Many authors put up drafts of their books as they write them, only to take them down once the book is published. I understand the reasons, but it’s nice when such a book stays available in electronic format. David MacKay’s book Information Theory, Inference, and Learning Algorithms is still available, even though it’s been published by Cambridge University Press.
Plus Magazine has a competition for new writers about mathematical subjects.
Week 230 of John Baez’s This Week’s Finds in Mathematical Physics is out. He has returned to one of his favorite subjects (and really, one of everyone’s favorite subjects), Dynkin diagrams. We covered some of the same topics here and here.
Modular forms have been thrust into mathematical prominence by Wiles’ proof of Fermat’s Last Theorem. Wiles in actuality proved a special case of the Shimura-Taniyama conjecture, which relates elliptic curves and modular forms.
Fred Calegari has written a nice introduction to the topic of modular forms in the guise of a book review of A first course in modular forms by Diamond and Shurman. (The review also features the best variant of the “kids today” sentiment I’ve seen recently: “With today’s Ipod generation more likely to study elliptic curves and modular forms before learning any class field theory…”
The latest issue of the Post-Autistic Economics Review is now out, available here. It has an interesting article by philosopher Donald Gillies arguing against the centrally-organized reviews of university research activities which British academics have had to endure these last 20 years, and which now look likely to be adopted in Australia, NZ and elsewhere. One argument he makes is that one’s peers are usually quite bad at judging the long-run impact and quality of one’s research, especially when the research is innovative, and Gillies gives the example of Frege’s Begriffsschrift, the first axiomatic treatment of propositional and predicate calculus. When this was published in 1879, it was slammed by Frege’s contemporaries, and it was only recognized for the seminal work it is two decades later. If Frege had been working in a British University a hundred years later, both he and his department may have faced termination by his university administration, given the hostility that his own peers felt towards his work; lots of departments have been closed, and academics made unemployed, as a result of the peer assessments of the British Research Assessment Exercise (RAE).
A longer version of Gillies’ paper is available on his web-site, here.