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You are here		cp4space.hatsya.com The exceptional Jordan algebra \| Complex Projective 4-Space
\|	\|	almostsuremath.com Algebraic Probability - Almost Sure	2.8 parsecs away Travel
\|	\|	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...	2.8 parsecs away Travel
\|	\|	qchu.wordpress.com Meditation on the Sylow theorems II \| Annoying Precision	4.2 parsecs away Travel
\|	\|	In Part I we discussed some conceptual proofs of the Sylow theorems. Two of those proofs involve reducing the existence of Sylow subgroups to the existence of Sylow subgroups of $latex S_n$ and $latex GL_n(\mathbb{F}_p)$ respectively. The goal of this post is to understand the Sylow $latex p$-subgroups of $latex GL_n(\mathbb{F}_p)$ in more detail and...	4.2 parsecs away Travel
\|	\|	thenumb.at Functions are Vectors	4.5 parsecs away Travel
\|	\|	[AI summary] The text discusses the representation of functions as vectors and their applications in various domains such as signal processing, geometry, and physics. It explains how functions can be treated as vectors in a vector space, leading to the concept of eigenfunctions and eigenvalues, which are crucial for understanding and manipulating signals and geometries. The text also covers different types of Laplacians, including the standard Laplacian, higher-dimensional Laplacians, and the Laplace-Beltrami operator, and their applications in fields like image compression, computer graphics, and quantum mechanics. The discussion includes spherical harmonics, which are used in representing functions on spheres, and their applications in game engines and glo...	4.5 parsecs away Travel
\|	\|	anuragbishnoi.wordpress.com The Rank-Ramsey problem \| Anurag's Math Blog	27.7 parsecs away Travel
\|		The Ramsey number $latex R(s, t)$ is the smallest $latex n$ such that every graph on $latex \geq n$ vertices either contains a clique of size $latex s$ or an independent set of size $latex t$. Ramsey's theorem implies that these numbers always exist, and determining them (precisely or asymptotically) has been a major challenge...	27.7 parsecs away Travel