In this Master's Thesis we give an overview of the algebraic structure of sets with a single binary operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. …
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This dissertation explores the ideational underpinnings of the rise of the west through a comparison of ancient Greek geometry, medieval Arabic algebra, and early modern European calculus. Blending insights from Thomas Kuhn, Michel Foucault, and William H. Sewell, I assert that …
This thesis concerns representation theory of the symmetric groups and related algebras. In recent years, the study of the “quiver Hecke algebras”, constructed independently by Khovanov and Lauda and by Rouquier, has become extremely popular. In this thesis, our motivation for s…
We study the -adic completion dD[1] of Berthelot's differential operators of level one on the projective line over a complete discrete valuation ring of mixed characteristic (0; p). The global sections are shown to be isomorphic to a Morita context whose objects are certain frac…
The Iwahori-Hecke algebras of finite Coxeter groups play an important role in many areas of mathematics. In this thesis we study the representation theory of the Iwahori-Hecke algebras of the Coxeter groups of type Bn and F4, in the unequal parameter case. We denote these algebr…
Recent studies of curriculum enactment suggest that different teachers enact the same curriculum materials in different ways (e.g., Cohen & Ball, 2001; Freeman & Poter, 1989; Manoucheri & Goodmann, 1998, 2000). The discrepancies have been attributed to deficiencies in teacher su…
Una singularidad algebrizable es el germen de una foliación holomorfa singular en (C2, 0) con singularidad aislada tal que es analÍticamente equivalente al germen de una foliación definida globalmente sobre una superficie proyectiva. La finalidad de este trabajo es exhibir un cr…
In recent years, mathematicians working in nonlinear algebra have actively explored the use of algebraic geometry, combinatorics and symbolic computations to answer questions in a diverse field of applications, with an emphasis on statistics and optimization. This dissertation i…
The random dynamics of a population evolving in time is a phenomenon worthy of mathematical study. From examining genetic drift and tracing genetic diseases to the recent increased interest in genetic ancestry reports, it is clear that there is a strong need for deepening and ex…