Math Textbooks: Too Much and Too Little Info

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In summary, the conversation discusses the difficulty of understanding math textbooks and suggests that a better method of teaching would be to present theorems and proofs separately with clear explanations in plain English. Various authors and books are mentioned, including the DE book by William E. Boyce and Richard C. DiPrima, which is highly recommended, and the book "Applied Math" by Gilbert Strang. The conversation also mentions the importance of paying attention to book recommendations in math forums and suggests authors such as Courant, Rudin, Spivak, and Apostol. The Goursat three-volume calculus book is also mentioned and its comparison to other authors is questioned.
  • #1
Fletcher
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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?
 
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  • #2
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 :biggrin:
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.
 
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  • #3
Fletcher said:
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
 
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  • #4
FrogPad said:

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
 
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  • #5
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?
 

1. Why are math textbooks often criticized for having too much information?

Math textbooks are often criticized for having too much information because they tend to include a lot of unnecessary content that can overwhelm students and make it difficult for them to focus on the most important concepts. This can also lead to a lack of depth and understanding of the material.

2. What are some potential consequences of having too much information in math textbooks?

Some potential consequences of having too much information in math textbooks include increased student confusion, lack of motivation to learn, and a decrease in critical thinking skills. It can also lead to students feeling overwhelmed and discouraged, which can negatively impact their overall learning experience.

3. How can having too little information in math textbooks also be problematic?

Having too little information in math textbooks can be problematic because it may not provide students with enough practice and examples to fully understand and apply the concepts. This can also lead to a lack of preparation for exams and a limited understanding of the subject.

4. What strategies can be used to balance the amount of information in math textbooks?

To balance the amount of information in math textbooks, teachers and textbook authors can focus on including only the most essential concepts and providing enough practice problems for students to gain a deeper understanding. They can also use visual aids and real-life examples to help students grasp the material.

5. How can teachers and students work together to effectively use math textbooks?

Teachers and students can work together to effectively use math textbooks by discussing the material and identifying the most important concepts to focus on. Teachers can also provide guidance on how to navigate the textbook and assign relevant practice problems. Students can also communicate their needs and ask for clarification when necessary.

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