ED 7199A. Dissertation.

This course provides one credit of structured time and faculty mentorship to support the independent design, conduct, and completion of original scholarly research. Doctoral students refine research focus, review relevant literature, implement appropriate research methodologies, analyze and interpret findings that contribute to knowledge in areas such as adult education, organizational leadership, professional, workplace, and community education. Instructional methodology includes individualized faculty consultation, guided research planning, and iterative review of scholarly writing and research progress. Through these activities, participants engage in sustained intellectual inquiry and apply principles of ethical research practice and scholarly rigor. A progress grade is assigned when adequate advancement toward research goals is demonstrated, and credit is awarded upon successful completion of the final dissertation defense.

ED 7199B. Dissertation.

This course provides 1 credit of structured time under the direct supervision of a dissertation advisor. Students independently design, implement, and complete original scholarly research that culminates in a written dissertation to contribute to the body of knowledge in the field. As part of dissertation hours, students develop and refine research questions, engage and synthesize relevant literature, identify and apply a methodology that aligns with their study purpose to collect and analyze data and report findings. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7299A. Dissertation.

This course provides two credits of structured time and faculty mentorship to support the independent design, conduct, and completion of original scholarly research. Doctoral students refine research focus, review relevant literature, implement appropriate research methodologies, analyze and interpret findings that contribute to knowledge in areas such as adult education, organizational leadership, professional, workplace, and community education. Instructional methodology includes individualized faculty consultation, guided research planning, and iterative review of scholarly writing and research progress. Through these activities, participants engage in sustained intellectual inquiry and apply principles of ethical research practice and scholarly rigor. A progress grade is assigned when adequate advancement toward research goals is demonstrated, and credit is awarded upon successful completion of the final dissertation defense.

ED 7299B. Dissertation.

This course provides 2 credits of structured time under the direct supervision of a dissertation advisor. Students independently design, implement, and complete original scholarly research that culminates in a written dissertation to contribute to the body of knowledge in the field. As part of dissertation hours, students develop and refine research questions, engage and synthesize relevant literature, identify and apply a methodology that aligns with their study purpose to collect and analyze data and report findings. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7310. Instructional Roles in Counseling, Leadership, Adult Education & School Psychology.

This seminar is intended to prepare graduate teaching and instructional assistants in the CLAS Department to function effectively in various instructional and instructional support roles. Required for first-year teaching assistants and GIAs. This course does not earn graduate degree credit. Repeatable with different emphasis.

ED 7311. Educational Philosophy in a Social Context.

This course examines the philosophical foundations of education from historical through current writings. It frames these foundations through the lens of the educational issues and challenges of today across local, regional, and global contexts. Readings include classical and current writings from literature across the field of education as well as other relevant disciplines. Emphasis is focused on connecting the philosophical foundations of education to policy, practice and scholarship in educational and community leadership.

ED 7312. Leadership and Organizational Change.

This course examines leadership and organizational change through a broad intellectual exploration of theoretical frameworks and contemporary research. Students analyze models of leadership, organizational dynamics, and change processes across varied institutional and professional contexts. Emphasis is placed on understanding how leadership practices influence organizational learning, decision-making, and transformation. Instructional methods include research seminars, case analyses, scholarly readings, and applied leadership assessments. Through critical dialogue and analytical writing, participants evaluate leadership theories and change strategies.

ED 7313. Advanced Studies in Adult Learning and Development.

This course examines advanced research and theoretical perspectives on adult learning and development as they apply to educational and community leadership. Students analyze characteristics of adult learners, models of adult cognitive and psychosocial development, and theories of adult learning, cognition, memory, and intelligence. Emphasis is placed on critically evaluating scholarly literature and applying principles of adult learning to leadership, instructional, and community contexts. The course supports doctoral students in developing theoretical foundations that inform research, professional practice, and dissertation inquiry.

ED 7314. Community Development for Educators.

This course examines theoretical and applied perspectives on learning, teaching, and leadership in community contexts. In this doctoral seminar students analyze community development frameworks, educator roles, and strategies for identifying and mobilizing community resources to support educational and organizational goals. Through engagement with scholarly literature, structured dialogue, and reflection on field-based experiences, participants examine contextual factors that intersect with adult education theory and practice. The course explores relationships among social structures, institutional contexts, and patterns of access and outcomes. Emphasis is placed on advanced analysis, design of learning environments, and the development of scholarly writing and presentation skills appropriate for doctoral-level study.

