Number theorist Emmanuel Kowalski has an interesting post about a truly open source math book on algebraic stacks. Not only can you download the entire 1302(?!) page book as a PDF file, you can get the complete LaTeX source files, and the whole thing is kept under version control so people can submit changes, etc.
I’ve been thinking that a similar approach would be good for textbooks. When I teach a course, I’m often frustrated by being unable to find a text that has everything I need. Or I do find such a text, but it’s poorly written in places, or aimed too high or low for my particular students. Or maybe there are theorems in the text that I’d like to assign as homework instead of lecturing on them. In such situations, it would be great if there was a whole collection of open-source textbooks that I could cut and paste from, massage the result a bit, and end up with something closer to the “perfect” text for a course.
Indeed, in the modern age, I’m not sure why people write conventionally published textbooks at the advanced undergraduate or graduate level. You can just throw a PDF on the web, and people can use e.g. Lulu to get printed copies (though within in a decade, I’d guess students will all prefer to have things on their Kindle). I suspect that many more people would use a text distributed for free, and the ego boast from this would more than make up for the very modest loss in revenue from book sales. (Note the dominance of Hatcher’s Algebraic Topology, which is freely downloadable, though of course that’s a fantastic book on it’s own merits, and so it might have achieved that status anyway.)
Of course, a key feature of the open source approach is allowing others to create their own versions of one’s book at will, which does lead to a certain loss of control that some might find unappealing. Still, I think it could be very good for the community if people went this route.
(As a side note, like all good math bloggers Emmanuel occasionally posts on 3-manifolds.)