Incidence Functions,
2010
University of Texas at El Paso
Incidence Functions, Yiyu Liao
Open Access Theses & Dissertations
In the mid 1960's, the incidence algebra was introduced in the seminal paper of Gian-Carlo Rota. He addressed the importance of the Mobius function in combinatorics. In particular, the incidence algebra of a locally finite poset plays an essentially unifying role in the theory of the Mobius function. One of the significant generalizations is the incidence algebra of a Mobius category introduced by Pierre Leroux. With the help from Mobius category, it was exciting to be able to extend the combinatorial results more broadly than just on posets. Before attempting to study this generalization of the Mobius function, we have …
Use Of Cognitive Constructs In Linear Algebra,
2010
University of Texas at El Paso
Use Of Cognitive Constructs In Linear Algebra, Azucena Zamora
Open Access Theses & Dissertations
Thesis analyzed the presence of two cognitive entities-- modes of thinking and metonymies and metaphors- in the reasoning of three students enrolled in a first year matrix algebra course at a southwest university via the responses given to a set of eight questions asked during one-on-one interviews. The findings of our analysis shed light on the cognitive constructs that students employ to form their understanding of linear algebra concepts. Furthermore, our findings provide clues about the ways in which students move from one mode of thinking to another in the context of varying levels of exposure to graphical, algebraic, and …
