CI 7302. Research Methods and Measurement in Education.

This course provides a comprehensive introduction to educational research with a focus on research design, research methods and methodology, and fundamental measurement issues in quantitative, qualitative, and mixed-methods research. Students examine various tenets, assumptions, and principles of research methods as applied to educational contexts. Students investigate various components of the research process ranging from research questions, data collection, data analysis, and dissemination. Outcomes include the development of a research study proposal according to ethical guidance from the Institutional Review Board.

CI 7303. Educational and Psychological Measurement and Assessment.

This course addresses philosophical and empirical foundations of measurement, assessment, testing, and evaluation relevant to educational and psychological research and practice. Topics include theories of testing; types of tests; test construction; observational rating scales; measurement interpretation; item analysis; factor analysis; psychometric reliability and validity; assessment selection; and examination and analysis of social, legal, and ethical considerations of measurement and assessment. Course content emphasizes applied learning through examining measurement instruments and their empirical evidence, analyzing data using statistical analysis software, and applying principles of test construction to constructs of interest to students. Students expand their knowledge and skills related to educational and psychological measurement and assessment with individualized emphasis in areas relevant to students’ research and practice.

CI 7310. Teaching in College.

This course introduces postsecondary pedagogical strategies and approaches for graduate teaching assistants and graduate instructional assistants. Topics include designing syllabi, collaborating with colleagues and teaching staff, using various instructional approaches, implementing active learning strategies, assessing learning, integrating technology into the classroom, and fostering students' cognitive, emotional, and behavioral engagement. Students examine principles of research-informed teaching and instructional approaches that facilitate college student learning and motivation. Completion of this course does not earn graduate degree credit.

CI 7326. Grant Development and Management.

This course guides doctoral students through the grant proposal writing process, including essential resources for managing funded programs in educational contexts. Students locate public and private funding sources and evaluate existing grant proposals for effectiveness. Course content emphasizes the entire lifecycle of a grant including the development of comprehensive budgets, management projects for accountability, and usage of electronic grant-seeking strategies. Through stakeholder interviews and collaborative needs assessments, students gain practical insights into the practitioner's perspective of grantsmanship and skills to develop professional funding applications in educational environments.

CI 7351. Beginning Quantitative Research Design and Analysis.

This course prepares students to engage with quantitative research in education. Students examine the role of research and theory, analyze quantitative research designs, and synthesize scholarly literature to develop meaningful research questions grounded in empirical literature. Emphasis is placed on applying statistical techniques using statistical software, such as data cleaning, management, and both descriptive and inferential analyses. Inferential statistics topics include descriptive statistics, t-tests, analysis of variance, chi-square, and correlation. Students learn to interpret statistical results and communicate findings through academic writing. Corequisite: CI 7302 with a grade of "C" or better.

CI 7352. Beginning Qualitative Design and Analysis.

This course introduces the qualitative research paradigm, focusing on the unique features and traditions of interpretive inquiry contextualized to postsecondary student success. Students examine qualitative methodologies, purposeful sampling techniques, and common data collection methods such as interviewing and observation. Course content emphasizes the role of the researcher as a primary instrument and provides foundational training in inductive data analysis. Through critical evaluation of existing studies and practical application, students learn to establish trustworthiness and rigor in their work. The seminar format encourages students to analyze the role of the researcher in qualitative inquiry while developing the technical skills necessary to interpret complex human experiences and educational phenomena. Corequisite: CI 7302 with a grade of "C" or better.

CI 7353. Intermediate Quantitative Research Design and Analysis.

This course focuses on intermediate quantitative research design and statistical methods of data analysis commonly applied in social science fields including education, psychology, and sociology. The general linear model and generalized linear model serve as a foundation for student examination of selected univariate and multivariate statistical techniques such as regression and analysis of variance. Course content emphasizes applied learning through evaluating published research, analyzing data using statistical analysis software, and formulating research questions, research designs, and data analytic plans. Students apply these quantitative methods and skills to address research problems in their area of inquiry. Prerequisite: CI 7351 with a grade of "C" or better.

CI 7354. Intermediate Qualitative Design and Analysis.

This course provides an advanced exploration of qualitative research, focusing on the intricate designs and analytical techniques required for doctoral-level inquiry. Students engage deeply with five primary traditions—narrative, phenomenology, grounded theory, ethnography, and case study—to align their research questions with appropriate methodologies. The curriculum emphasizes the rigorous collection of diverse data types and the application of sophisticated coding and thematic analysis strategies. Students critically evaluate existing studies to develop analytical clarity and methodological coherence and ethical research practices. Through both collaborative and independent work, students transform raw observations into analytically coherent qualitative interpretations. Prerequisite: CI 7352 with a grade of "C" or better.

CI 7355. Mixed Methods in Research and Evaluation.

This course provides an advanced exploration of mixed methods research design and program evaluation within the context of developmental education. Students investigate the philosophical underpinnings and practical applications of integrating qualitative and quantitative data to address complex educational problems. Course content emphasizes the selection of appropriate mixed methods frameworks—such as convergent, explanatory sequential, and exploratory sequential designs—to enhance the validity of research findings. Students develop comprehensive evaluation plans, focusing on professional practice commonly examined in evaluation literature and data-driven decision-making. Through analytical critiques and the creation of a formal research proposal, students develop the skills necessary to guide scholarly research and program evaluation. Prerequisite: CI 7351 and CI 7352 both with grades of "B" or better.

CI 7358. Advanced Seminar in Qualitative Research.

This course provides an advanced exploration of the historical, philosophical, and theoretical underpinnings that ground qualitative inquiry. Students examine the distinctions between theoretical and conceptual frameworks, learning how to leverage diverse social theories to shape research design. Coursework emphasizes the holistic process of aligning ontological stances with rigorous analytic methods to interpret complex data. Through careful analysis and application of theoretical and methodological texts aligned to their research goals, students develop necessary skills to independently produce advanced qualitative research. Prerequisite: CI 7352 and CI 7354 both with grades of "B" or better.

CI 7359. Advanced Seminar in Quantitative Research.

This course examines advanced quantitative analysis techniques relevant to students' research interests. Examples of seminar topics include structural equation modeling, hierarchical linear modeling, path analysis, moderation analysis, propensity-score matching, missing data analysis and imputation, non-parametric analyses, advanced regression analysis, meta-analysis, and other univariate and multivariate statistical methods relevant to students' research. Students build quantitative research skills through evaluating published research, analyzing data using advanced statistical analysis software, and generating complex research designs. Students develop specialized knowledge of selected quantitative methods to advance their research goals. Prerequisite: CI 7351 and CI 7353 both with grades of "B" or better.

CI 7378. Independent Study.

This course allows doctoral students to engage in independent, faculty-guided study of a selected topic or applied area in postsecondary student success, emphasizing analytical inquiry and specialized learning beyond regularly offered courses. Students examine specialized topics through the analysis of scholarly literature, application of appropriate research methods, and synthesis of findings into a structured project. Activities may include, but are not limited to, literature review, analytical writing, or applied project work, as appropriate to the topic and learning plan. The scope, methods, and deliverables of the course are determined in consultation with the supervising faculty member. Emphasis is placed on independent, inquiry-based learning consistent with disciplinary standards. The independent study may be repeated once for credit with different emphasis.

