Low Dimensional Topology

September 18, 2009

An open source mathematics book

Filed under: Pedagogy — Nathan Dunfield @ 2:13 am

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.)


  1. Amen to that. One of the reasons (not the only one of course) Hatcher’s book is so good is that many students who read the book e-mail him corrections and suggestions for improvement. Professor Hatcher incorporates these (at least the corrections) in real time. So the book evolves and gets better and better.
    Also, if people had a hand in altering a book to their taste, more books would actually get read, instead of skimmed, glanced at, etc.

    Comment by Mayer A. Landau — September 18, 2009 @ 11:31 am | Reply

  2. […] source and teaching math, I haven’t looked into it yet, but it sounds like a great idea. Not unrelated, a talk on the […]

    Pingback by Stones Cry Out - If they keep silent… » Monday Highlights — September 21, 2009 @ 8:46 am | Reply

  3. I think most university bookstores will allow you to assemble-your-own text, taking bits and pieces from various texts, and giving each publisher the respective fraction of the cost of each text used. It’s a fairly popular device here, though more in the arts than in math.

    I find during office hours with students it’s far more convienient to look up topics on Wikipedia than to open the textbook — especially with service-type calculus courses that have phonebook sized texts. I wonder how awkward it would be to support a course only using Wikipedia and forgetting conventional texts altogether. Problem lists would be perhaps the biggest issue.

    Comment by Ryan Budney — September 26, 2009 @ 12:04 pm | Reply

  4. I think one major problem with most textbooks is that low-dimensional topology is example-driven, but the examples are rarely included. I think it’s useful, for instance, to see how one calculates the fundamental group of knot complements, and shows its abelianization is Z by using Mayer-Vietoris, Hurwitz’s theorem, etc, differential geometry of space curves, classification of surfaces, covering spaces via simplicial methods (maximal cave construction), holonomy, etc., concrete calculation of the Bockstein boundary or Steenrod square or even Poincare dual of something concrete… I don’t really know books which stress such things. But I’d think they would be perfect material for an open-source book!

    Comment by Daniel Moskovich — September 29, 2009 @ 10:48 pm | Reply

  5. I really like Rolfsen’s “Knots and Links” for pretty much exactly what Daniel is getting at. It’s a pleasant read, you get to work out many of the details by hand. Some aspects of the book are not very explicit, but once you’ve done enough examples you understand how some things work. I asked Rolfsen — apparently he’s only taught a single course out of that textbook.

    Comment by Ryan Budney — October 4, 2009 @ 6:16 pm | Reply

  6. […] Project is following a similar model.  Moreover, Nathan Dunfield of Low Dimensional Topology has proposed that the stacks model be applied to textbooks (I assume the stacks book is more of a reference).  […]

    Pingback by Open source textbooks « Delta Epsilons — October 10, 2009 @ 6:14 pm | Reply

  7. […] mailing list touting my textbooks (Diffy Qs and Real Analysis), and one of the responses linking this post gave me an idea. Perhaps I should start a sort of sourceforge.net for math textbooks. Simply set up […]

    Pingback by Sourceforge.net for Math Texbooks « The Spectre of Math — May 20, 2010 @ 3:14 pm | Reply

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