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I will describe what I mean by the above with an example.

Suppose you are a professor, about to teach a first Calculus course in a university. There are dozens, if not hundreds, of calculus books out there. How do you choose which one to use as a reference for your course? You may narrow it down to a few books, but how do you actually read the ones in the final list to make a choice?

In another example, continuing from the preceding one, maybe you just choose the one you used as a student, but next month a new Calculus book comes about and attracts a lot of attention. How do you read it to know if, next semester, you could use it instead of the original one?

I cannot possibly believe a math professor has the time to study them in depth to know what they contain, what are their pros/cons, etc, as, at least in my experience, it takes from weeks to months to read a book in depth, doing some exercises, even if you already know most of the contents.

So do they just read the books like a novel? Do a quick en-passant through each one to have some idea of the differences?

I would really like to know the answer, since, as a student, every good book I know has been recommended by someone else - but, at some point, I would like to be able to make my own judgement.

Thanks in advance!

EDIT: Just to clarify, I know there is no "correct" answer (which is why this is a soft-question), but I would really like people who have been through this' opinions/techniques.

EDIT 2: As requested, this question has been ported to the Math Educators SE. You can find it at How do mathematicians read math books?

Gauss
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    For regularly occurring courses like calculus, if a professor gets assigned to teach that, I doubt many are concerned about which book is being used. I think they often just keep using the book that school typically uses, e.g. Stewart Calculus. For upper level courses, I think most just choose a book they like. I highly doubt they are trying to choose the optimal over all possibilities. I have had professors who used a book for a course because they heard good things about it, without reading it first (just reading the contents, and skimming it), to see if they like it. – Joe Jun 13 '21 at 13:35
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    As far as Calculus goes, most books are exactly the same as far as the presentation of the topic goes. They barley contain different results, or change stuff. Some construct $\mathbb{R}$, others do not. How they construct $\mathbb{R}$ can be different too. This applies to other fields too. When you study more advanced topics there are more different approaches to different topics, and the literature is way more diverse. But the beginner's literatur is almost always just the same, where the authors change it up in writing style, and exercises. The exercises however will still be similar. – Cornman Jun 13 '21 at 13:37
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    If you want to read a book, just take some and get starting. Maybe at some point you will notice it is not for you, and then you can try a different book. Then maybe you will get to know different authors and writing styles, and choose like that. Once you are more familiar with reading math books, you can then study more advanced books, that leave more to the reader and so on. Maybe books you struggled with before. For example, I like the writing style of Rotman. However I find the exercises in his books to easy, but that makes them good to study alongside a lecture, or as introduction. – Cornman Jun 13 '21 at 13:39
  • Calculus is also at the beginning of the "food chain" in mathematics. Other considerations besides the quality of the book come into place. Stewart's Calculus is a good example, an awful and expensive book, yet widely used. – plop Jun 13 '21 at 13:40
  • @plop I do not know the book of Stewart, but may I ask what you think makes it awful? – Cornman Jun 13 '21 at 13:40
  • It lies to the student: One example among many, claims a certain steps integrate all rational functions, while they don't really do. It presents inappropriate techniques, which set up students for failure: Example, trigonometric substitution. And it is huge, with really thin pages. With that much space I would expect them not to be missing stuff and lying about it. And it is expensive. – plop Jun 13 '21 at 13:50
  • I don't think this question is appropriate on MSE. It's about the professional practice of mathematics educators and not about mathematics. – Rob Arthan Jun 14 '21 at 02:00
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    Good point, maybe post here: https://matheducators.stackexchange.com/ – Joe Jun 14 '21 at 03:02

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