CI 7386. Directed Research.

This course provides doctoral students an opportunity to participate in a faculty member’s research team. Course tasks include aspects of assisting in a research study from identifying a researchable topic, reviewing the literature, producing research questions, designing research and methodology, analyzing results, drawing conclusions and implications, and producing a publishable manuscript draft. The goal of the course is to provide scaffolded and guided practice in research in postsecondary student success. This course is repeatable once with either the same faculty supervisor or a different supervisor.

CI 7390. Dissertation Proposal Development.

This course provides support for students approaching the dissertation stage to clarify a research problem and develop a preliminary dissertation proposal. Course instruction addresses dissertation proposal development and is responsive to students’ research problems and methodological approaches. Course tasks include identifying a researchable topic, reviewing relevant literature, generating research questions, and designing appropriate research methods. The goal of the course is to provide structured opportunities for feedback and guided development while crafting a dissertation research proposal. Approval from the dissertation chair is required for enrollment. Prerequisite: CI 7351 and CI 7352 and [CI 7353 or CI 7354 or CI 7355] all with grades of a "B" or better.

DE 7199. Dissertation.

This course supports the completion of original, independent research in postsecondary student success under the direct supervision of the student’s dissertation research advisor. Students analyze theoretical perspectives, methodological approaches, and analytical strategies relevant to their dissertation studies. Course content emphasizes evaluation of research design, data collection and analysis, and scholarly argumentation. Through sustained engagement with the research process, students assess the coherence, rigor, and contribution of their work to the field. During candidacy, continuous enrollment in dissertation coursework is required.

DE 7299. Dissertation.

This course supports the completion of original, independent research in postsecondary student success under the direct supervision of the student’s dissertation research advisor. Students analyze theoretical perspectives, methodological approaches, and analytical strategies relevant to their dissertation studies. Course content emphasizes evaluation of research design, data collection and analysis, and scholarly argumentation. Through sustained engagement with the research process, students assess the coherence and rigor of their work within disciplinary expectations. During candidacy, continuous enrollment in dissertation coursework is required.

DE 7301. Understanding Learners in Postsecondary Contexts.

This course provides students with foundational knowledge on the evolution, characteristics, demographics, goals, and needs of learners in Postsecondary and Developmental Education contexts. Course content emphasizes analyzing the internal factors, including the cognitive, affective, and psychosocial needs of students, and external contextual factors, such as social, policy, and institutional systems. These are examined analytically as influences on learner experiences that impact learners' educational experiences. Students explore the history of the field of postsecondary and developmental education and its contemporary applications. Students conduct careful analysis of scholarly literature to explore multiple facets of postsecondary learner development.

DE 7302. Policy Structures in Developmental Education.

This course examines the historical and contemporary policy structures shaping developmental education and postsecondary student success. Students analyze theoretical foundations and empirical research guiding developmental education structure and placement across postsecondary systems, and evaluate the legal and policy implications that can influence students' educational outcomes. Through interdisciplinary inquiry, students synthesize research and policy documents on curricular, institutional, and system-level dimensions of developmental education policy, practice, and reform across local, state, and national levels.

DE 7303. Teaching and Learning in Developmental Education.

This course focuses on principles for effective teaching and learning in developmental education, including institutional development, learner development, intellectual development, and self-development. Topics include theories of teaching and learning, pedagogies, assessment and evaluation techniques, and research‑supported practices. Through a survey of foundational and contemporary scholarship on pedagogies and empirical research examining practices to support adult and postsecondary learners, students examine the interrelated factors that shape postsecondary student success in developmental education and related contexts.

DE 7305. Education in Multicultural Contexts.

This course examines learner development across the PK–16 education system using multicultural analytical frameworks that are examined comparatively and grounded in established educational theory and research. Students analyze school structures, instructional practices, and policy contexts to understand how educational pathways are formed and how learning environments influence the progress of various populations of learners. Course content focuses on the range of factors that may shape educational experiences across grade levels and contexts. Through research projects and presentations, students evaluate a variety of multicultural educational models and varying institutional practices. Assessment emphasizes analysis, synthesis of research, and effective written and oral communication.

DE 7321. The Community College.

This course examines the history, development, organization, functions, and contemporary issues of American community colleges, emphasizing their role in postsecondary student success. Students explore student populations, governance, campus culture, administrative procedures, support services, curricular patterns, faculty composition, and the integration of developmental and adult education. Course content emphasizes understanding how institutional structures, policies, programs and practices support student learning, engagement, and retention. Students evaluate community college structures, policies and programs, and analyze and compare strategies used to address student success in postsecondary settings.

DE 7322. Learning Support Services in Postsecondary Settings.

This course addresses theory, research, and practice in non-course-based learning support services in postsecondary contexts. Course topics include postsecondary tutoring, supplemental instruction, academic coaching, mentoring, advising, research support, and related services provided in learning support contexts such as student success centers, writing centers, and early alert systems. Students investigate scholarly and practical issues related to administering and providing learning support services. Course content emphasizes application of theory and research to the development and implementation of pedagogical and administrative approaches to analyze how services are designed to address varied student needs as described in the literature.

DE 7323. Academic Support for Students with Learning Disabilities.

This course examines learning disabilities and executive function differences affecting academic performance in postsecondary education. Students review theoretical perspectives related to the etiology and characteristics of learning disabilities and analyze the physical, cognitive, social, and emotional dimensions of students with learning disabilities across the lifespan. Course content applies learning and teaching theories to instructional strategies, academic interventions, and assessment practices to support college students with learning disabilities. Students evaluate research and neuropsychological literature relevant to postsecondary instruction, examine principles of effective teaching and curriculum design, and review federal and state legislation governing services and disability accommodations in postsecondary settings.

DE 7324. Teaching Learning Strategies and Critical Thinking in Postsecondary Contexts.

This course addresses theory, empirical research, and pedagogical practices that inform how teachers and other educational practitioners facilitate students’ development of learning strategies, problem solving, and critical thinking in postsecondary contexts. Course content emphasizes applied learning through evaluating existing curriculum and instruction related to learning strategies and critical thinking, with consideration of both historical and contemporary perspectives in research and practice. Students integrate research-based recommendations into teaching demonstrations and curriculum designs that examine instructional approaches related to strategic thinking. Students expand their knowledge and skills related to teaching learning strategies and critical thinking through synthesizing scholarly and applied literature to address gaps in the field.

DE 7327. Student Motivation and Self-Regulation.

This course examines research-based theories of student motivation and self-regulation across developmental and postsecondary contexts. Students analyze major theoretical frameworks, including overlapping and competing perspectives, and consider their implications for educational practice. Course content addresses social influences on motivational and self-regulatory processes. Through review and synthesis of scholarly literature, students evaluate empirical findings and methodological approaches to consider applications to educational settings, including interventions and programs. The course prepares students to engage with motivation and self-regulation as complex, multidimensional constructs in academic contexts.

DE 7380. Managing Postsecondary Transition and Developmental Education Programs.

