Originally posted by Palynkamath would've been immensely easier for me had I done the excercises to begin with. without solid routine, it all begins to fall into pieces at higher levels, causing many times more work holding it all together.
That's because you had/have bad teachers. If anyone tells you that the best way to learn mathematics is by doing exercises, then he doesn't know what he's talking about.
all basic math should be trained until you can't get it wrong. until it's simply unconscious and immediate pattern recognition, not thinking. thinking is too slow and error prone.
exactly like with chess.
Maths is easy. It's all about logic.
Take the concept of infinity for example.
To understand it you just need to apply it to an everyday object - a horse say.
Now lets think about the horse - it has legs at the back (two of them) and forelegs.
Two + four makes six - an even number. But six is an odd number of legs for a horse to have. Now ... the only number that is both odd and even at the same time is infinity.
Therfore horses have an infinite number of legs.
Easy.
This goes to explain why you can get so many horsepowers into small cars.
Originally posted by duecerthey usually skip all the interesting stuff.
they sap my creativity and my will to live😞
this is Math:
http://images.google.fi/images?hl=fi&source=hp&q=fractals&oq=fractals&um=1&ie=UTF-8&sa=N&tab=wi
this is Math:
http://images.google.fi/images?um=1&hl=fi&safe=off&tbs=isch%3A1&sa=1&q=cellular+automata&aq=f&oq=&start=0
this is Math
and this is Math
Originally posted by wormwoodI disagree completely. 🙂
math would've been immensely easier for me had I done the excercises to begin with. without solid routine, it all begins to fall into pieces at higher levels, causing many times more work holding it all together.
all basic math should be trained until you can't get it wrong. until it's simply unconscious and immediate pattern recognition, not thinking. thinking is too slow and error prone.
exactly like with chess.
Mathematics was never about doing exercises for me. That's why I love it! I can't think of anything more boring that repeating exercises. I think that's the sure way of getting bored with it.
2 edits
Originally posted by Palynkawhat happens when you get thrown a real world differential equation, and you need to do something concrete on top of it? can you do anything productive with it? would you have any idea what kind of tries you should be looking at first?
I disagree completely. 🙂
Mathematics was never about doing exercises for me. That's why I love it! I can't think of anything more boring that repeating exercises. I think that's the sure way of getting bored with it.
I should know them but my mind would blank out. because my routine is crap, and I remember the stuff only in a very general sense. and you can't really solve anything but the most basic school book examples (of anything) without having been exposed to hundreds of different patterns, any more than you can play like kasparov by simply learning the rules and thinking long enough. which would mean that general knowledge was useless in any real world situation. - you need to develop intuition for what kind of patterns to look for, and the only way to that is being exposed to massive amounts of variations of the topic.
btw, I 100% agree about bad teachers and boredom otherwise. but there's just no way getting around the exercises. well, there is, but skipping them is gonna multiply your workload instead of reducing it.