Date of Award:

5-2025

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

Brynja R. Kohler

Committee

Brynja R. Kohler

Committee

Kristy Bloxham

Committee

James S. Cangelosi

Committee

Sindura Kularajan

Committee

Zhaohu Nie

Abstract

Graduate programs in mathematics are intended to develop experts in mathematics. As part of a graduate program, many students are expected to engage in a qualifying examination that can serve myriad purposes. This dissertation investigates real analysis qualifying examinations at the master's level through a nation-wide survey of institutions in the Association of Public and Land-Grant Universities (APLU). This study reveals the practices in administration of real analysis qualifying exams, institutions reported offering traditional, pencil-and-paper exams and generally asked students to prepare individually using previously administered exams. The survey results show that approximately two in three APLU institutions offering master's degrees in mathematics assess real analysis in some form, including traditional exams or coursework. When a qualifying exam is given, the majority of institutions offer students two exam attempts to pass. Furthermore, the content of qualifying exams was studies. Results showed that exam items fell into one of two areas: Advanced Calculus and Real Analysis (i.e., measure theory), with further sub-areas defined based on an analysis of textbooks in-use. Of the sample of qualifying exams from nine institutions, five institutions emphasized Advanced Calculus, three emphasized Real Analysis and one had a roughly even ratio of Advanced Calculus and Real Analysis content. The content analysis was validated using three coders. This dissertation offers a framework connecting the memory demands on the student required to transfer from the task to the solution. Coders applied this framework and results show over half of the items required a high level of memory demands, or transfer, and approximately 15% required simple knowledge-level understanding. Data about content and transfer levels of exam items are contained in this dissertation.

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