This course focuses on theoretical and practical elements of managing postsecondary transition programs, with emphasis on developmental education programs. Course content focuses on including how to lead and manage developmental education programs as well as postsecondary transition programs such as summer bridge programs. Students apply leadership models and research to existing practice, analyze various transition programs, and apply course concepts to develop and refine management approaches and program structures. Students expand their knowledge and skills related to managing postsecondary transition and developmental education programs by synthesizing scholarly literature to generate original ideas that identify areas for further research and scholarly discussion.

DE 7381. Practicum in Postsecondary Student Success.

This course provides students with an opportunity to gain hands-on experiences conducting a field-based project related to postsecondary student success in an authentic setting at a host institution. Students complete a one-semester, 150-hour practicum in an approved institution or agency outside of their own employment. Practicum students participate in leadership activities at the practicum site involving program planning, management, budgeting, and evaluation. With mentorship from a supervising faculty member, students draft a project overview and action plan.

DE 7399. Dissertation.

This course supports the completion of original, independent research in postsecondary student success under the direct supervision of the student’s dissertation research advisor. Students analyze theoretical perspectives, methodological approaches, and analytical strategies relevant to their dissertation studies. Course content emphasizes evaluation of research design, data collection and analysis, and scholarly argumentation. Through sustained engagement with the research process, students assess the coherence, rigor, and contribution of their work to the field. During candidacy, continuous enrollment in dissertation coursework is required.

DE 7599. Dissertation.

This course supports the completion of original, independent research in postsecondary student success under the direct supervision of the student’s dissertation research advisor. Students analyze theoretical perspectives, methodological approaches, and analytical strategies relevant to their dissertation studies. Course content emphasizes evaluation of research design, data collection and analysis, and scholarly argumentation. Through sustained engagement with the research process, students assess the coherence, rigor, and contribution of their work to the field. During candidacy, continuous enrollment in dissertation coursework is required.

DE 7699. Dissertation.

This course supports the completion of original, independent research in postsecondary student success under the direct supervision of the student’s dissertation research advisor. Students analyze theoretical perspectives, methodological approaches, and analytical strategies relevant to their dissertation studies. Course content emphasizes evaluation of research design, data collection and analysis, and scholarly argumentation. Through sustained engagement with the research process, students assess the coherence, rigor, and contribution of their work to the field. During candidacy, continuous enrollment in dissertation coursework is required.

DE 7999. Dissertation.

This course supports the completion of original, independent research in postsecondary student success under the direct supervision of the student’s dissertation research advisor. Students analyze theoretical perspectives, methodological approaches, and analytical strategies relevant to their dissertation studies. Course content emphasizes evaluation of research design, data collection and analysis, and scholarly argumentation. Through sustained engagement with the research process, students assess the coherence, rigor, and contribution of their work to the field. During candidacy, continuous enrollment in dissertation coursework is required.

ENG 7300. Language Issues in Multicultural Environments.

This course examines language issues arising in multicultural environments through sociolinguistic, descriptive, and semantic perspectives. Students analyze language variation, multilingualism, and language contact phenomena across diverse communities. Topics include the role of language in education, writing across cultural contexts, and the relationship between language and social identity. The course investigates how sociolinguistic research methods inform understanding of writing and communication in multilingual settings. Students evaluate competing scholarly frameworks used to describe patterns of language use and their implications for educational and professional contexts.

ENG 7314. Specializations in Professional and Technical Communication Topics.

This course provides advanced study in specialized areas of technical and professional communication outside primarily technology-focused contexts. Topics vary by semester and may include grant and proposal writing, government and public sector communication, health and medical communication, environmental communication, nonprofit communication, policy writing, crisis communication, science communication, or community-based professional writing. Students engage relevant theoretical frameworks and disciplinary scholarship while producing applied, genre-specific deliverables. Emphasis is placed on rhetorical analysis, audience adaptation, ethical considerations, and professional standards within specialized contexts. The course may be repeated with different emphases for up to twelve hours of graduate credit.

ENG 7316. Foundations in Rhetoric and Composition.

This course examines theoretical, pedagogical, and methodological foundations in the field of rhetoric and composition. Students analyze major scholarly traditions, research methods, and instructional approaches that shape the discipline. Topics may include writing pedagogy, digital writing, pedagogical theory, and writing in public and civic contexts. The course emphasizes critical engagement with foundational texts and the application of disciplinary frameworks to questions of writing, teaching, and inquiry. Students evaluate competing perspectives within the field and assess their implications for scholarship and practice. Repeatable with different emphases for up to nine hours of English credit.

ENG 7317. Specializations in Rhetoric and Composition.

This course examines specialized areas within rhetoric and composition, providing theoretical, pedagogical, methodological, and administrative grounding in focused topics. Students analyze scholarship, methods, and practices relevant to the selected area of emphasis. Topics may include writing center theory and administration, writing across the curriculum, literacy studies, and contemporary areas of rhetorical theory. The course emphasizes critical engagement with disciplinary scholarship and the application of specialized knowledge to questions of writing, rhetoric, and institutional practice. Students evaluate research and competing frameworks within the area of specialization. The course may be repeated with different emphases.

ENG 7326. Contemporary Composition Theory.

This course examines the history of writing instruction in the university and the theories of writing and composing that inform contemporary composition studies. Students trace the development of major theoretical traditions in the field, analyzing how evolving conceptions of writing have shaped instructional practices and disciplinary inquiry. Topics include historical and contemporary approaches to composition theory, the relationship between theory and pedagogy, and current scholarly debates within the discipline. Students engage with foundational and recent scholarship to evaluate how theoretical frameworks inform research and the teaching of writing.

ENG 7383. Studies in Rhetorical Theory.

This course examines rhetorical theory from classical traditions through contemporary scholarship. Students analyze major rhetorical concepts, movements, and debates that have shaped the discipline across historical periods. Topics may include classical rhetoric, modern and postmodern rhetorical theory, and the application of rhetorical frameworks to areas such as composition studies and technical communication. The course emphasizes close engagement with primary theoretical texts and the development of analytical skills for interpreting rhetorical traditions within their intellectual and historical contexts. The course may be repeated with different emphases.

MATH 7111. Seminar in Teaching.

Seminar on individual study projects concerned with selected problems in the teaching of mathematics. This course does not earn graduate degree credit.

MATH 7188. Seminar in Mathematics Education.

This course requires students to participate in weekly research seminars in mathematics education that emphasize scholarly discussion, critical engagement with current research, and professional communication. Students attend presentations by faculty, visiting scholars, and peers, and they contribute to seminar dialogue through questioning and discussion. Each student delivers at least one formal research presentation during the semester, drawing on original research, dissertation work, or a critical analysis of existing literature in mathematics education. The course supports the development of research communication skills, familiarity with ongoing research agendas, and participation in the professional community. This course is repeatable for credit when seminar content varies.

MATH 7199A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester.

MATH 7299A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

MATH 7301. Studies in Mathematics.

This course provides foundational preparation in graduate mathematics for students entering doctoral study in mathematics or mathematics education. Topics may include essential concepts and methods from advanced algebra, analysis, topology, discrete mathematics, and proof-based reasoning, depending on student background and program needs. Emphasis is placed on strengthening mathematical maturity, rigorous communication, abstraction, and the transition to graduate-level expectations in reading, writing, and problem solving. This course may be repeated and does not earn graduate degree credit.

MATH 7302. History of Mathematics.

