Titlebook: Algorithms and Complexity in Mathematics, Epistemology, and Science; Proceedings of 2015 Nicolas Fillion,Robert M. Corless,Ilias S. Kotsir

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Algorithms and Complexity in Mathematics, Epistemology, and Science978-1-4939-9051-1Series ISSN 1069-5265 Series E-ISSN 2194-1564

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https://doi.org/10.1007/978-3-642-58403-9; extremely difficult and complex mathematical theorems have been verified. This paper discusses the prospects of doing something comparable for elementary physics: what it would mean, the challenges that would have to be overcome; and the potential impact, both practical and theoretical.

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,An Applied/Computational Mathematician’s View of Uncertainty Quantification for Complex Systems, emphases given to stochastic Galerkin and stochastic sampling methods, including sparse-grid methods in the latter case. We close with a brief foray into where UQ in the PDE setting is going moving forwards.

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,Computational Aspects of Hamburger’s Theorem,quation? Two “rules of thumb” for performing such discoveries via numerical computations are demonstrated for functional equations satisfied by Dirichlet eta function, Ramanujan tau .-function, and Davenport–Heilbronn function..A conjectured discrete version of Hamburger’s theorem is stated.

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1069-5265 tate of the art discussions by experts on a broad collectionACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a s

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https://doi.org/10.1007/978-3-7091-9951-0 ethics both possess similar distinctions between pure and applied. I explore some of the similarities and draw methodological lessons from them. We can use these lessons to explore how and why Freiling’s refutation of the continuum hypothesis might be justified.