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I accept theorems on faith, without proof.

Sorry, just found the analogy funny. My point is: I really do not like math textbooks (I refer to the calculus/DE level textbooks I have, and my memory from high school of finding math textbooks nearly unreadable). They seem to employ the least effective method of imparting knowledge by simultaneously giving too much and too little information. Here's what I mean. Typically you'll see something like this:

Up until now we have only dealt with ... But what about the case that... Recall from last section [equation]. [long semi-proof-ish derivation with intermittent brief lines of text that ultimately isn't easily digested] Hence we have [some theorem] [theorem is highlighted in a special block] [examples] [problems]

I find when I read a math textbook I cannot follow it without taking a step back and figuring out what the purpose of various segments of text are. I often think I would find textbooks easier to follow if it were just a series of theorems and proofs separated by headings. In any case a completely mathless, "plain english" explanation of what's going on should always be present. It is a math textbook yes, but isn't the purpose to teach?

Sorry, just found the analogy funny. My point is: I really do not like math textbooks (I refer to the calculus/DE level textbooks I have, and my memory from high school of finding math textbooks nearly unreadable). They seem to employ the least effective method of imparting knowledge by simultaneously giving too much and too little information. Here's what I mean. Typically you'll see something like this:

Up until now we have only dealt with ... But what about the case that... Recall from last section [equation]. [long semi-proof-ish derivation with intermittent brief lines of text that ultimately isn't easily digested] Hence we have [some theorem] [theorem is highlighted in a special block] [examples] [problems]

I find when I read a math textbook I cannot follow it without taking a step back and figuring out what the purpose of various segments of text are. I often think I would find textbooks easier to follow if it were just a series of theorems and proofs separated by headings. In any case a completely mathless, "plain english" explanation of what's going on should always be present. It is a math textbook yes, but isn't the purpose to teach?

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