This course emphasizes the development of mathematics and the accomplishments of mathematicians who contributed to its progress across cultures and historical periods. Topics include the emergence of major mathematical ideas, the historical development of algebra, geometry, calculus, and other significant areas, original and secondary historical sources, and the cultural and philosophical settings in which mathematics evolved. Students will be able to explain the historical significance of various mathematical achievements and discuss connections between earlier developments, contemporary mathematical thought, and the teaching and learning of mathematics.

MATH 7303. Analysis I.

This course covers measure theory with special emphasis on the Lebesgue measure. Topics include the outer measure, sigma-algebra of measurable sets, properties of measurable sets, Borell-Canteli lemma, non-measurable sets, Cantor-Lebesgue function, Lebesgue measurable functions, pointwise limits, simple approximations, and Littlewood’s three principles. Additional attention may be given to convergence theorems, and the role of approximation theory in modern analysis. Emphasis is placed on rigorous proof, abstract reasoning, and the analytical foundations needed for advanced work in real analysis, probability, and related mathematical fields.

MATH 7306. Current Research in Math Education.

This course examines foundational and contemporary research in mathematics education with attention to the social, political, and economic trends that shape research agendas in local, state, national, and international settings. Topics include major themes in mathematics education research, research traditions and methods, contemporary debates in the field, and the interpretation of scholarly literature within broader educational contexts. Students will be able to discuss contemporary and historical trends and issues in mathematics education, develop skills for written synthesis of academic arguments, and identify research areas of interest and develop expertise in those areas.

MATH 7307. Algebra I.

This course examines the structure and methods of modern algebra with emphasis on group‑theoretic foundations and select topics from ring theory. Topics include permutation groups, symmetry groups, Sylow theorems, and selected topics from ring theory. Additional attention is given to homomorphisms, quotient structures, and related algebraic constructions that support advanced study in abstract algebra. Emphasis is placed on rigorous proof, structural reasoning, and the analysis of algebraic systems that arise throughout advanced mathematics. The course prepares students for further doctoral‑level work in algebra and related fields by strengthening abstract reasoning and proof‑writing skills.

MATH 7309. Topology I.

This course studies point-set topology at the doctoral level. Topics include topological spaces, continuous functions, connectedness, compactness, countability, separability, metrizability, CW complexes, simplicial complexes, nerves, and dimension theory. Additional attention may be given to product and quotient constructions, subspace topology, and examples that connect foundational topology to later study in geometry, algebra, and analysis. Emphasis is placed on rigorous proof, precise use of definitions, and structural reasoning in abstract topological settings.

MATH 7313. Analysis II.

This course covers the theory of integration with special emphasis on Lebesgue integrals. Topics include the Lebesgue integral for bounded, finitely supported, and measurable functions, convergence theorems, differentiability of monotone functions, absolute continuity, Lp spaces, and Lp completeness. Additional attention may be given to convergence theorems, and the role of integration theory in modern analysis. Emphasis is placed on rigorous proof, abstract reasoning, and the analytical foundations needed for advanced work in real analysis, probability, and related mathematical fields. Prerequisite: Math 7303 with a grade of "B" or better.

MATH 7315. Calculus of Variations.

This course examines the theoretical foundations of the calculus of variations with emphasis on variational principles and their applications. Topics include properties of functionals, first and second variations, extremal problems, Euler–Lagrange equations, and stability theory. The course considers variational formulations in multiple settings. Emphasis is placed on rigorous analysis, derivation of variational conditions, and interpretation of solutions. The course prepares doctoral students for advanced research involving variational methods and related analytical techniques. Prerequisite: MATH 7303 with a grade of "B" or higher.

MATH 7317. Algebra II.

This course examines advanced algebraic structures of rings and fields at the doctoral level. Topics include rings, ideals, modules, polynomial rings, the Euclidean algorithm, finite fields, and field extensions, along with an introduction to Galois theory and selected geometric applications. Emphasis is placed on rigorous proof, structural reasoning, and the analysis of algebraic systems that support advanced study in algebra, geometry, number theory, and related areas of mathematics. The course prepares students for further doctoral‑level work by strengthening abstract reasoning, proof construction, and the ability to connect algebraic structures across mathematical disciplines. Prerequisite: MATH 7307 with a grade of 'B' or better.

MATH 7319. Topology II: Algebraic Topology.

This course covers the fundamental concepts and tools of algebraic topology. Topics include the fundamental group, covering spaces, homotopy type, the higher homotopy groups, singular homology theory, and the computation of homology groups via exact sequences and applications. Additional attention may be given to representative examples, computational methods, and the role of algebraic invariants in distinguishing and analyzing topological spaces. Emphasis is placed on rigorous proof, structural reasoning, and the use of algebraic methods to study topological phenomena. Prerequisite: MATH 7307 and MATH 7309 with grades of 'B' or better.

MATH 7321. Graph Theory.

This course studies graph theory at an advanced level with emphasis on both structural and applied aspects of graphs. Topics include trees, connectivity of graphs, Eulerian graphs, Hamiltonian graphs, planar graphs, graph coloring, matchings, factorizations, digraphs, networks, and network flow problems. Attention may also be given to algorithms, optimization questions, and representative applications in discrete mathematics and related fields. Emphasis is placed on rigorous proof, structural analysis, and graph-theoretic reasoning.

MATH 7323. Theories of Knowing and Learning in Mathematics Education.

This course surveys the major theories of knowing and learning that have influenced mathematics education. Topics include behaviorism, constructivism, sociocultural theories, situated cognition, and other theoretical perspectives used to explain how learners develop mathematical understanding. Attention is given to how these theories define knowledge, learning, teaching, and participation, and to the ways they shape curriculum, research, and classroom practice in mathematics education. Students will be able to compare theoretical frameworks and interpret their implications for the teaching and learning of mathematics.

MATH 7324. Curriculum Design & Analysis.

This course examines, analyzes, and evaluates the various concepts, topics, methods, and techniques related to curriculum design in mathematics education for grade levels P-16. Topics may include curriculum theory, the historical development of mathematics curricula, standards and policy, curricular coherence across grade bands, implementation issues, and the evaluation of instructional materials and curricular models. Students will be able to analyze curricular materials, evaluate design principles, and analyze relationships among curriculum, instruction, assessment, and equity in mathematics education.

MATH 7328. Instructional Techniques & Assessments.

This course examines, analyzes, and evaluates the various concepts, topics, methods, and techniques of instruction in mathematics education and the related assessment procedures for grade levels P–20. Topics may include instructional design, teaching practices, classroom discourse, formative and summative assessment, task design, feedback, evaluation of student thinking, and the interpretation of assessment data in mathematics education. Students will be able to apply research-based perspectives on teaching and learning to classroom practices and to evaluate alignment among mathematical learning goals, instructional decisions, and assessment practices.

MATH 7331. Combinatorics.

This course is a study of fundamental principles of combinatorics. Topics include permutations and combinations, the Pigeonhole principle, the principle of inclusion–exclusion, binomial and multinomial theorems, special counting sequences, partitions, posets, extremal set theory, generating functions, recurrence relations, and the Pólya theory of counting. Emphasis is placed on rigorous proof, enumeration methods, structural reasoning, and the analysis of finite discrete structures that support further study in combinatorics, graph theory, and related areas of mathematics.

