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You really don't see that type of text appear until university these days. Most grade school, and highschool math texts that I have seen attempt to show you whe

You really don't see that type of text appear until university these days. Most grade school, and highschool math texts that I have seen attempt to show you where most things come from, and attempt to show the steps. Now, this doesn't mean that they do so in an effective way (there's often that random ass step which doesn't make any sense at all), but they do try. The struggle mostly comes from situations where a) people just can't follow the explanations at all, since the reasoning is not explained well enough, or there are jumps too large, or b) people who have trouble adapting past strategies and concepts to more novel situations. For example, they might know how to solve some class A of word problems, but once you switch the word problems to solving the equation in the other direction, they just get lost. I think most of the 'left as an exercise for the reader' stuff appears once you get to a high enough level that you a) assume that the reader is proficient enough and b) that the reader actually cares enough about the subject to be able to do so. For example, my friends taking a bunch of pure math subjects get that crap all the time. "So we've proved X theorem for Y case, Z will be left as an exercise", and they eat it up (partly because it really is an exercise). Now, I still think a lot of the time, it's inappropriate, and just used cause the writer is lazy, or has used up too much space on diagrams (especially in physics textbooks...).

gersh 16y ago
In high level texts, the "obvious" problems often aren't easy. I think there is a strong element of mathematician arrogance. If you can't figure it out, you don't deserve to know. This may go all the way back to Pythagorus, who ran a secretive cult. There are actual exercises, where solving it is just a matter of applying some concept. However, a lot of math books have things where you have beat your head against the wall to figure them out. Although, the internet has made it easier to lookup, nowadays. School textbooks often try to make things simpler. However, when these texts are written based off of older texts, which skip steps, they may inherit the style of the older works.

gersh 16y ago

In high level texts, the "obvious" problems often aren't easy. I think there is a strong element of mathematician arrogance. If you can't figure it out, you don't deserve to know. This may go all the way back to Pythagorus, who ran a secretive cult. There are actual exercises, where solving it is just a matter of applying some concept. However, a lot of math books have things where you have beat your head against the wall to figure them out. Although, the internet has made it easier to lookup, nowadays. School textbooks often try to make things simpler. However, when these texts are written based off of older texts, which skip steps, they may inherit the style of the older works.