ED 7315. Models of Inquiry: Understanding Epistemologies.

This course surveys the philosophical paradigms and epistemologies informing different research models of inquiry and examples of how they have been actualized methodologically in educational and social science research. Paradigms to be examined, compared, and critiqued include positivism, post-positivism, constructivism, interpretivism, critical inquiry, transformative inquiry, postmodernism, poststructural inquiry, and pragmatic inquiry. This course will help students understand the multiple theories and methodologies commonly employed for investigating research problems, and to identify a framework for their own independent dissertation research.

ED 7316. Advanced Studies in Adult Development.

This course examines contemporary theories and advanced scholarship in adult development, with attention to fundamental developmental changes across adulthood and their implications for educational practice. Students analyze theoretical frameworks and empirical research that inform understanding of cognitive, social, and psychosocial development in adult populations. Emphasis is placed on evaluation of research and the generation of new insights relevant to adult, professional, and community education contexts. Instructional methods include research seminars, critical literature reviews, student-led discussions, and analytical writing. Enrollment is restricted to Ph.D. in Adult, Professional, & Community Education students or with instructor permission.

ED 7317. Instructional Leadership for Organizational Change.

This course introduces students to the major stream of research on instructional leadership and organizational change in the field of education. This literature serves as the foundation for analyzing models of leadership and change in education through various theoretical, conceptual, and epistemological frameworks and lenses. Emphasis is placed on examining the relationship between instructional supervision, professional development, and curriculum development. The course includes experiential applications that bridge theory and practice. Prerequisite: Instructor approval.

ED 7318. Advanced Studies in Adult Learning.

This course examines research and theoretical literature related to adult learning, including characteristics of adult learners, major and alternative learning theories, intelligence, aging and wisdom, and learning in digital contexts. Students engage in advanced analysis of foundational and emerging scholarship to examine conceptual frameworks and empirical findings. Emphasis is placed on critical synthesis, theoretical integration, and the development of original scholarly insights. Instructional methods include research seminars, student-led critiques, comparative theory analyses, and extended analytical writing. By the conclusion of the course, participants are expected to evaluate and synthesize adult learning theories to inform advanced scholarship and design theoretically grounded educational interventions. Enrollment is restricted to doctoral program students in the APCE major or with instructor permission.

ED 7319. Foundations of Educational and Community Leadership.

This course examines the foundations of educational and community leadership from different philosophical, psychological, ethical, technological, and theoretical perspectives. Specific attention is given to interrogating the purpose of education, the history of educational and community leadership in the U.S. and global contexts, and how leadership shapes teaching and learning. Selected topics related to educational and community leadership to be explored include decision and policy making, school contexts, schools as learning communities, the change process, action plans, and research-based school improvement models and networks.

ED 7320. Literature Review for Research Writing.

This course will engage students in an analytical exploration of scholarly literature connected to a selected research topic within adult, professional, community, or lifelong education. Through this process, they investigate how existing publications address their research questions, identify major perspectives in the field, and evaluate the strength of various arguments. The course emphasizes developing the ability to synthesize ideas, construct clear and well supported positions, and recognize areas where knowledge remains limited or underdeveloped. By the end, students produce a coherent literature review that both reflects the current state of research and highlights opportunities for further inquiry. Prerequisite: ED 7352 or ED 7351, all with a grade of "B" or better.

ED 7321. Historical and Philosophical Foundations and Contemporary Issues in Adult Education.

This course explores the historical and philosophical foundations that shape the study and practice of adult, professional, and community education across a variety of settings. Students investigate major intellectual traditions, influential thinkers, and key movements that have informed the field’s development. Attention is given to how philosophical perspectives guide educational purposes, values, and approaches to teaching and learning. By examining historical contexts and evolving practices, students gain a deeper understanding of how adult education has responded to societal needs and how foundational ideas continue to influence contemporary theory, policy, and professional practice. Prerequisite: Core courses or instructor’s permission.

ED 7322. Human Resource and Professional Development.