MATH 7342. Research in Undergraduate Mathematics Education I.

This course examines the theoretical foundations of Research in Undergraduate Mathematics Education (RUME). Students study historical and contemporary theoretical perspectives that inform research on the teaching and learning of mathematics at the undergraduate level. Emphasis is placed on critically reading, analyzing, and interpreting research literature in the field. Students will be able to discuss how theoretical frameworks shape research questions, methodologies, and interpretations within RUME. Prerequisite: Math 7306 with a grade of a "B" or better.

MATH 7344. Research in Undergraduate Mathematics Education II.

This course examines advanced research design and development in Research in Undergraduate Mathematics Education (RUME). Through a topic-driven analysis of current RUME literature, students will examine how research is designed and conducted in relation to the teaching and learning of advanced undergraduate mathematics topics such as proof, calculus and analysis, abstract algebra, linear algebra, and differential equations. At the end of the course, students will be able to connect theoretical perspectives to research questions, methodologies, and data interpretations. Students will be able to design and execute research studies in RUME that are appropriate for dissertation-level work. Prerequisite: MATH 7306 and MATH 7342 with grades of a "B" or better.

MATH 7346. Quantitative Research Analysis in Mathematics Education.

This course surveys research techniques used in quantitative analysis for mathematics education. Topics include experimental design, statistical analysis, and the use of appropriate design methodologies to achieve the strongest possible evidence to support or refute a knowledge claim. Additional attention may be given to measurement, validity, inferential reasoning, interpretation of quantitative findings, and the alignment of research questions, methods, and evidence. Students will be able to evaluate the quality of quantitative studies and design rigorous quantitative research in mathematics education. Prerequisite: MATH 7306 and MATH 7325 with grades of 'B' or better.

MATH 7352. Introduction to Qualitative Research in Mathematics Education.

This course introduces doctoral students to principles and techniques of qualitative research as applied to mathematics education. Topics include qualitative research design, sampling strategies, data sources, methods of constant comparison, and conceptualizations of validity and rigor within qualitative research paradigms. Students examine how qualitative methodologies are used to investigate teaching and learning in mathematics education and how such studies are evaluated within the scholarly literature. At the end of the course, students will be able to implement basic qualitative methodologies, interpret qualitative data, and critique published research. Prerequisite: Math 7306 with a grade of "B" or better.

MATH 7354. Advanced Qualitative Research.

This course examines advanced qualitative research methods used in mathematics education. Emphasis is placed on techniques for qualitative data collection and analysis, including interpreting data and representing findings. Topics include qualitative research design, data collection strategies, analytic frameworks, trustworthiness, ethics, and methodological coherence. Through engaging in sustained analyses of qualitative evidence, students will be able to apply established qualitative methods to research problems in mathematics education. Students will be able to critique qualitative methods, evaluate published studies, and discuss strengths and weaknesses of various approaches relative to the aims of the research problem. Prerequisite: MATH 7352 or ED 7352 with a grade of "B" or better.

MATH 7356C. Action Research in Mathematics Education.

This course examines the theoretical foundations, methodological approaches, and practical considerations of action research in mathematics education. Emphasis is placed on the systematic study of instructional practices, curriculum design, assessment strategies, and classroom‑based problem solving. Students analyze published action research studies, evaluate issues of validity, ethics, and rigor, and design an original action research proposal grounded in relevant literature. The course supports the development of research questions, data collection strategies, and analytic techniques appropriate for educational settings. Attention is given to the role of reflective practice and evidence‑based decision making in mathematics education contexts. Prerequisite: MATH 7346 or MATH 7352 or ED 7352 with a grade of "B" or better.

MATH 7358. Advanced Quantitative Research in Mathematics Education.

This course examines advanced quantitative research methods used in mathematics education. Topics include experimental design, statistical modeling, multivariate and multilevel analysis, and methodological considerations for producing and interpreting quantitative evidence. Emphasis is placed on aligning research questions with appropriate quantitative designs and analytic strategies, as well as critically evaluating the strength and limitations of quantitative findings. Students will be able to investigate questions in mathematics education using advanced quantitative techniques and to interpret and evaluate published research literature in mathematics education. Prerequisite: MATH 7346 with a grade of "B" or better.

MATH 7361. Seminar in Advanced Mathematics.

This course is a doctoral‑level seminar in advanced mathematics, where course content varies by offering and is determined by faculty expertise and student research interests. Topics are drawn from areas such as analysis, algebra, topology and geometry, applied mathematics, or probability and statistics. Instructional modality will be appropriate for the topic and determined by the instructor, and may include student‑led presentations, guided discussion, collaborative problem analysis, or directed study of advanced literature. This course may be repeated for credit when the seminar topic differs.

MATH 7363A. COMPLEX ANALYSIS.

This course is a brief introduction to the complex number system and the basic point-set topology of the complex plane, followed by a proof-based and rigorous study of the principal results in the analysis of functions of a single complex variable. Topics may include analytic functions, contour integration, the Cauchy integral theorem and formula, Laurent series, residues, conformal mappings, and selected extensions to more advanced geometric viewpoints such as Riemann surfaces. Emphasis is placed on rigorous proof, conceptual understanding, and the role of complex analysis in advanced mathematics.

MATH 7363B. NUMERICAL ANALYSIS.

This course examines advanced numerical analysis techniques for the analysis and implementation of mathematical algorithms. Emphasis is placed on the theoretical foundations of numerical methods, including stability, convergence, consistency, and error analysis, as well as practical implementation using computational and computer algebra systems. Symbolic, numerical, and graphical techniques are used to analyze algorithm performance. Applications are drawn from mathematics, science, and engineering. Instructional modality will be appropriate for the topic and determined by the instructor.

MATH 7363C. Functional Analysis.

This course examines foundational results and methods in functional analysis at the doctoral level. Core topics include the Hahn-Banach theorem, the uniform boundedness principle, and the open mapping theorem, along with their consequences for normed linear spaces and Banach spaces. Additional topics may include bounded linear operators, dual spaces, weak topologies, and selected applications to analysis and partial differential equations. Emphasis is placed on rigorous proof, abstract reasoning, and the role of functional analytic techniques in modern mathematics. Prerequisite: MATH 7303 with a "C" or better.

MATH 7363E. Numerical Analysis II.

This course examines advanced numerical methods for the solution of partial differential equations. Emphasis is placed on the analysis and numerical implementation of algorithms for linear and selected nonlinear partial differential equations. Topics may include finite difference, finite element, and spectral methods; stability, consistency, and convergence analysis; and the solution of large linear systems arising from discretized PDEs. Applications are drawn from mathematics, science, and engineering to illustrate methodological principles rather than prescribe applied outcomes. Prerequisite: MATH 7363B with a grade of a "C" or better.

MATH 7363F. Functional Analysis II.

This course examines advanced topics in functional analysis with a focus on infinite‑dimensional vector spaces and their applications. The course studies spaces of functions, measures, and distributions, emphasizing the structural and analytical differences between finite‑ and infinite‑dimensional settings. Topics may include Banach and Hilbert space theory, Fourier transform methods, bounded and unbounded linear operators, and selected aspects of operator theory. Attention is given to the role of functional analysis in modern analysis, partial differential equations, and numerical analysis. Emphasis is placed on rigorous proof, abstract reasoning, and the development of techniques used to analyze complex mathematical problems. Prerequisite: MATH 7363C with a grade of "C" or better.

