination ...[text shortened]... agination, if a bit different from the parts of your imagination that you use in English etc.
Originally posted by wormwoodThat's the French school of Math originated by the Bourbaki group.
I was always taught you should shy away from any kind of visualisation of mathematical concepts, as it will only work in specific situations and thus restrict the ability to apply the abstract concept.
Many things can't be visualized in maths but a lot of people think that some kind of visual analogy can be very helpful at times.
Anyway anyone who ever done demonstrations and proofs by himself kniows that a lot of imagination goes into it. One clear way to see this is to try hard and hard to prove something and not being able to do it. Then you see the proof and can't you can't help but smile at the other fellow imagination in doing it.
A guy that is strongly critical of Bourbaki and their teachings is Vladimir Arnold a very strong russian mathematician with some very polarized and highly interesting views on math.