This course examines the methods, practices, and issues involved in facilitating learning for occupational, professional, and volunteer roles. Emphasis is placed on theory-informed approaches to human resource and professional development across organizational and community contexts. Through seminar discussions, case analyses, and applied inquiry activities, participants analyze models of workplace learning, conduct needs assessments, and examine organizational factors that influence learning and development initiatives. Instructional methods include critical engagement with scholarly literature, collaborative dialogue, and applied design tasks. Expected outcomes include the development of advanced competencies in analyzing, designing, and evaluating workplace learning initiatives and the ability to apply theory-informed frameworks to varied adult, professional, and community education settings. Prerequisite: Core courses or instructor’s permission.

ED 7324. Problems and Strategies in Program Planning Seminar.

This course examines advanced problems and strategic approaches in program planning across educational, professional, and community contexts. Emphasis is placed on principles and procedures of systematic planning, contemporary issues and trends, and the use of needs assessment and data-informed decision making. Students will engage with goal setting, stakeholder analysis, and evaluative frameworks to design responsive and sustainable learning programs. Through inquiry and review of theoretical and applied scholarship, the course develops advanced competencies for planning initiatives that address complex human, organizational, and community needs. Prerequisite: Core courses or instructor’s permission.

ED 7325. Socioecological Dynamics in Learning Communities.

This course examines interdisciplinary scholarship from education, history, economics, sociology, and anthropology to analyze socioecological dynamics within learning communities. Students study how individual, organizational, and community‑level factors shape educational contexts using established conceptual and theoretical frameworks. Emphasis is placed on critically analyzing contextual factors in learning environments and evaluating research‑based approaches for understanding systems and processes in schools and educational community settings.

ED 7326. Educational Policy as Practice.

This course examines the historical, theoretical, and philosophical foundations of educational policy as it operates in practice across educational and community contexts. Students analyze how policies are developed, interpreted, implemented, and evaluated at local, state, and federal levels using established policy analysis frameworks. Emphasis is placed on examining institutional norms, governance structures, and documented policy effects relevant to educational and community leadership. The course supports doctoral students in developing research‑informed perspectives on policy design, implementation, and outcomes.

ED 7334. Processes for Educational Evaluation and Analysis.

This course focuses on the development of knowledge and skills to facilitate the evaluation and analysis of educational programs and initiatives in school and community contexts. It addresses assessment and analysis of student learning at the individual, classroom, school, and system levels, as well as teacher and program evaluation. Emphasis is placed on bridging theory and practice through the development and application of educational evaluation and analysis tools to inform pedagogy, leadership, and community development. Prerequisite: Instructor approval.

ED 7341. Dissertation Proposal Development.

This course supports doctoral students in education as they develop a dissertation proposal consisting of an introduction to the study, review of literature, and methodology, as well as appendices and supporting materials to implement a dissertation study. In a seminar format, students commit to the study of a research problem, analyze relevant scholarly literature, and select an appropriate research design aligned with their questions and theoretical/conceptual framework. Instruction strategies may include guided workshops, peer review, faculty feedback, and milestone-based drafting. Emphasis is placed on clarity of argumentation, methodological rigor, and alignment among research components. By the conclusion of the course, students will produce a draft of their proposal suitable for continuing work with their dissertation advisors. Prerequisite: ED 7351 and ED 7352, and ED 7353 or ED 7354, all with a grade of "B" or better.

ED 7345. Human Resources and Instructional Management.

This course provides a comprehensive analysis of human resource administration and instructional improvement. The curriculum integrates the legal frameworks of personnel management with the practical application of staff supervision, appraisal, and professional development. It bridges administrative functions with instructional strategy by examining curriculum planning, curriculum alignment, and student assessment. The course culminates in an original, instructor-directed research project, ensuring students synthesize theoretical knowledge with empirical inquiry.

ED 7347. The Superintendency.

Through a methodology of case study analysis and reflective practitioner inquiry, students will evaluate the complex intersections of administrative theory and local district governance. The scope of this course encompasses Texas-specific leadership standards, school board-superintendent relations, strategic management, and the social responsibilities and ethical standards required to lead public institutions. Students will engage in a targeted investigation of contemporary governance issues and professional ethics as defined by the State Board for Educator Certification (SBEC). As an expected outcome, students will demonstrate mastery of these competencies by designing and executing an original research project that addresses a critical challenge in district-level leadership.

