I imagine it varies by publisher, but I was just working with a student who uses the textbook Big Ideas Math Accelerated: A Common Core Curriculum by Larson and Boswell, and I found an error within minutes of looking at the book. What do I do with this information? (It's entirely possible the correct answer is: just live with it.)
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1$\begingroup$ And, especially with very good students, we should admit that books are not the perfect authorities some often pretend... so, if it seems wrong, maybe it is... and we investigate (as opposed to appealing to higher authority). Of course, this runs into trouble when "correctness" is about artificial issues such as notation and terminology. :) $\endgroup$– paul garrettApr 5, 2018 at 0:21
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$\begingroup$ Might be related: matheducators.stackexchange.com/q/13096/77 $\endgroup$– JRNApr 5, 2018 at 1:28
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Treat it like any other book you find a mistake in: send a letter or email to the author by way of the publisher. I would wait until the end of the term and send all the feedback in at one time, then.
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$\begingroup$ Perhaps before doing even that: check the publisher's web site to see if they already have an Errata document for that book. $\endgroup$ Apr 5, 2018 at 11:30
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$\begingroup$ During 1993-1996 I taught 2 to 3 classes each semester from the 1993 edition of Mathematical Ideas by Charles D. Miller, Vern E. Heeren, and E. John Hornsby, and early on I happened to notice the following in the inside back cover's mathematical time-line, among the items listed for "1900 A.D. to 1950 A.D.": Kurt Godel shows that Cantor's continuum hypothesis cannot be proved, based on axioms of formal set theory. There is also a comment about Paul Cohen (Godel not mentioned) on p. 94 that essentially says Cohen, in the early 1960s, showed the continuum hypothesis (continued) $\endgroup$ Apr 5, 2018 at 12:31
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$\begingroup$ can neither be proved nor disproved from the "axioms of formal set theory". The correct version is that Godel showed that the continuum hypothesis cannot be disproved and that Cohen showed that the continuum hypothesis cannot be proved. I thought about writing the authors, but put it off and then forgot about it. At some later time (March or April 1995?) I found myself talking to John Hornsby at one of the yearly MAA Louisiana/Mississippi Section meetings, mentioning how I frequently I was teaching from his book and its nice selection of topics. (continued) $\endgroup$ Apr 5, 2018 at 12:38
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1$\begingroup$ Then I mentioned the Cantor/Godel stuff, and he asked me to come by his book table later in the conference when the book would be available for me to show him, which I did, and he thanked me profusely and made some notes. I said that I seriously doubt any student would notice this (might be different in today's easy look-up on internet era), but he was very concerned about getting something like this correct. Anyway, I'm curious as to whether this was fixed in later editions --- does anyone have an 8th or later edition of this book to check whether it was corrected? $\endgroup$ Apr 5, 2018 at 12:45
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$\begingroup$ FYI, this excerpt from p. 36 of the 1986 edition is not exactly the same as it appears in the 1993 edition, but it's fairly close. $\endgroup$ Apr 5, 2018 at 12:54