Math Textbooks: Too Much and Too Little Info

[Fletcher]

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?

 

[ranger]

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]

Sounds like a James Stewart text

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?

There are certain things that cannot be explained without "mathless" language. I do understand what your point is though. It is for such reasons I've taken a liking to authors such as Bob Miller, W. Michael Kelley, and the DE book by William E. Boyce and Richard C. DiPrima is nothing short of magnificent. If you plan on getting a DE book, this is the one. There is this other DE book, Differential Equations and Boundary Value Problems, by C. Edwards and D. Penney; this is the worst DE book ever! The authors write like a bunch of newbs with no organization whatsoever and the language is nothing special.

 

[FrogPad]

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?

Check out Strang's Applied math,
https://www.amazon.com/dp/0961408804/?tag=pfamazon01-20

 

[arevolutionist]

Check out Strang's Applied math,
https://www.amazon.com/dp/0961408804/?tag=pfamazon01-20

Gilbert Strang... That is the professor from MIT; I enjoyed his Calculus book. Though, I only read a few sections of it.

http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm

 

[MathematicalPhysicist]

this is why you should pay attention to advice given in maths forums about books.
and take books written by people such as courant,rudin,spivak,apostol, etc.
btw, iv'e looked at the books of goursat, how would you folks rate goursat three volumes on calcs compared with the above authors?