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homotopytypetheory.org
| | rakhim.org
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| | mattbaker.blog
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| | I'm teaching Graduate Algebra this semester, and I wanted to record here the proof I gave in class of the (existence part of the) structure theorem for finitely generated modules over a PID. It's a standard argument, based on the existence of the Smith Normal Form for a matrix with entries in a PID, but...
| | xorshammer.com
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| | There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax's Theorem. Ax's Theorem: For all polynomial functions $latex f\colon \mathbb{C}^n\to \mathbb{C}^n$, if $latex f$ is injective, then $latex f$ is surjective. Very...
| | coornail.net
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| Neural networks are a powerful tool in machine learning that can be trained to perform a wide range of tasks, from image classification to natural language processing. In this blog post, well explore how to teach a neural network to add together two numbers. You can also think about this article as a tutorial for tensorflow.