ED 7349. School Finance and Business Management.

This course focuses on how public schools are financed. The methodology for this course utilizes quantitative financial analysis and comparative modeling to deconstruct district funding formulas and budgetary allocations. The scope includes an in-depth investigation of state and local revenue sources, principles of taxation, and the legal frameworks governing school fund accounting and business management. Students will further examine the technical processes of budget development and the ethical implications of resource management in a school environment. As an expected outcome, students will translate theoretical fiscal knowledge into practice by completing an original research project that proposes a data-driven solution to a real-world district financial challenge.

ED 7351. Beginning Quantitative Research Design and Analysis.

This course introduces quantitative research methods and foundational analytic techniques applicable to social science inquiry, with emphasis on adult learning, K-20 education, and human resource development contexts. The course examines philosophical and pragmatic foundations of quantitative inquiry, including ontology and epistemology, as well as principles of measurement, research design, and statistical analysis for experimental and non-experimental studies. Instruction is delivered through seminar discussions, guided statistical exercises, and applied data analysis activities using relevant datasets. Participants engage with methodological literature and practice interpreting statistical findings. Expected outcomes include the ability to design quantitative studies, apply appropriate analytic procedures, and interpret results in relation to research questions in K-20 education, leadership, adult, professional, and community education. Prerequisite: Core and Concentration courses or instructor’s permission.

ED 7352. Beginning Qualitative Design and Analysis.

This course introduces students to the qualitative paradigm, providing them with a foundational understanding of the distinctive features of qualitative research and qualitative methodological traditions. Emphasis is placed on the most common approaches to qualitative research, underlying assumptions and frameworks utilized in this approach, the intricacies of designing a qualitative study, and common techniques and procedures in qualitative research. Topics covered include data collection methods, analysis processes, the role of the researcher, ethical considerations and trustworthiness, and ways to evaluate qualitative research. Prerequisite: Core and Concentration courses or instructor’s permission.

ED 7353. Intermediate Quantitative Research Design and Analysis.

This course extends doctoral students’ quantitative research capabilities through the examination and application of intermediate to advanced statistical modeling techniques relevant to research and evaluation in education, leadership, and organizational improvement contexts. Attention is given to theoretical foundations of measurement, research design, model specification, and statistical inference within general linear and nonlinear analytic frameworks. Instruction is delivered through a seminar format that integrates methodological literature review, guided statistical exercises, and applied data analysis using statistical software such as SPSS, SAS, R, or STATA. Participants examine and apply regression and structural equation modeling approaches using platforms such as AMOS, Mplus, or lavaan. Expected outcomes include the capacity to design, implement, interpret, and report advanced quantitative analyses for educational research and evaluation contexts. Prerequisite: ED 7351 with a grade of "B" or better, or instructor’s permission.

ED 7354. Intermediate Qualitative Design and Analysis.

This course provides an in-depth examination of the design and implementation of qualitative research using a seminar format and applied inquiry model. Emphasis is placed on advanced qualitative research traditions, theoretical foundations, traditional and contemporary scholarly literature. Students engage in fieldwork, systematic data collection, and iterative data analysis. The course incorporates hands-on training opportunities to explore qualitative research software for data management, coding, and analytic memo development. Instructional methods include examination of relevant literature, research design workshops, peer debriefing, guest speakers, research presentations, and methodological simulations. The course focuses on strategies for designing rigorous qualitative studies that are situated within established research traditions. Prerequisite: ED 7352 with a minimum grade of "B", or instructor’s permission.

ED 7357. Advanced Study in Action Research.

This course provides advanced study of action research, emphasizing its theoretical foundations, methodological practices, and ethical and practical issues. Students examine traditions of action research and develop advanced skills in designing, conducting, and evaluating action research studies in educational, professional, and community contexts. Particular attention is given to participatory inquiry, practitioner scholarship, and research quality. The course supports students in applying action research to adult, professional, and community education or educational and community leadership settings and serves as an appropriate elective for doctoral majors in these areas.

ED 7359. Seminar in Quantitative Research.