MATH 7366C. Teaching Teachers (In-Service; Pre-Service).

This course examines research‑based approaches to the preparation and professional development of mathematics teachers. Topics include the education of pre‑service and in‑service teachers, theoretical frameworks in teacher learning, and models of mathematics teacher education. The course analyzes research literature, policy documents, and professional standards relevant to mathematics teacher preparation, treating these sources as objects of scholarly study rather than prescriptive mandates. Students will be able to evaluate research-based models of professional development, compare perspectives, and discuss the implications of differing approaches to the teaching and learning of mathematics. Prerequisite: MATH 7306 with a grade of 'B' or better.

MATH 7366D. Teaching Specialized Content.

This course provides an in-depth study of a specialized content area in mathematics with emphasis on teaching and learning. The specific content area will vary by instructor and their specialization. Some examples include geometry, quantitative reasoning, probability and statistics. Attention is given to implications for curriculum, classroom practice, teacher professional development, theories of teaching and learning, and methods for research. Students will be able to interpret, discuss, and synthesize scholarly work on the focal topic.

MATH 7366E. Developmental Mathematics Curriculum.

This course examines research, development, and evaluation related to developmental mathematics curricula. Emphasis is placed on the study of curriculum scope and sequence, instructional goals, and design principles underlying developmental mathematics programs. The course analyzes research literature, research‑based models, and selected policy and professional documents relevant to developmental mathematics, treating these materials as objects of scholarly inquiry rather than prescriptive mandates. Students examine how curricular frameworks are designed, evaluated, and revised in response to research findings.

MATH 7367B. Advanced Group Theory.

This course examines advanced topics in group theory at the doctoral level. Topics may include solvable, p‑solvable, and nilpotent groups; group actions; transfer theorems; simple groups and composition series; the generalized Fitting subgroup; automorphism groups; classical groups; and linear representations of groups. Emphasis is placed on structural results, proof techniques, and the role of group theory in modern algebra. The course develops rigorous reasoning and abstraction skills necessary for advanced study and research in algebra. Prerequisite: MATH 7307 with a grade of "C" or better.

MATH 7369C. Low-Dimensional Topology.

This course introduces advanced topics in low‑dimensional topology at the doctoral level. Topics include the study of surfaces, knots and links, 3‑manifolds, and selected aspects of 4‑manifold theory. Emphasis is placed on foundational results, key techniques, and current research directions in low‑dimensional topology. Students examine how geometric, algebraic, and topological methods are used to analyze low‑dimensional spaces. The course develops rigorous reasoning and familiarity with ideas central to contemporary research in topology, preparing students for further study and research in geometric and topological fields. Prerequisite: MATH 7307 and MATH 7309 with grades of "C" or better.

MATH 7369D. Characteristic Classes.

This course examines vector bundles and characteristic classes at the doctoral level. Topics include Stiefel-Whitney classes, Chern classes, the Euler class, and Pontrjagin classes, with emphasis on their definitions, properties, and methods of computation. Additional topics may include applications to manifold immersion and embedding problems. The course explores how characteristic classes serve as fundamental tools in topology and geometry, connecting algebraic, geometric, and topological techniques. Emphasis is placed on rigorous proof, abstract reasoning, and the role of characteristic classes in contemporary mathematical research. Prerequisite: MATH 7317 and MATH 7319 with grades of a "C" or better.

MATH 7369E. Differential Geometry.

This course examines modern tools and methods of differential geometry at the doctoral level. Topics include smooth manifolds, Riemannian metrics, connections, covariant derivatives, geodesics, curvature, and intrinsic and extrinsic geometric computations. Additional topics may include hyperbolic geometry, Lie groups, Chern-Weil theory, surfaces of prescribed mean curvature, the Gauss-Bonnet theorem, and the Cartan-Hadamard theorem. Emphasis is placed on rigorous proof, geometric intuition, and the role of differential geometry in contemporary mathematical research. Prerequisite: MATH 7307 and MATH 7309 with grades of "C" or better.

MATH 7371A. Advanced Graph Theory.

This course is an advanced study of graph theory, emphasizing both classical results and modern research directions selected by the instructor. Topics may include Turán‑type problems, Ramsey theory, extremal graph theory, random graph theory, algebraic graph theory, domination and distance parameters, and selected applications. The course focuses on theoretical frameworks, proof techniques, and the analysis of graph structures that arise in contemporary combinatorics. Students engage with foundational and current research results to develop advanced problem‑solving skills and mathematical maturity, preparing them for independent research in graph theory and related areas. Prerequisite: MATH 7321 with a grade of "B" or better.

MATH 7371B. Advanced Combinatorics.

This course provides an advanced study of combinatorics with emphasis on both classical structures and modern theoretical developments. Topics may include block designs, Latin squares, combinatorial optimization, coding theory, matroids, difference sets, and finite geometry. The course focuses on rigorous definitions, proof techniques, and the analysis of combinatorial structures that arise across mathematics. Students examine foundational results and selected contemporary work to develop advanced problem‑solving skills and mathematical maturity. The course prepares students for further research in combinatorics and related areas of mathematics. Prerequisite: MATH 7331 with a grade of 'B' or better.

MATH 7371C. Combinatorial Number Theory.

This course provides an advanced study of fundamental techniques in combinatorial number theory. Topics may include additive number theory, Waring’s problem, and probabilistic methods in number theory. Emphasis is placed on rigorous definitions, proof techniques, and structural analysis of number‑theoretic problems using combinatorial methods. Students engage with classical results and selected modern developments to build mathematical maturity and research readiness. The course is designed to support doctoral‑level study by strengthening abstract reasoning skills and preparing students for advanced research in number theory and related areas. Prerequisite: MATH 7331 with a grade of 'B' or better.

MATH 7371D. Discrete Optimization.

This course provides an advanced study of fundamental techniques in discrete optimization. Topics may include linear programming, integer and nonlinear integer programming, dynamic programming, matroids, and computational complexity, as well as classical optimization problems such as scheduling, location, transportation, postman, and traveling salesman problems. The course emphasizes rigorous problem formulation, mathematical modeling, and algorithmic analysis. Students examine theoretical foundations and complexity considerations, including NP‑completeness, to assess problem feasibility and solution approaches. The course prepares students for advanced research and applications in optimization, operations research, theoretical computer science, and applied mathematics. Prerequisite: MATH 7321 and 7331 with grades of "B" or better.

MATH 7371F. Probabilistic Methods in Discrete Mathematics.

This course provides an advanced study of probabilistic techniques used in discrete mathematics. Topics may include linearity of expectation, alterations, second‑moment methods, the Lovász local lemma, correlation inequalities, martingales, the Poisson paradigm, and pseudo‑randomness. These methods are applied to problems arising in graph theory, combinatorics, combinatorial number theory, combinatorial geometry, and the analysis of algorithms. Emphasis is placed on rigorous proofs, careful probabilistic reasoning, and the interpretation of random structures. The course prepares students for advanced research by developing mathematical maturity and familiarity with probabilistic tools central to modern discrete mathematics. Prerequisite: MATH 7321 and 7331 with grades of "B" or better.

