The CRing project: open source, massively collaborative commutative algebra?

[The present post is an announcement of the CRing project, whose official webpage is here.]

Like most mathematics students, I spend a lot of time writing stuff, for instance homework assignments and (of course) blog posts. So I have a lot of random, unorganized write-ups littered around my hard drive, which might be useful to others if organized properly, but which currently slumber idly.

Last semester, I took a fairly large amount of notes for my commutative algebra class (about 160 pages). I made the notes available on my webpage, and was pleased with the reception that they received from my classmates. After seeing Theo-Johnson Freyd’s projects, I decided that it might be a productive exercise to edit the notes I had taken into a mini-textbook. I quickly made progress, since the basic structure of the book was already set by the lectures. I decided early on that the work was going to be open source: to me, it seemed the best way to ensure that anyone who wanted could freely access and modify it.

But I think the project is bigger now. Namely, instead of an open source textbook, I want a massively collaborative open source textbook. This is to say that I don’t want it to be my work anymore, but my work as well as, and more importantly, the work of enthusiastic professors, procrastinating graduate students, nerdy high-schoolers,  or whoever else wishes to contribute. The goal is to end with an openly available textbook suitable for a beginner familiar only with elementary abstract algebra, but which will provide adequate preparation for the serious study of algebraic geometry.

So, I present you the CRing project.

 

Open source textbooks

Well, it seems that the Bourbaki 2.0 idea I suggested some time back wasn’t entirely absurd: as a commenter pointed out, the Stacks 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).  Additionally, he asks why conventional textbook publishing, even for individual authors, is still necessary in the day of the internet when it is more efficient to distribute material online.   Some people have apparently listened to these ideas; Jacob Lurie, for instance, has put his treatise on higher topos theory on the arXiv, and Allen Hatcher has made available his well-known text on algebraic topology on his webpage. 

I’d very much like to see this trend continue; there are surely people out there who would like to learn mathematics beyond the introductory calculus and linear algebra level–when there are no longer massive surpluses of texts on one topic–but may not be affiliated with a university for various reasons, and may not want to fork over the substantial sums that conventionally printed textbooks cost these days.  At least for authors, I don’t think there’s much money to be made in algebraic topology writing, and math professors have nice salaries anyway, so why not?

 

Bourbaki 2.0: Or, is massively collaborative mathematical exposition possible?

Warning: I have very little knowledge about these topics (even less than usual).

The Problem

One of my goals is to learn mathematics independently. I’ve had lots of trouble especially in certain areas such as algebraic geometry, where the preqrequisites are large and interconnected. When reading books nowadays, I frequently come across words I don’t know with (sometimes) recommended supplementary sources. But I can’t really learn the definition of say, a Cohen-Macaulay ring, just from reading Hartshorne’s short blurb or Wikipedia without actually seeing some properties of these rings proved, so I go to the supplementary sources. When I looked up, say, Matsumura’s book on commutative algebra, I then find that I am expected to know what derived functors are to understand depth. Time to find another book!