This course examines processes for developing and refining research problems relevant to educational leadership and adult, professional, and community education contexts. Participants formulate research questions and consider the alignment of research design, measurement, and analysis as integrated components of scholarly inquiry. The course supports the preparation of dissertation proposal Chapters 1 and 3 and introduces structural elements of competitive grant proposals. Instruction is delivered through a student-centered seminar format that incorporates scholarly literature review, methodological critique, and applied data analysis activities. Participants examine and justify appropriate quantitative approaches, including multivariate methods and structural equation modeling, using statistical software. Expected outcomes include the ability to conceptualize theoretically grounded research problems, design methodologically coherent studies, and prepare components of dissertation and grant proposals. Prerequisite: ED 7351 and ED 7353, all with a grade of "B" or better.

ED 7364. Personal, Team, and Professional Development in Education.

This course focuses on the interconnectivity and development of individuals and teams to acquire the knowledge, skills, and dispositions needed in professional education contexts to improve educational organizations, teaching, and learning. Because of its focus on education, it is recommended only for doctoral students preparing for careers in educational settings. Topics covered in the course include models of personal, team and professional development strategies to increase self-awareness and support team dynamics in educational settings, and the implementation of professional development using shared leadership structures, reflective practice, and dialogue.

ED 7378. Problems in Education.

This course examines individual problems or selected topics in education, allowing focused study of specialized or emerging areas within the field. Content varies based on student interests and program needs, and the course may be repeated for additional credit with approval of the program coordinator. Through directed readings, research, and applied inquiry, students engage deeply with a defined topic. Students are expected to produce a substantive scholarly or applied project demonstrating advanced understanding of the topic or issue under study.

ED 7379. Independent Study.

This course provides students with the opportunity to pursue advanced, self-directed inquiry in a specialized area aligned with their scholarly and professional interests. Under the supervision of a faculty mentor, students design a focused plan of study that integrates relevant theory, research, and critical analysis. Emphasis is placed on intellectual rigor, methodological clarity, and scholarly production. The course supports individualized learning goals, contributes to doctoral research development, and fosters advanced competencies in independent scholarship and academic inquiry.

ED 7389B. Seminar in International Educational Research: Chile.

This course develops theoretical knowledge, methodological skills, and scholarly capacity for international educational research. It focuses on research within the complex educational environment of Chile, involving seminar components held at the university and research fieldwork in Chile. International research is framed as a form of service learning. Restricted to students in the PhD in Education program.

ED 7389C. Advanced Theory in Qualitative Research.

This course features advanced study in qualitative research methods. The course studies such methods as ethnography, case study, phenomenology, narrative analysis, post-qualitative research, grounded theory, or more advanced qualitative research in general and their constitutive field techniques. Prerequisites: Introduction to Qualitative Research and Intermediate Qualitative Research.

ED 7389D. Advanced Theory in Qualitative Research: Narrative Research.

The purpose of this course is to explore the possibilities of narrative research. The course will provide an overview of narrative inquiry, look at various theories and corresponding examples of research, and explore, analyze, and interpret data using narrative methods. Prerequisites: Introduction to Qualitative Research and Intermediate Qualitative Research.

ED 7389L. Writing for Publication.

This course focuses on developing scholarly writing skills for publication within students’ fields of study. Under instructor guidance, students draft, revise, and refine a manuscript suitable for submission to a peer‑reviewed outlet. Emphasis is placed on developing a clear scholarly rationale, integrating relevant literature, selecting appropriate frameworks, aligning methodology and findings, and drawing well‑supported conclusions. The course also addresses identifying suitable journals, adhering to disciplinary writing styles, and navigating the manuscript submission and review process.

ED 7389M. Shifting Demographics in Texas: Exploring Education, Democracy and Healthy Communities.

Students will explore the shifting population in Texas through multiple frames including historical, sociological, anthropological and political. Class will canvas the literature and emerging community conditions as a vehicle for imagining possible theoretical, policy and local responses to the conditions we see in schools and local communities.

ED 7389P. International Comparative Adult, Community, and Higher Education Research and Study: Italy.