MATH 7371G. Applied Discrete Mathematics.

This course introduces fundamental concepts in applied discrete mathematics, including logic, Boolean algebra, binomial coefficients, graph theory, and combinatorics. Emphasis is placed on the application of discrete mathematical methods to problems arising in areas such as algorithmic complexity and network theory. Topics may vary by instructor, allowing flexibility in the selection of applications and discrete structures. The course focuses on rigorous reasoning, problem formulation, and the use of discrete techniques to analyze applied problems.

MATH 7371H. Combinatorial Networks.

This course provides an advanced study of combinatorial networks, focusing on the use of combinatorial methods to model and analyze interconnected structures. The course introduces fundamental concepts as well as selected recent developments in the field. Emphasis is placed on structural reasoning, abstraction, and rigorous mathematical analysis of networks arising in discrete settings. Students examine theoretical frameworks used to represent complex relationships and dependencies within networked systems. The course is designed for graduate students preparing for research in mathematics and related disciplines and develops mathematical maturity, proof‑based reasoning, and familiarity with modern research directions. Prerequisite: MATH 7307 with a grade of "B" or better.

MATH 7371I. Advanced Set Theory.

This course introduces foundational methods and structures used in contemporary set theory research. Topics include the axioms of Zermelo-Fraenkel set theory with Choice (ZFC), ordinals and cardinals, transfinite recursion, and the von Neumann universe. The course also examines selected advanced topics such as large cardinals, Gödel’s constructible universe, and forcing techniques. Emphasis is placed on formal proof methods, internal model construction, and independence results.

MATH 7373B. Partial Differential Equations I.

This course examines foundational theory and methods for partial differential equations at the graduate level. Topics include typical equations arising in mathematical physics, first‑order equations and the Cauchy problem, classification of second‑order equations, and the Cauchy problem for hyperbolic equations. Additional topics include Duhamel’s principle, potential theory and elliptic equations, the maximum principle, and parabolic equations. Emphasis is placed on rigorous analysis, solution techniques, and interpretation of results within a mathematical framework. The course develops analytical tools essential for advanced study in applied mathematics, analysis, and related fields.

MATH 7373C. Partial Differential Equations II.

This course examines advanced theory of partial differential equations with emphasis on existence and uniqueness results for boundary value problems. Topics include linear evolution equations, variational and non‑variational techniques, Hamilton–Jacobi equations, and conservation laws. Emphasis is placed on rigorous reasoning, theoretical foundations, and connections between partial differential equations, analysis, optimization, and numerical methods. The course builds on prior graduate‑level study of partial differential equations and prepares students for advanced research and coursework in applied and theoretical mathematics. Prerequisite: MATH 7373B with a grade of "B" or better.

MATH 7373G. Spectral Methods.

This course examines spectral methods for the numerical solution of differential equations. Emphasis is placed on spectral collocation techniques and the efficient numerical implementation of algorithms. Topics include Fourier and Chebyshev methods applied to ordinary and partial differential equations arising in areas such as fluid mechanics, wave phenomena, and quantum mechanics. The course addresses accuracy, stability, and computational efficiency of spectral algorithms. By integrating theoretical analysis with computational practice, the course prepares students for advanced study and research involving high‑accuracy numerical methods for differential equations. Prerequisite: MATH 7363E with a grade of "B" or better.

MATH 7378A. Problem Solving, Reasoning, and Proof.

This course examines fundamental concepts of mathematical problem solving, logical reasoning, set theory, and proof within mathematics education. Students study how these concepts are developed, represented, and analyzed across mathematics curricula spanning pre‑college through undergraduate levels P-20. Emphasis is placed on theoretical perspectives, research findings, and instructional frameworks related to reasoning and proof. Through examination of curricular materials and educational practices spanning pre-school through college, students will be able to discuss how these concepts are introduced and developed. Prerequisite: MATH 7306 with a grade of "B" or better.

MATH 7378B. Connecting and Communicating Math.

This course examines one of the basic principles involved in mathematics education: Connecting and Communicating Mathematics. This fundamental theme will be reviewed, researched, and discussed. Prerequisite: MATH 7306.

MATH 7378C. Students’ Mathematical Ideas.

This course examines research‑based perspectives on students’ mathematical ideas and ways of thinking. Emphasis is placed on understanding how students conceptualize mathematical concepts, reason about mathematical problems, and develop mathematical understanding across educational contexts. The course surveys theoretical frameworks and research methodologies used to study students’ mathematical thinking, treating instructional practices and learning theories as objects of scholarly inquiry. Students analyze and interpret students’ mathematical reasoning, evaluate and critique research on student thinking, and synthesize findings across empirical studies. Prerequisite: MATH 7306 with a grade of a "B" or better.

MATH 7378G. Discourse Processes, Traditions, and Analysis in Mathematics Education.

This course examines theories, traditions, and methods of discourse analysis as applied to mathematics education. Drawing on interdisciplinary perspectives from the humanities and social sciences, the course focuses on how discourse is conceptualized, studied, and analyzed in mathematical settings. Students examine theoretical frameworks and methodological approaches used to investigate classroom discourse, mathematical communication, and meaning‑making in mathematics learning. Students explain how different discourse traditions are used to address research questions in mathematics education. Prerequisite: MATH 7306 with a grade of "B" or better.

MATH 7385. Independent Study in Mathematics.

This course provides an individualized graduate‑level study opportunity in mathematics under the supervision of a faculty member. Students investigate a focused topic selected in consultation with the supervising faculty member, engaging with advanced mathematical concepts, methods, and literature appropriate to the chosen area. Emphasis is placed on developing depth of understanding, rigorous reasoning, and scholarly independence. The specific content is determined by the instructor and may include directed readings, problem analysis, or research‑oriented activities. This course may be repeated for credit when the topic emphasis differs.

MATH 7386. Independent Study in Mathematics Education.

This course provides an individualized doctoral‑level study opportunity in mathematics education under the supervision of a faculty member. Students investigate a focused topic selected in consultation with the supervising faculty member, examining relevant research, theories, and methodological approaches. Emphasis is placed on developing scholarly depth, engaging critically with the literature, and applying appropriate analytical or research‑based approaches within the chosen topic area. Instructional modality and expectations are determined by the instructor and may include directed readings, research activities, or analytical projects. This course may be repeated for credit when the topic of emphasis differs.

MATH 7387. Consulting.

This course focuses on developing skills in the collaborative practice of mathematics and statistics. The course will consist of class discussion, readings, and different projects. Topics include the application of mathematics or statistics to solve real-world problems through case studies and collaborative projects, as well as the application of ethical considerations to their professional practice. Taking this course will allow students to gain skills in problem solving and providing mathematical and statistical consulting services.

MATH 7389. Internship.

This course provides a supervised internship experience designed to develop practical and professional skills in mathematics or mathematics education. Students work under the guidance of a faculty supervisor while engaging in applied activities in industry, government agencies, educational institutions, or other approved settings. Internship experiences must directly contribute to the student’s understanding of mathematical applications or mathematics education practice. Emphasis is placed on the integration of academic knowledge with professional experience, reflective analysis of applied work, and communication of outcomes through written documentation or presentations.

MATH 7396. Mathematics Education Research Seminar.

