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Multilinear Proofs, Part I: Cubes & Roots
| | www.ethanepperly.com
Vandermonde Matrices are Merely Exponentially Ill-Conditioned - Ethan N. Epperly
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| | qchu.wordpress.com
Meditation on the Sylow theorems I | Annoying Precision
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| | As an undergraduate the proofs I saw of the Sylow theorems seemed very complicated and I was totally unable to remember them. The goal of this post is to explain proofs of the Sylow theorems which I am actually able to remember, several of which use our old friend The $latex p$-group fixed point theorem...
| | almostsuremath.com
Algebraic Probability - Almost Sure
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| | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists...
| | mattbaker.blog
Fitting ideals of modules | Matt Baker's Math Blog
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| In my previous post, I presented a proof of the existence portion of the structure theorem for finitely generated modules over a PID based on the Smith Normal Form of a matrix. In this post, I'd like to explain how the uniqueness portion of that theorem is actually a special case of a more general...