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Open source textbooks October 10, 2009

Posted by Akhil Mathew in General, math education.
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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? September 7, 2009

Posted by Akhil Mathew in General, math education.
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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!  (more…)