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I’m currently interested in textbooks, especially the ones in math and physics that are used at the high school, undergraduate and graduate levels and, given the experience of the people on this website in using and teaching from these textbooks I’d appreciate your opinion on the following questions:

1) How do you choose which textbooks to use for your courses? (Which criteria do you employ? E.g. appropriate selection of exercises, etc.)

2) How have textbooks in your discipline(s) changed over the years (e.g. legibility, use of figures/examples, number of exercises given, how challenging they are, use of online resources,…)? (if they have changed at all) and do you find these changes beneficial or detrimental?

3) Do (and how) your criteria for choosing a textbook change when choosing an undergraduate or graduate textbook?

I welcome all of your comments regarding these and other questions related that you may deem relevant.

Thank you all for your time.

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    $\begingroup$ Unfortunately, too often, the abundance and cost of the online homework system is the guiding factor. Certainly excellence of exposition and great in-text problems are easily beat by a different book which happens to fit some existing publisher-level agreement at some universities. The academic freedom to not use online homework and/or to choose one's textbook is a luxury which too many of us may soon loose. $\endgroup$ – James S. Cook Feb 26 at 3:16
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    $\begingroup$ Question also asked at academia.stackexchange.com/q/144663/12339, but closed there because of lack of focus. $\endgroup$ – J W Feb 26 at 12:31
  • $\begingroup$ See also matheducators.stackexchange.com/questions/4477/… $\endgroup$ – Chris Cunningham Feb 26 at 14:39
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1) Primarily I choose textbooks based on the needs of the class (and the students's backgrounds and goals) and what it is preparing for.

  • For high school, if it's for AP tests or IB tests at the end of the year, I'll very likely try to find textbooks (or materials) that explicitly state they help prepare students for that. The best books contain questions that are similar to the actual tests, or at least cover the topics necessary. Not to say I'm teaching to the test, but, for example, I need students to be good with AP-style multiple choice since there is a large multiple choice section on the test.
  • For undergraduate, a deciding factor would depend on if it's math for math majors or non-math majors. Book for math majors would need to have lots of definitions, proofs, and questions that can't be solved simply by calculation, and would need to be discussed during office hours. Books for non-math majors, I'd probably look for books that worked-out solutions since they'd probably focus quite a lot on computation and seeing the steps will help them self-study if they get mistakes.
  • For graduate, I'd probably stick to classic texts that have been used for decades for the core content and suggested readings but I'd honestly expect students at that level to go to the library and look up additional content on their own.
  • Personally, I find graduate level texts easier to navigate since there's comparably less of them. For Real Analysis, for example, it seems that 95%+ of instructors in North America use the same 10 books by Rudin, Royden, Folland, Stein + Shakarchi, Kolmogorov + Fomin, Wheeden + Zygmund, Leib + Loss, etc.

2) I've only been teaching for just over 10 years but in my times I've found that books have become more colourful and more full of visuals. Meta-book changes are mostly technological in the sense of online resources that have links to videos or applets that demonstrate concepts, or questions that need a computer or calculator to be solved.

  • In terms of difficulty, I feel that many newer books are getting easier but that might be due to how many are for introductory courses and are helping bridging the gap between modern students and classic texts. For example, if you had to use Rudin's Principles of Mathematics in 3rd year after only using, say, Stewart's Calculus in 1st and 2nd years, then that would be extremely steep learning curve, and you'd probably need to have an additional course (or book) about mathematical proof. But, now there are books like Abbot's Understanding Analysis which provide modern students more of a stepping stone to classic texts. Eventually, if they get higher up, students will eventually encounter the classic difficult texts, but it probably won't be as much of a "baptism by fire" as it could have been.

