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Logic and Foundations of Mathematics Commons

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2013

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Articles 31 - 33 of 33

Full-Text Articles in Logic and Foundations of Mathematics

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz Jan 2013

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

Journal of Humanistic Mathematics

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …


Numerical Solution Of The Helmholtz Equation For The Superellipsoid Via The Galerkin Method For The Dirichlet Problem, Yajni Warnapala, Hy Dinh Jan 2013

Numerical Solution Of The Helmholtz Equation For The Superellipsoid Via The Galerkin Method For The Dirichlet Problem, Yajni Warnapala, Hy Dinh

Arts & Sciences Faculty Publications

The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation fora smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was: x = cos …


Logic, Truth And Inquiry (Book Review), G. C. Goddu Jan 2013

Logic, Truth And Inquiry (Book Review), G. C. Goddu

Philosophy Faculty Publications

Mark Weinstein’s, Logic, Truth and Inquiry is an ambitious and provocative case for a theory of truth and warrant strength that will undergird an “account of argument in the broad sense of current argumentation theory” (p. 12). I begin with a very schematic synopsis of Weinstein’s rich discussion through his six chapters. Weinstein himself notes that his arguments are “frequently presented in broad outline” (p. 1), so my quick sketch will be even broader. I conclude with some brief observations about both what the book leaves unresolved and the merits of Weinstein’s intriguing book.