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More on Princeton Companion to Mathematics aka ‘PCM’.

Quite a few of the single Companion chapters are available from the authors’ own web sites… I gave links to Terry Tao and Tim Gowers blogs below.

Gordon Slade wrote the chapter ‘Probabalistic Models in Critical Phenomena‘

Its a nice overview of whats been happening in this area, with sections about Critical Phenomena, Branching Processes, Random Graphs, Percolation, Ising Model, Random Cluster model and also introduces SLE the Stochastic-Loewner-Evolution work by Oded Schramm, Wendelin Werner etc.

If you’ve never heard of this stuff heres a motivator of sorts, by yours truly –

**Eclectic recent math-goodness :**

Two nice video talks by Terry Tao on Random Matrices and Additive Combinatorics here

A programmers intro to the practical aspects of Flow Graphs at topcoder algorithm tutorials

**PCM**

Last but not least the superb ‘Princeton Companion to Mathematics‘.

In a nutshell, PCM is a readable survey-guide to modern math by the experts. Some links –

- The intro page autoplays a podcast interview with Tim Gowers, the editor
- Contents list with some downloadable sample chaptes

- Terry Taos many PCM contributions are discussed/previewed at his blog
- ‘Mathematics and Money’ chapter apparently has an intro to Quantitative Finance by Mark Joshi
- ‘Numerical Analysis’ sample chapter mentions John Butcher, a great ex prof from Auckland Uni.

Should be in print Nov 2008. Hopefully more articles from Tim Gowers’ and Terry Tao’s blogs will make it out in book form, with the momentum this will generate…