Doctor of Philosophy, The Ohio State University, 2004, Mathematics

We introduce the notions of the Baer and the quasi-Baer properties in a general module theoretic setting. A module M is called (quasi-) Baer if the right annihilator of a (two-sided) left ideal of End(M) is a direct summand of M. We show that a direct summand of a (quasi-) Baer module inherits the property. Every finitely generated abelian group is Baer exactly if it is semisimple or torsion-free. Close connections to the extending property and the FI-extending property are exhibited and it is shown that a module M is (quasi-) Baer and (FI-) 퓚-cononsingular if and only if it is (FI-) extending and (FI-) 퓚-nonsingular. While we show that direct sums of (quasi-) Baer modules are not (quasi-) Baer, we prove that an arbitrary direct sum of mutually subisomorphic quasi-Baer modules is quasi-Baer and that every free (projective) module over a quasi-Baer ring is always a quasi-Baer module. Some results, related to direct sums of Baer modules and direct sums of quasi-Baer modules, are also included. A ring over which every module is Baer is shown to be precisely a semisimple Artinian ring. Among other results, we also show that the endomorphism ring of a (quasi-) Baer module is a (quasi-) Baer ring, while the converse is not true in general. A characterization for this to hold in the Baer modules case is obtained. We provide a type theory of Baer modules and decomposition of a Baer module into into five types, similar to the one provided by Kaplansky for the Baer rings case. This type theory and type decomposition is applied, in particular, to all nonsingular extending modules. Applications of the results obtained are included.

Committee: Syed Rizvi (Advisor) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2023, Anatomy

Neurophobia, defined as the fear of and lack of confidence with clinical neurology, is a well-documented phenomenon in medical students and junior doctors. Previous studies have identified low knowledge of basic neuroanatomy as one of the largest drivers of neurophobia, often stemming from ineffective pedagogical approaches. It is thought that neurophobia begins when students first encounter academic neuroscience; however, the prevalence and associated risk factors of neurophobia in undergraduate students is not known. Investigating these relationships in this population is relevant because they represent a pipeline for future neurologists and associated healthcare professionals. Furthermore, interventions for phobias are most effective when started early. The aim of the first study was to provide an in-depth analysis of the prevalence and factors contributing to neurophobia among undergraduate students enrolled in an introductory neuroanatomy course at The Ohio State University. The presence of neurophobia in this population was found to be comparable to that reported in medical students and junior doctors. Additionally, neurophobic students were found to have significantly higher cognitive load, assessment anxiety, and perceived difficulty, as well as lower intrinsic motivation, self-efficacy, and course grades compared to their non-neurophobic peers. This highlights the urgent need for early intervention, suggesting that techniques to manage cognitive load and enhance motivation could be beneficial. Based on the principles of cognitive load theory, self-determination theory, and social cognitive theory, 11 e-learning modules were developed for the two most difficult blocks in the undergraduate neuroanatomy curriculum. Featuring interactive slides with toggleable animations, practice questions with explanations, video content, and clinical scenarios, these modules aimed to manage cognitive load and enhance motivation of neuroanatomy learners. The aim of the sec (open full item for complete abstract)

Committee: Eileen Kalmar (Advisor); James Cray Jr (Advisor); Claudia Mosley (Committee Member); Christopher Pierson (Committee Member) Subjects: Anatomy and Physiology; Neurology; Neurosciences

Doctor of Education (Ed.D.), University of Findlay, 2024, Education

Professional development (PD) hours are required for licensure renewal for the more than 110,000 teachers in Ohio. Despite being entrenched in the culture of education; many teachers view PD negatively. In this qualitative study, three structures of PD are studied to determine their impact on teacher attitudes. These three structures are online learning modules, professional conference/self-guided PD, and cohort/professional learning communities (PLC). The PD models are analyzed through the theoretical framework of andragogy, or the adult learning theory. There are six principles of andragogy, and these ideas were central to the questions in both a Google Form survey and semi-structured interview questions. There were 76 survey participants that fit the criteria of an Ohio teacher that had been through the licensure renewal process at least once and had engaged in all three models of PD being studied. Six of these participants were chosen to be interviewed via Zoom to gather more in-depth explanations as to why they answered the survey questions the way they did. The research determined that the more aligned to the principles of andragogy the PD structure is, the more positively it is received by the teachers. Conferences/self-guided PD were viewed most positively, followed by cohort/PLCs, and finally online modules; the first encompassed all six of the tenets of andragogy, cohort/PLCs included five out of six, and online modules comprised only one of the principles. This research has implications for those that plan and execute PD, especially at the district level. To elicit positive attitudes toward professional development, the model employed should prioritize the principles of andragogy.

Committee: Kara Parker (Committee Chair) Subjects: Adult Education; Continuing Education; Education; Teacher Education; Teaching

Doctor of Philosophy, The Ohio State University, 2008, Mathematics

In a family of projective complex algebraic varieties, all nonsingular fibers are topologically equivalent; in particular, their cohomology groups are isomorphic. Near the “boundary,” where the varieties acquire singular points, this is no longer the case. The theory of variations of Hodge structure provides strong tools to understand the local behavior near points on the boundary; these have been used, for instance, to prove that the locus of Hodge classes is a union of algebraic varieties (by Cattani, Deligne, and Kaplan). Recently, there has been interest in global questions related to the behavior at the boundary, especially for the family of all hypersurfaces (of large degree) of a given smooth projective variety. Green and Griffiths introduced the concept of the “singularity” of a normal function; following their ideas, Brosnan, Fang, Nie, and Pearlstein, and de Cataldo and Migliorini proved that the Hodge conjecture is equivalent to the existence of such singularities. In this dissertation, we investigate the boundary behavior of cohomology classes in families (in the above sense), from several different points of view. We also obtain new interpretations for the singularity of a normal function in the family of hypersurface sections of sufficiently large degree.

Committee: Herbert Clemens (Advisor); Fangyang Zheng (Committee Member); Linda Chen (Committee Member); Qinghua Sun (Committee Member) Subjects: Mathematics