Ars Mathematica

All analysts are uptight nerds and all algebraists are dirty hippies. Discuss.

One important thread in computer science is the study of extensions of the lambda calculus. The lambda calculus is a model of computation that uses rewrite rules based on a simple notion of a function. The rho calculus extends the lambda calculus to allow more general rewrite rules based on pattern matching. For a survey, see the paper Matching Power or the web site The Rho-Calculus Home Page.

Via Lambda the Ultimate.

A couple of years ago, the Notices of the AMS featured an article on noncommutative geometry a la Connes: Quantum Spaces and Their Noncommutative Topology by Joachim Cuntz. The hallmark of this approach is the heavy reliance on K theory. The first few pages of the article are fairly elementary (and full of intriguing pictures), before the K theory takes over.

I’ve come across an interesting weblog devoted to the philosophy of mathematics: Philosophy of Real Mathematics, by David Corfield.

Physicists are developing an alternative to special relativity, called Doubly Special Relativity. (When the Wikipedia article for this first appeared, people were so sure that the name had to be a joke that the article was nominated for deletion.) Doubly special relativity, which currently is somewhere in between an idea and an actual full-fledged theory, depends on two parameters, the speed of light and the Planck mass (this puts the two in “doubly”). For an introduction, see Introduction to Doubly Special Relativity by Jerzy Kowalski-Glikman.

Mathematical skills and aptitude are best examined by oral examinations, not written ones. Discuss.

according to Business Week.

according to a report in the latest PLUS e-magazine.

H. Jerome Keisler has made freely available his calculus textbook, Elementary Calculus: An Approach Using Infinitesimals. The book is based on Abraham Robinson’s rigorous foundations for infinitesimals.

I realize that I have been a bit out of touch recently, but I feel ashamed that I just realized that my mathematical great-grand parent Raul Bott passed away Dec 20th.