3) Generally, I like books that either have the first chapter be "As you should know..." for non-math major courses and/or the last chapter be "As you will know..." for math major courses

  • For non-math majors, with introductory calculus books, my favourites contain pre-calculus and high school algebra at the front. It eases them into the course and it's allows them to know what is required (or assumed) knowledge. It also probably shows that it will be a computation-heavy course which don't need too much proof.
  • For math majors, with introductory real analysis books, my favourites contain a chapter on measure theory at the end. It obviously won't be on the course outline, but I do like how I can teach with an end in mind and say, "when we're nearly done this book, this is what your next course will be about."
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    $\begingroup$ For example, if you had to use Rudin's Principles of Mathematics in 3rd year after only using, say, Stewart's Calculus in 1st and 2nd years, then that would be extremely steep learning curve, and you'd probably need to have an additional course (or book) about mathematical proof. But, now there are books like --- FYI, my take on this: It was once quite common in U.S. universities for students to take a year-long course in advanced calculus after the elementary calculus sequence and before a real analysis course (I'm thinking of 1950s-1970s), (continued) $\endgroup$ – Dave L Renfro Feb 26 at 12:12
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    $\begingroup$ with advanced calculus slowly being phased out in the 1970s through the 1980s to allow more room for discrete math topics that students increasingly involved with computer science took. The vacuum was filled with the now commonly taught 1-semester "transition to advanced mathematics" type courses that were more specifically targeted towards preparing students maturity-wise for upper level abstract algebra and analysis courses. $\endgroup$ – Dave L Renfro Feb 26 at 12:13
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    $\begingroup$ @Robbie_P_math thank you very much for your detailed answer; regarding the fact that "...it seems that 95%+ of instructors in North America use the same 10 books by Rudin, Royden, Folland, Stein + Shakarchi, Kolmogorov + Fomin, Wheeden + Zygmund, Leib + Loss, etc." it would be very interesting to see which texts are most adopted across the US (and other countries as well) for various courses; do you know if there is a website/database/etc. that keeps track of this? $\endgroup$ – lorenzo Feb 27 at 10:36
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I teach at a community college, so all of what I have to say applies to the first two years of undergraduate study.

I've been trying for years to get my department to consider OER (Open Educational Resources) aka books that are Creative Commons instead of copyright. Our students are usually on very tight budgets, and cheaper books means less hours at a low-paying job and more study time.

This has finally happened, and it's a mixed blessing. They picked the OpenStax books for Calculus, and for Algebra. They aren't very good (imo), but free is a great start. The draw was that they have online homework available. (I don't use it.)

I have found that it's nearly impossible to know how good a book will be before actually using it for a semester.

I am using this (free) book for Discrete Math. It doesn't have enough exercises, but there's another free book that I can supplement with (here). I might change over the next time I teach this course.

If you are interested in free textbooks, AIM (American Institute of Mathematics) has an Open Textbook Initiative, with books they've approved. I often start there.

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For about 25 years, in upper-division undergrad as well as graduate courses, I have created notes to accompany all courses I give. Yes, this takes some energy. Also, by the time I started this, I'd been teaching such courses for almost 20 years, so had some experience.

Especially after it became possible to create typeset notes as fast as one could type, the classic problems about "following/not-following the book" could be made to evaporate. Instead of worrying about the impression "the assigned text" would create in students' minds, I could create notes that would follow my intended lectures+discussions. And revise as needed, upon consideration of students' reactions!!!

Another part of my motivation was the ridiculous prices of math textbooks...

... paired with the exaggerated but deliberate encyclopedic-ness of "popular" textbooks: to be a widely accepted text, one must not omit any of the favorite (if idiosyncratic) topics of any instructors. In contrast, if one is not aiming for universal adoption, one can omit less-important things, having the desirable effect that what remains is arguably more important. (The requirements of a good text are not the same as those of a good reference...)

Similarly, I do not create any sort of unlimited number of exercises, especially not make-work ones, but try to focus on genuinely important issues. And I write out complete discussions of these. Yes, year-to-year, this certainly ruins the "surprise" or "secret" aspects, but that seems to me inescapable. The fact that the number of really important basic questions in grad-level math is not unlimited is not a reason to create "new" questions that are silly. (And I think that it is wildly inefficient and silly to pretend that everyone should reprove everything for themselves, e.g.)

Also, I've noticed that being the author of course notes (or actual physical books) gives an instructor greater credibility in the eyes of students... and even if they're "notes" rather than a physical book, creation of the thing does demonstrate commitment and effort.

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