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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 –

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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


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 –

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…