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www.chriswarbo.net | ||
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theorydish.blog
I recently finished my qualifying exam for which I surveyed worst-case to average-case reductions for problems in NP. As part of my survey, I reviewed recent results on average-case hardness in P (a.k.a. average-case fine-grained hardness). I would like to give an overview of some of these results in a series of blog posts, and... |
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andrew222651.com
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jakevdp.github.io
[AI summary] The author explains the Cooley-Tukey Fast Fourier Transform algorithm, analyzes its mathematical symmetries, and provides optimized Python implementations ranging from naive matrix multiplication to vectorized NumPy solutions. |
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thenumb.at
Or, where does that \(\sin\theta\) come from? Integrating functions over spheres is a ubiquitous task in graphicsand a common source of confusion for beginners. In particular, understanding why integration in spherical coordinates requires multiplying by \(\sin\theta\) takes some thought. The Confusion So, we want to integrate a function \(f\) over the unit sphere. For simplicity, lets assume \(f = 1\). Integrating \(1\) over any surface computes the area of that surface: for a unit sphere, we should end... |
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