This course examines international and comparative research in adult, community, and higher education through an in-depth study of educational contexts in Italy. The course develops advanced theoretical knowledge, comparative frameworks, and methodological skills for analyzing educational systems across cultural and national settings. Particular attention is given to adult, community, and higher education within Italy’s complex educational environment. Instruction is organized through a university-based seminar combined with supervised fieldwork in Italy, incorporating scholarly readings, structured discussion, and guided observation. Participants analyze educational practices using comparative research frameworks and document findings through academic writing and presentation. Prerequisite: Should the student not be able to participate in the international component of the course, a domestic alternative can be discussed prior to enrollment.

ED 7389Q. Schools, Communities and Race in a Democratic Society.

The class explores race through a personal lived perspective. This class will view race as a social construct. Students will interrogate the phenomena of race through multiple lens and frames, including but not limited to, an ontological perspective, its use in organizations, and its use in re-segregating society.

ED 7389R. Understanding the Self in Scholarly and Leadership Contexts.

This course examines theoretical and interdisciplinary perspectives on self, professional identity, and context as they relate to educational and community leadership. Students analyze how contextual influences shape professional roles, leadership practice, and scholarly inquiry. Emphasis is placed on critically examining conceptual frameworks that support self‑understanding as an analytic lens within schools, organizations, and communities. Through engagement with scholarly literature, students develop research‑informed perspectives that support leadership development, reflective practice, and ongoing doctoral study in educational and community leadership.

ED 7389S. Human-Centered Perspectives and Approaches in Education.

This course examines interdisciplinary theories, frameworks, and methodologies associated with human‑centered perspectives and approaches in education. Students analyze how human‑centered approaches are conceptualized and applied across educational research, policy, and practice. Topics may include learning environments, personalization, knowledge construction, community‑based learning, and emerging applications such as human‑centered design and artificial intelligence. Emphasis is placed on critically evaluating scholarly literature and considering how human‑centered frameworks inform educational inquiry, leadership practice, and dissertation research within educational and community contexts.

ED 7389T. LGBTQIA+ Issues in Educational Leadership.

This course examines the intersectionality of gender identity, sexual orientation, and other identities within the educational context, offering a nuanced exploration of the social, legal, and psychological aspects that influence LGBTQIA+ experiences in schools. Participants will engage in critical discussions on policy development, cultural competence, and leadership strategies that promote diversity, equity, and inclusion. The course is designed to address the unique challenges and opportunities facing educational leaders in fostering inclusive and affirming environments for LGBTQIA+ individuals.

ED 7389U. The Theory and Pedagogy of Paulo Freire.

This course introduces students to the major theoretical and pedagogical contributions of Brazilian educator and philosopher Paulo Freire, situating his work within broader traditions of social and educational theory. Although Freire wrote primarily about education, the course is appropriate for graduate students in education and across the social sciences seeking to examine theories related to classroom pedagogy, literacy, adult education, and education policy, including perspectives on education and social change.

ED 7389V. Applied Linguistics for English Language Teaching Instructors.

This course provides an advanced examination of the linguistic foundations necessary for teaching English to adults in varied educational settings. Emphasis is placed on morphology, syntax, semantics, phonology, and sociolinguistics, with attention to their application in grammar, vocabulary, spelling, and pronunciation instruction. The course also explores discourse and conversation analysis as analytical tools for interpreting oral and written language in adult learning environments. Instructional methodology includes critical analysis of linguistic research, applied text analysis, and the design of research-informed instructional models. Expected outcomes include advanced analytical competence, the integration of linguistic theory with pedagogy, and scholarly contributions to adult English language education.

ED 7389W. Literacy and English Language Teaching Assessment and Evaluation.

This course examines language assessment and evaluation practices for adult learners, with emphasis on literacy and English language learning. Doctoral students review assessment constructs and the social and historical contexts that have shaped evaluation practices in adult literacy and English language teaching programs. The course explores traditional evaluation and alternative assessment concepts, including issues of reliability, validity, accountability, holistic assessment, portfolio assessment, formative and summative assessment. Instructional methodology includes seminar discussions, analysis of assessment instruments, case studies, research reviews, and applied test design projects. This course develops advanced skills to critically analyze evaluation frameworks, interpret assessment data, and design contextually appropriate language assessment tools for adult learning settings.

ED 7399A. Dissertation.

