Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item Approaches sto Proof in Geometry Textbooks: Comparing Texts from the 1980s and 2000s(2013) Kelley, Genevieve Demos; Edwards, Ann R; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Eight American textbooks were studied, four each from the 1980s and the 2000s, with the purpose of identifying differences between the two groups of textbooks in their approaches to teaching proof and proof writing. All of the exercises in each text were coded using parameters established by the author for proofs, types of proof, and other justification and reasoning tasks. Additionally, numbers of proofs in the exposition of each textbook were determined. Thematic analyses of attention to form, presentation of theorems, and introduction to proof and proof writing were also included in the research design. Results suggest both quantifiable and qualitative differences in students' opportunities to engage in and practice proof writing as found in the exercises. Other differences in the newer textbooks include a conjecture-based approach to theorems, greater attention to placing proof in the context of mathematical reasoning, and emphasis on alternatives to the two-column form.Item How to Prove a Differential Form of the Generalized Second Law(2011) Wall, Aron Clark; Jacobson, Theodore A; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A new method is given for proving the semiclassical generalized second law (GSL) of horizon thermodynamics. Unlike previous methods, this method can be used to prove that entropy increases for arbitrary slices of causal horizons, even when the matter fields falling across the horizon are rapidly changing with time. Chapter I discusses how to define the GSL, and critically reviews previous proofs in the literature. Chapter II describes the proof method in the special case of flat planar slices of Rindler horizons, assuming the existence of a valid renormalization scheme. Chapter III generalizes the proof method to arbitrary slices of semiclassical causal horizons, by the technique of restricting the fields to the horizon itself. In the case of free fields it is clear that this restriction is possible, but for interacting fields the situation is murkier. Each of the three parts has been, or will be, separately published elsewhere.Item A Tale of Two Courses; Teaching and Learning Undergraduate Abstract Algebra(2007-11-21) Fukawa-Connelly, Timothy P; Campbell, Patricia F; Fey, James T; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The abstract algebra course is an important point in the education of undergraduate mathematics majors and secondary mathematics teachers. Abstract algebra teachers have multiple goals for student learning, and the literature suggests that students have difficulty meeting these goals. Advisory reports have called for a move away from lecture toward investigation-based class sessions as a means of improving student understanding. Thus, it is appropriate to understand what is happening in the current teaching and associated learning of abstract algebra. The present study examined teaching and learning in two abstract algebra classrooms, one consciously using a lecture-based (i.e., deduction-theory-proof, or DTP) mode of instruction and the other an investigative approach. Instructional data was collected in classroom observations, and multiple written instruments and a set of interviews were used to evaluate student learning. Each instructor hoped students would develop a deep and connected knowledge base and attempted to create classroom environments where students were constantly engaged as a means of doing so. In the lecture class, writing proofs was the central activity of class meetings; nearly every class period included at least one proof. In the investigative class, the processes of computing and searching for patterns in various structures were emphasized. At the end of the semester, students demonstrated mixed levels of proficiency. Generally, students did well on items that were relatively familiar, and poorly when the content or context was unfamiliar. In the DTP course, two students demonstrated significant proficiency with analytical argument; the remainder demonstrated mixed proficiency with proof and very little proficiency with other content. The students in the investigative class all seemed to develop similar levels of proficiency with the content, and demonstrated more willingness to explore unknown structures. This study may prompt discussions about the relative importance of developing proof-proficiency, students' ability to formulate and investigate hypotheses, developing students' content knowledge, and students' ability to operate in and analyze novel structures.