[BossingAround]

Honestly, this seems needlessly painful to me. Of course, you can be scanning each sentence for a proposition, then pause, and try to reason it out, thus spending 4 weeks on like 5 pages of a 10-page chapter. But is that the best use of your time?

The bigger problem is that not every thing that the author says is within your level of reasoning. Some very simple things can be exceedingly hard to prove, and you, as a learner, don't know which is which. That's why there are the problems at the end of the chapter, which are designed for the level that you should have attained by the end of the chapter. Without solutions though, you have no way to check your understanding, and you are forced to try and squeeze every little problem from the text.

Not having solutions is simply not suitable for a self-learner. It is sufficient for a class settings, where you can ask the professor if your solution is correct.

To me, a good compromise is to provide solutions to every odd- (or even-) numbered problem. Thus, the self learners have at least half of the problems within their reach, and t he teachers can assign the other half of the problems.

[enriquto]

> spending 4 weeks on like 5 pages of a 10-page chapter. But is that the best use of your time?

Look at it as the best use of paper :)

Many math books are dense. They don't bullshit you around. Spending several hours on a single page is the normal usage.

[moomin]

Yeah, and for better or for worse, it is the best arrangement. I remember ploughing through Alan Baker’s number theory book. You have to sit with a pencil and paper and convince yourself of half the steps, but you sure as hell know the material afterwards. And you do need the skills you gain by doing this.

[082349872349872]

> And you do need the skills you gain by [engaging].

The slogan I've heard is: "Mathematics is not a spectator sport."

[moomin]

I haven’t heard that one before but it’s on the nose. I have heard Euclid’s much older “There is no royal road to geometry”.