Physical Sciences and Mathematics Commons^™

Non-Academic Support Math Faculty Members Provide In Developmental Accelerated And Corequisite Support Courses In California Community Colleges, David Vakil '92

Doctoral Dissertations

To guide practitioners of rapidly evolving developmental math reform in community colleges, this study surveyed California community college math faculty who taught accelerated developmental courses or corequisite support courses. The survey was conducted during the early implementation phase of both course types, during spring and fall 2018 terms. This study measured faculty’s self-reported provision of forms of non-academic support, frequency of implementation, and reasons faculty believed the support would help students succeed. The literature review guided grouping non-academic support into five forms: nurturing, helping students’ motivation, providing a growth mindset theory of intelligence, helping provide social integration, and helping to …

Equidimensional Adic Eigenvarieties For Groups With Discrete Series, Daniel Robert Gulotta '03

Doctoral Dissertations

We extend Urban's construction of eigenvarieties for reductive groups G such that G(R) has discrete series to include characteristic p points at the boundary of weight space. In order to perform this construction, we define a notion of "locally analytic" functions and distributions on a locally Q_p-analytic manifold taking values in a complete Tate Z_p-algebra in which p is not necessarily invertible. Our definition agrees with the definition of locally analytic distributions on p-adic Lie groups given by Johansson and Newton.

Borel Complexity Of The Isomorphism Relation For O-Minimal Theories, Davender Singh Sahota '99

Doctoral Dissertations

In 1988, Mayer published a strong form of Vaught's Conjecture for o-minimal theories (1). She showed Vaught's Conjecture holds, and characterized the number of countable models of an o-minimal theory T if T has fewer than 2K ° countable models. Friedman and Stanley have shown in (2) that several elementary classes are Borel complete. This work addresses the class of countable models of an o-minimal theory T when T has 2N ° countable models, including conditions for when this class is Borel complete. The main result is as follows.

Theorem 1. Let T be an o-minimal theory in a countable …