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rjlipton.com | ||
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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... | |
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ncatlab.org
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| | | | | [AI summary] The text is a comprehensive overview of twisted K-theory, its mathematical foundations, and its applications. It traces the origins of the theory to seminal works in the 1960s and 1970s, discusses its formulation in terms of Fredholm bundles, and explores its connections to other areas of mathematics such as operator algebras, topology, and noncommutative geometry. The text also delves into the role of twists in K-theory, particularly those arising from cohomology classes in degrees 0, 1, and 3, and highlights the significance of these twists in the context of index theory, loop groups, and string theory. A wide range of references is provided, covering both foundational and more recent developments in the field, as well as related topics such a... | |
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0fps.net
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| | | | | Last time, we showed how one can use symmetric tensors to conveniently represent homogeneous polynomials and Taylor series. Today, I am going to talk about how to actually implement a generic homogeneous polynomial/symmetric tensor class in C++. The goal of this implementation (for the moment) is not efficiency, but rather generality and correctness. If there... | |
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vitalyobukhov.wordpress.com
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| | | Visit the post for more. | ||