This course engages students in collaborative mathematics education research through supervised faculty mentorship and structured seminar activities. Students identify a researchable problem in mathematics education, review and synthesize relevant literature, formulate a research question, and design an appropriate methodology. Students analyze data using methods aligned with the study design, interpret results, and articulate conclusions and limitations consistent with scholarly standards. Emphasis is placed on research ethics, methodological rigor, and clear academic writing. Students create a draft research manuscript suitable for scholarly review or further development. Prerequisite: MATH 7356 and [ED 7352 or MATH 7352 or MATH 7346] with grades of "B" or better.

MATH 7399A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

MATH 7599A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

MATH 7699A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

MATH 7999A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

RDG 7301. Theory and Research of Literacy.

This course examines the theoretical and empirical foundations of literacy and literacy development with an emphasis on literacy in postsecondary contexts. Students investigate how learners construct meaning from text through various perspectives, including psychological, cognitive, sociocultural, psycholinguistic, and transactional theories, and use these varied literacy theories to inform research methodologies, instructional practices, and definitions of literacy. With an emphasis on historical shifts and key research-based frameworks within postsecondary literacy, course content supports students in the application of multiple lenses to literacy education in postsecondary educational contexts and settings.

RDG 7302. Theory and Research of College Basic Literacy.

This course critically examines the theory, research, and practice of basic literacy instruction within postsecondary contexts. Students analyze historical and contemporary curricular approaches to college literacy, with particular attention to their theoretical foundations and pedagogical implications. Emphasis is placed on the application of research-based instructional strategies that support college learners’ development in phonemic awareness, decoding, vocabulary, fluency, and comprehension. Through systematic analysis of scholarly and professional literature, students evaluate competing perspectives on basic college literacy and assess how basic literacy strategies can be integrated into college lesson plans in alignment with research-based practices. The course culminates in the design of integrative, evidence-driven frameworks that examine or evaluate curricular models for addressing foundational literacy development.

RDG 7303. Theory and Research of College Academic Literacy.

This course examines academic literacies in postsecondary contexts from cognitive, psycholinguistic, and sociocultural perspectives. Content includes academic, workplace, and multiliteracies and their influence on engagement with texts and tasks across educational and professional settings. The course addresses assessment of learners’ literacy strengths and needs and analysis of instructional frameworks related to vocabulary development, comprehension processes, and strategic reading across multiple text sources. It also examines contextual factors that influence academic literacy development and their implications for instructional planning and practice in postsecondary environments.

RDG 7304. Theory, Research, and Teaching of Literacy Development for Multilingual Learners.

This course examines scholarship from the fields of language acquisition, literacy studies, and education to analyze historical and contemporary issues in language and literacy teaching and learning. Students analyze and apply theories of language and literacy development to evaluate instructional practices and materials used with multilingual learners, including how these approaches address language awareness, literacy development, and the role of learners’ prior knowledge and experiences in academic settings. Prerequisite: RDG 7301 with a grade of a "B" or better.

RDG 7305. Theory and Research of Postsecondary Literacy Assessment.

This course examines literacy assessment theory, research, policy, and practice in postsecondary contexts. Content includes the nature of literacies required for college-level learning and a range of assessment instruments, including high-stakes, placement, diagnostic, classroom-based, and qualitative measures. Topics address accountability frameworks, standards-based curricula, assessment approaches in the literature, and principles of reliability, validity, and interpretation. The course also examines analysis of assessment tools and data and contemporary issues in postsecondary literacy assessment.

RDG 7306. Literacy Research Seminar.

This course explores research and policy papers in literacy and literacy education, with a focus on methodology, conclusions, and implications for future research. In this doctoral seminar, students discuss historical issues and current trends related to multiple facets of the field of postsecondary literacy, collaboratively agreed upon by students and the instructor. Through careful analysis of scholarly literature, discussion, presentations, and analytical activities, students explore the development of the field of postsecondary literacy and its contemporary applications.

RDG 7307D. Multimodal Critical Discourse Studies.

This course introduces multimodal critical discourse studies through examination of theoretical frameworks based on multimodal semiotics. Content includes analysis of relationships between language, visual elements, and social contexts using analytic approaches such as transitivity analysis, visual analysis, and multimodal metonymy and metaphor analysis. The course also examines representations of students, instructional practices, and postsecondary education in institutional and policy contexts. Emphasis is placed on the application of multimodal discourse analysis tools in research design within postsecondary settings.

RDG 7307E. Theory, Research, and Practice of Disciplinary Literacies.

This course examines core principles of disciplinary literacies. Students will examine the theory, research, and pedagogical practices of literacies across the disciplines with an emphasis on understanding the potential for postsecondary learners and Developmental Education practices.

RDG 7307F. Curriculum Design in Postsecondary Developmental Education.

This course explores the principles and processes of curriculum design and implementation in postsecondary contexts. Students examine relevant research, trends, and issues within the professional and scholarly literature to inform curriculum decision-making in college and university settings. Students build skills in assessing instructional needs, designing contextually responsive curricula, and examining factors that shape educational practice. Emphasis is placed on synthesizing the scholarly literature on college curriculum design and applied inquiry through investigations in curriculum planning, analysis, and assessment. Course content provides rigorous training for constructing curriculum frameworks and developing postsecondary curricula that align instructional goals, assessment strategies, and broader institutional priorities.

RDG 7371. Theory and Research of Postsecondary Integrated Reading and Writing Pedagogy.

This course examines theories, research, and pedagogical models that inform integrated reading and writing instruction in postsecondary contexts. Content includes historical and contemporary perspectives on academic literacies, with emphasis on the interaction of reading and writing processes. The course addresses interpretation of literacy performances and the selection of instructional strategies, materials, and programmatic models that build on learners’ existing literacies. It also examines how theoretical frameworks, disciplinary traditions, and policy contexts inform curriculum design and instructional planning, as well as the development of research frameworks related to integrated reading and writing pedagogy.

RDG 7372. Theory and Research of New Literacies Studies in Developmental Education.

This course focuses on the theory, research, and applications of New Literacies Studies in postsecondary developmental literacy. Content includes theories and models that conceptualize literacies as socioculturally mediated and connected to identity, discourse, and community participation. The course examines multiple literacies relevant to postsecondary education, including academic, workplace, community, and multimodal literacies. It also addresses the use of research in New Literacies Studies to inform instructional strategies and research design in postsecondary learning environments.

RDG 7373. Community Literacies.

This course focuses on exploring, understanding, refining, and reflecting on literacy as social practices within families and communities. Students investigate how family and community literacies inform research on curriculum and instruction for PK-16 school settings, adult literacy programs, and informal learning environments. Students examine scholarly literature related to literacy studies, composition and rhetoric, adult literacy, and multilingualism. Through the completion of a community service learning project, students explore research as a means to inform college literacy instruction and literacy education more broadly.

RDG 7374. Theory, Research and Practice of Disciplinary Literacy.

This course examines core principles of disciplinary literacies. Students analyze theory, research, and pedagogical practices related to literacies across academic disciplines, with attention to how these approaches are studied and applied in postsecondary contexts. Students read and evaluate empirical research, reports, policy documents, and related materials to examine the role, function, and documented outcomes of disciplinary literacy in higher education.