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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!

Just to clarify, I know there is no "correct" answer, but I would really like people who have been through this' opinions/techniques. Also, I used calculus only as an example, so the same question can be asked regarding any type of math book.

PS: This is a port of my original (now closed) question on MSE, which was asked to be ported over to this community

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    $\begingroup$ It's almost certainly a bad idea to use a new book. These have many errors. For something like calculus, pick a time-honored classic because you can get cheap older editions and there is a wealth of educated opinions on the strengths and weaknesses of such texts. I personally looked at about 6-10 texts to see what's out there for the course and for proofs... $\endgroup$ Jun 14 at 23:47
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    $\begingroup$ Relying on a broad range of trusted peers and recommenders lightens the load substantially. Also, changing books is so painful that you don't want to do it more than once a decade. $\endgroup$
    – Adam
    Jun 15 at 1:56
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    $\begingroup$ Even then the cycle is usually something like Thomas -> Reform Text -> Steward -> Reform Text -> Thomas -> etc. $\endgroup$
    – Adam
    Jun 15 at 1:59
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    $\begingroup$ @Gauss as a graduate student I taught from Calculus and Concepts by Stewart. I think that may be the worst version of his text. After that, when I was hired as faculty, I learned from older faculty about texts like Apostol. As I wrote my own notes, I found Apostol was helpful to break from orthodoxy. I've not read any of these cover to cover. What is important is to come to your own ownership of calculus, no author can do that for you. Anyway, I don't have a favorite text, but there are a few of which I have low opinions. Ultimately, the problem is one size does not fit all... $\endgroup$ Jun 15 at 22:08
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    $\begingroup$ I've suggested an edit to the title to match the question better. Note that "mathematicians reading math books" (the former title) is likely very different from "math professors selecting textbooks" (the content of the question body). Consider mathematicians doing research, say. Also edited tags a bit. $\endgroup$ Jun 16 at 18:58
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One of my favorite mathematicians, when it comes to teaching, once wrote:

Can one learn mathematics by reading it? I am inclined to say no. Reading has an edge over listening because reading is more active - but not much. Reading with pencil and paper on the side is very much better - it is a big step in the right direction. The very best way to read a book, however, with, to be sure, pencil and paper on the side, is to keep the pencil busy on the paper and throw the book away. (Halmos, R.P., 1975).

So, supplementary to other answers, if I had a choice, how do I decide what book to use for teaching? Here are some thoughts:

  • Usually I look at the problems: Are they providing the opportunities to learn what is required?
  • Is chapter organization in a way that allows me to structure learning processes as intended?
  • I look at the exposition of some critical instances and examples. how are they explained. E.g. in calculus, how is the notion of a derivative explained?
  • Not to neglect: The "look and feel" of a book is important. Is language respectful and accessible and figures and graphics of high quality?

Actually, one could possibly write a book about 'what are quality books in math' and not come to an end. But to me, a main question is: Does the book help me to engage students to actively do mathematics? Put another way: What mathematics does the book provide in order to keep the pencil of my students busy? And no, I don't throw the book away :-).


Halmos, P.R. (1975). The Teaching of Problem Solving, the first section in: Halmos, P. R., Moise, E. E., & Piranian, G. The Problem of Learning to Teach. The American Mathematical Monthly, 82(5), 466–476.

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    $\begingroup$ I mostly agree, though it is interesting that you go for the problems first. They are certainly one of the most important parts of a class, but they are also the part of a book that is easiest to replace while teaching. Personally, I'd rather teach using a well written text and spend an extra hour each week to compile a problem sheet from different sources than use a mediocre text which allows me to just tell them "do problem 1-5 from this chapter". $\endgroup$
    – mlk
    Jun 15 at 7:03
  • $\begingroup$ @SCS That's exactly the kind of answer I was looking for, thank you! Out of curiosity, about how long does it take you to do this? $\endgroup$
    – Gauss
    Jun 15 at 12:38
  • $\begingroup$ @Gauss Thanks; glad to provide a helpful answer. It's difficult to judge. in some cases it's immediate (to rule books out), in other cases it takes me up to an hour, I would say... $\endgroup$
    – SCS
    Jun 15 at 18:15
  • $\begingroup$ @mlk, I guess that depends on how you intend to structure learning processes (see point 2 on my list). Actually, I like the problems be instead of the reading, so it's not about "doing problems 1-5" after reading theory. As an example from high school, there is the old classic by Dan Mayer: 3-ACT tasks from school book problems - start at 4:20. Thus I actually find the replacement of problems not so easy. $\endgroup$
    – SCS
    Jun 19 at 5:01
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I think this answer depends completely on the professor and the department.

