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mathscholar.org | ||
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thenumb.at
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| | | | | [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... | |
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inquiryintoinquiry.com
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| | | | | Introduction The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus noted and named by G.W.Leibniz, who stated and proved it in the following manner. If a is b and d is c, then ad will be bc. This is a fine theorem, which is proved in this way: a is b, therefore... | |
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micromath.wordpress.com
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| | | | | Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 1998 (TeX file). Professor Anthony W. Knapp P O Box 333 East Setauket, NY 11733 Dear editor, I am pleased to see so... | |
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mathematicaloddsandends.wordpress.com
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| | | I recently learned of Craig's formula for the Gaussian Q-function from this blog post from John Cook. Here is the formula: Proposition (Craig's formula). Let $latex Z$ be a standard normal random variable. Then for any $latex z \geq 0$, defining $latex \begin{aligned} \mathbb{P}\{ Z \geq z\} = Q(z) = \dfrac{1}{\sqrt{2\pi}} \int_z^\infty \exp \left( -... | ||
