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divisbyzero.com | ||
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chessapig.github.io
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| | | | | [AI summary] A personal math diary where the author records and explains complex mathematical concepts, inspired by John Baez, with an index of topics ranging from Euler-Maclaurin formulas to index theorems. | |
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xahlee.info
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| | | | | [AI summary] The post curates a collection of free verified math textbooks ranging from high school number theory to graduate-level topics like category theory and differential geometry. | |
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akos.ma
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| | | | | From the wonderful book by Ian Stewart, here are the equations themselves; read the book to know more about them. | |
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djalil.chafai.net
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| | | This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for... | ||
