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What is the standard practice when finding errors in a recent graduate textbook?
The word "recent" should be read as "published less than a decade ago".
Email the author.
What I do is mutter under my breath, build up a list of twenty or thirty errors at a time, then e-mail the author the list. The author will not be very happy with you if you e-mail him or her every single error in its own e-mail.
Twenty or thirty errors at a time? I think of myself as a reasonably careful reader (and certainly I own many graduate level math texts), but I rarely find thirty errors in an entire book. What are these books that are so thoroughly riddled with errors? (I may regret asking this, and I certainly wouldn't on the main site, but I can't seem to help myself.)
I confess that sometimes I do and sometimes I don't contact the author about errors (usually one at a time!). Thinking about when I do so, here's what I came up with: I am much more likely to email the author of a very good, carefully written book than a book which is in general sloppily written, because I feel like the former author will want to hear about it and take it into account, whereas the latter author probably won't. (Edit: this also partially answers the question in the previous paragraph: after I see more than a few errors, I tend to stop keeping track.) Moreover, although I don't think I take this into account, a really good book is more likely to get a later printing or edition in which the errors will be fixed and possibly my name will show up in the acknowledgments, a very minor form of immortality. For instance, I am acknowledged in the latest edition of Silverman's Friendly Introduction to Number Theory, even though -- as far as I can remember -- my main contact with him about this book was to say that I really enjoyed the FoxTrot comics and wished there were more.
By the way, very few authors post errata pages on their websites (or anywhere else that google can find them), which I think should be more prevalent. I seem to recall that some months ago there was a movement to set up a math errata webpage. What happened with that?
Twenty or thirty errors at a time? I think of myself as a reasonably careful reader (and certainly I own many graduate level math texts), but I rarely find thirty errors in an entire book. What are these books that are so thoroughly riddled with errors? (I may regret asking this, and I certainly wouldn't on the main site, but I can't seem to help myself.)
Well, since I got permission from the author to put my own list of errata publicly on the web (although I am technically required to send him a link to the list, I wouldn't really count this as a list, so I am not going to e-mail him yet), I guess it's fine for me to say which book I'm talking about in particular: Lurie's Higher Topos Theory contains a lot of very confusing (although always fixable with enough mathematical maturity) errors, especially in Chapter 2 and Appendices 2 and 3. Strangely enough, there are never typos in the prose of the text, and they are all concentrated in the mathematics itself. I think that most of these errors are artifacts left over from when sections were rewritten (variables are named wrong or inconsistently within a proof, sometimes one must assume that certain maps are weak equivalences for the proof to be true, etc.). (Someone on the nLab suggested calling these sorts of errors mathematical palimpsests). Perhaps one of the most frustrating persistent errors appears from A.2.8 onwards through the rest of the book:
(a minor digression for the readers not familiar with the terminology)
There are two model structures on the functor category A^D when A is a model category (we might that A is combinatorial for some technical reasons). Given as follows:
W: The weak equivalences are those natural transformations a:F->G who are weak equivalences object-by-object
F_proj: The projective fibrations are natural transformations a:F -> G that are fibrations object-by-object
C_inj: The injective cofibrations are natural transformations a:F -> G that are cofibrations object-by-object
These generate model structures by taking the model structures generated by (C_inj,W) (the injective model structure), and (llp(F_proj), W) (the projective model structure) (this is not a very easy theorem in general, although Cisinski gives a very concise and conceptual proof in the case when A is a Grothendieck topos equipped with a Cisinski model structure (see Asterisque 308).
We call all of the relevant classes of morphisms with the prefix of the name of that model structure, so maps in C_inj\cap W would be called trivial injective cofibrations, and rlp(C_inj\cap W), the morphisms with the right lifting property with respect to this class, would be called the class of injective fibrations.
However, sometimes even within the same proof, Lurie will start calling injective cofibrations "weak cofibrations", trivial injective cofibrations "trivial weak cofibrations", injective fibrations "strong fibrations", and trivial injective fibrations "injective strong fibrations". Similarly, the (trivial) projective fibrations become the "(resp. trivial") weak fibrations", and the (trivial) projective cofibrations become the "resp. (trivial) strong cofibrations".
Two problems: First, none of these renamed terms are defined anywhere in the book, and second, it is an extremely confusing error, since one is first given the impression that there is a "strong model structure" and a "weak model structure", which would be getting it precisely wrong. I suspect that Lurie realized the unwisdom of this naming scheme and attempted to change it, but either he missed a couple of them, or lapsed into using his older terminology from time to time.
One thing that you can do (and should do) is stay away from sloppy publishers. I will never, ever again select a book published by OUP as a textbook because of my experience with Rossmann's "Lie groups: an introduction through linear groups". I feel safe in speaking publicly about it because the abnormal quantity of errors has been duly noted in two published reviews of it, one by Anthony Knapp and another by Peter Trapa. While many of the errors are typographical (wrong fonts, missing words or symbols), the proof of the central theorem in the book is so badly garbled that Knapp's review contains a list of line by line corrections to it. Never mind copy editing and proofreading, things must be really falling apart at OUP, because they can't even ship books correctly: the first desk copy I requested never arrived, so I requested another one, and a few weeks later Aerospace Engineering department called me and said that they were about to through away a package addressed to a non-existing person when someone thought of looking up the name in the university directory - that's where the second copy ended up!
[Comment deleted.]
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