You ask specifically about a freshman calculus text. At many schools, there are ten or twenty sections of this class every semester, so there is a tendency to want to agree on the same book for the entire department. This becomes an especially important issue if the book is non-free and sold as a single volume that covers two semesters. In this situation, the individual professor has zero choice, so there is no issue. There may be a textbook selection committee or a specific faculty member who does administrative work for all sections of the class.

The majority of faculty are adjunct. They typically have zero choice about books, especially because they're often hired at the last minute.

If someone is fortunate enough to have the choice, then I think the criteria are entirely individual. I would personally be looking for a free book. Many professors are locked into a certain book because they're used to using the ancillaries for that book. Some people have pet topics, and if their topic isn't included, they won't consider the book.

90% of commercial texts for a subject like freshman calc are extremely similar in terms of the exposition, artwork, and problems. A professor may have preferences on certain things, but they can judge those things without reading a 1000-page book from cover to cover. For instance, they may want a book that's structured so that they can skip some of the material on limits.

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  • $\begingroup$ Could you please elaborate your final paragraph a little more? What I’d like to know is precisely how the professor judges those things you mentioned without reading the 1000 pages in detail. How much is read and how, for instance? Exposition specifically seems like something that would take a sizable read to grasp, for example… $\endgroup$
    – Gauss
    Jun 14 at 23:37
  • $\begingroup$ +1. I think this answer could be improved even more by adding other reasons to not even begin considering new books (some from comments elsewhere). E.g.: (a) high switching cost when a course has been developed and runs reasonably, (b) large likelihood of errors and low quality in new 1st edition books, etc. $\endgroup$ Jun 17 at 14:43
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I will address the related question of how to find textbooks. You have to do this before you can select one, which the other answers address nicely.

A good place to start is with the AIM Open Textbook Initiative. From their site:

The American Institute of Mathematics (AIM) seeks to encourage the adoption of open source and open access mathematics textbooks. The AIM Editorial Board has developed evaluation criteria to identify the books that are suitable for use in traditional university courses. The Editorial Board maintains a list of Approved Textbooks which have been judged to meet these criteria.

I count 19 broad topics, most with multiple texts. My experience with a few of these has been overwhelmingly positive, with a very high average production value.

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I know you asked about mathematicians and college texts, but perhaps my experience in elementary school would be worthwhile. Several times I was asked to evaluate new texts for our curriculum. Since I taught only math to grades 1-6, my input was considered worthwhile.

When looking at new books:

  1. I looked to see what topics were covered. For example, our coverage of geometry such as perimeter/area was poor, and when we replaced the books I looked to make sure this deficiency would be taken care of.
  2. I looked to see if there were a range of problems for weak, average, and strong students. I also checked to see if these were clearly marked, as the average elementary school teacher wouldn't be able to make a judgement easily.
  3. I looked to see if the plan for the curriculum was realistic in terms of time.
  4. I checked how problem solving was taught.
  5. I looked to see if there were new approaches for teaching things and considered if the time spent training the teachers would be a worthwhile tradeoff for the new approach.
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    $\begingroup$ Thank you for your answer! I think the general idea does not require it to be college level, so don't worry - I really appreciate the help! Out of curiosity, about how long did it take you to do this? $\endgroup$
    – Gauss
    Jun 16 at 18:47
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    $\begingroup$ I believe I did it over the course of 2 weeks. I am not sure how much time I spent. Sometimes when I get a hold of a math book, I lose all track of time. $\endgroup$
    – Amy B
    Jun 17 at 17:59
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I am fortunate enough that I can choose my own. I typically just recommend certain classics and use my own book in class. It has always worked quite well since I do not use the typical textbooks used in most average American colleges/college Math courses. I usually tell them to get my book (since I draw heavily from the exercises there) and then I share with them an entire bibliography of books that are optional for them to buy or borrow from wherever they find them.

How do I select them? I tend to select classics over the newer texts that do not really give an emphasis on the things I want covered. So, for example, I always recommend Apostol or Spivak. I give things from a more theoretical, less "applied" approach.

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