This course provides three credits of structured time and faculty mentorship to support the independent design, conduct, and completion of original scholarly research. Doctoral students refine research focus, review relevant literature, implement appropriate research methodologies, analyze and interpret findings that contribute to knowledge in areas such as adult education, organizational leadership, professional, workplace, and community education. Instructional methodology includes individualized faculty consultation, guided research planning, and iterative review of scholarly writing and research progress. Through these activities, participants engage in sustained intellectual inquiry and apply principles of ethical research practice and scholarly rigor. A progress grade is assigned when adequate advancement toward research goals is demonstrated, and credit is awarded upon successful completion of the final dissertation defense.

ED 7399B. Dissertation.

This course provides three credits of structured time under the direct supervision of a dissertation advisor. Students independently design, implement, and complete original scholarly research that culminates in a written dissertation to contribute to the body of knowledge in the field. As part of dissertation hours, students develop and refine research questions, engage and synthesize relevant literature, identify and apply a methodology that aligns with their study purpose to collect and analyze data and report findings. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7599A. Dissertation.

This course provides five credits of structured time and faculty mentorship to support the independent design, conduct, and completion of original scholarly research. Doctoral students refine research focus, review relevant literature, implement appropriate research methodologies, analyze and interpret findings that contribute to knowledge in areas such as adult education, organizational leadership, professional, workplace, and community education. Instructional methodology includes individualized faculty consultation, guided research planning, and iterative review of scholarly writing and research progress. Through these activities, participants engage in sustained intellectual inquiry and apply principles of ethical research practice and scholarly rigor. A progress grade is assigned when adequate advancement toward research goals is demonstrated, and credit is awarded upon successful completion of the final dissertation defense.

ED 7599B. Dissertation.

This course provides five credits of structured time under the direct supervision of a dissertation advisor. Students independently design, implement, and complete original scholarly research that culminates in a written dissertation to contribute to the body of knowledge in the field. As part of dissertation hours, students develop and refine research questions, engage and synthesize relevant literature, identify and apply a methodology that aligns with their study purpose to collect and analyze data and report findings. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7699A. Dissertation.

This course provides six credits of structured time and faculty mentorship to support the independent design, conduct, and completion of original scholarly research. Doctoral students refine research focus, review relevant literature, implement appropriate research methodologies, analyze and interpret findings that contribute to knowledge in areas such as adult education, organizational leadership, professional, workplace, and community education. Instructional methodology includes individualized faculty consultation, guided research planning, and iterative review of scholarly writing and research progress. Through these activities, participants engage in sustained intellectual inquiry and apply principles of ethical research practice and scholarly rigor. A progress grade is assigned when adequate advancement toward research goals is demonstrated, and credit is awarded upon successful completion of the final dissertation defense.

ED 7699B. Dissertation.

This course provides six credits of structured time under the direct supervision of a dissertation advisor. Students independently design, implement, and complete original scholarly research that culminates in a written dissertation to contribute to the body of knowledge in the field. As part of dissertation hours, students develop and refine research questions, engage and synthesize relevant literature, identify and apply a methodology that aligns with their study purpose to collect and analyze data and report findings. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7999A. Dissertation.

This course provides nine credits of structured time and faculty mentorship to support the independent design, conduct, and completion of original scholarly research. Doctoral students refine research focus, review relevant literature, implement appropriate research methodologies, analyze and interpret findings that contribute to knowledge in areas such as adult education, organizational leadership, professional, workplace, and community education. Instructional methodology includes individualized faculty consultation, guided research planning, and iterative review of scholarly writing and research progress. Through these activities, participants engage in sustained intellectual inquiry and apply principles of ethical research practice and scholarly rigor. A progress grade is assigned when adequate advancement toward research goals is demonstrated, and credit is awarded upon successful completion of the final dissertation defense.

ED 7999B. Dissertation.

This course provides nine credits of structured time under the direct supervision of a dissertation advisor. Students independently design, implement, and complete original scholarly research that culminates in a written dissertation to contribute to the body of knowledge in the field. As part of dissertation hours, students develop and refine research questions, engage and synthesize relevant literature, identify and apply a methodology that aligns with their study purpose to collect and analyze data and report findings. While conducting dissertation research and writing, students must be continuously enrolled.

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.