Doctor of Philosophy (Ph.D.) Major in Mathematics Education

ED 7199A. Dissertation.

Original research and writing in Education-Adult, Professional and Community Education, to be accomplished under direct supervision on the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7199B. Dissertation.

Original research and writing in Education-School improvement, to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7299A. Dissertation.

Original research and writing in Education-Adult, Professional and Community Education, to be accomplished under direct supervision on the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7299B. Dissertation.

Original research and writing in Education-School improvement, to be accomplished under direct supervision of the dissertation advisor. 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 the time of Plato through current writings. It frames these foundations through the lens of educational challenges of today. Readings include classical and current writings.

ED 7312. Leadership and Organizational Change.

This course will familiarize students with different perspectives on organizations, different paradigms by which they might be viewed, and a survey of research done on organizations, organizational leadership and change.

ED 7313. Advanced Studies in Adult Learning and Development.

This advanced seminar will examine research and theoretical literature on a variety of topics including: characteristics of adult learners; models of adult cognitive and psychosocial development; adult cognition, memory, and intelligence; and principles for facilitating adult learning. Restricted to Ph.D. in Education degree, Major in School Improvement.

ED 7314. Community Development for Educators.

Examines models and methods of community development as relevant to the practice and scholarship of formal and non-formal education.

ED 7315. Models of Inquiry: Understanding Epistemologies.

This course examines the philosophies informing different research epistemologies, and examples of how these can be actualized methodologically. Philosophies to be analyzed include feminism, and race-based theory. This course will help students see the multiple possibilities for conducting research.

ED 7316. Advanced Studies in Adult Development.

This course examines current theories of adult development, fundamental developmental changes in adulthood, and the implications for practice in adult education. Restricted to students admitted to the Education Ph.D. Program- APCE major or with permission of instructor.

ED 7317. Instructional Leadership for Organizational Change.

This course will introduce students to the major stream of research on instructional leadership and organizational change in education while analyzing models of leadership and change from critical, systemic, and cross-cultural context lenses. The relationship between instructional supervision, professional development, and curriculum development, with experiential applications will also be explored. Prerequisite: Instructor approval.

ED 7318. Advanced Studies in Adult Learning.

This advanced seminar will examine research and theoretical literature on a variety of topics related to adult learning such as: characteristics and diversity of adult learners; key theories of adult learning; alternative perspectives on adult learning; intelligence, aging and wisdom; and learning in the digital age. Restricted to students admitted to the Education Ph.D. Program – APCE major or with permission of instructor.

ED 7319. Foundations of Educational and Community Leadership.

This course examines the philosophical, political, psychological, cultural, ethical, and technological foundations of educational and community leadership, with a focus on the purpose of education and history of educational and community leadership in American education and how leadership shapes teaching and learning. Some topics related to educational and community leadership to be explored include decision and policy making, school culture, schools as learning communities, the change process, action plans, and research-based school improvement models/networks.

ED 7320. Literature Review for Research Writing.

In this seminar course, students conduct a careful examination of a body of literature related to a research topic in adult/professional/community/lifelong education. The literature review tests research questions in relation to what is published about a topic, discusses various positions, crafts coherent arguments and addresses knowledge gaps. Prerequisites: ED 7352 or ED 7351, all with a grade of "B" or better. Restriction: Doctoral standing.

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

Examines historical and philosophical foundations for the study and practice of adult professional, and community education in formal and non-formal settings; and contemporary issues in adult education in a “learning society.” Prerequisites: Core courses or instructor’s permission.

ED 7322. Human Resource and Professional Development.

Examines the methods, practices, and issues of facilitating learning related to occupational, professional, and volunteer roles. Prerequisites: Core courses or instructor’s permission.

ED 7324. Problems and Strategies in Program Planning Seminar.

Addresses principles and procedures, issues and trends, utilization of assessment, goal setting, and other effective strategies for developing learning opportunities and programs responsive to human, professional, and community needs. Prerequisites: Core courses or instructor’s permission.

ED 7325. Sociocultural Dynamics in Learning Communities.

This course draws on interdisciplinary literature to explore social, cultural, historical, and political dynamics and its implications on education for people, organizations, and communities. This will involve an exploration of the sociocultural dynamics in learning communities through a personal lived perspective and through the ecologies of knowing framework (Guajardo et al., 2013; Guajardo et al., 2016): self, organization, and community. Prerequisite: Instructor approval.

ED 7326. Policy and Politics as Practice.

This course examines the historical and theoretical underpinnings informing educational policy, politics, and social justice. It addresses both the micro and macro levels of the context, values, and cultural norms guiding policy and politics as practice in a democratic society. Prerequisite: Instructor approval.

ED 7327. Education Policy Development.

This course equips students with the skills needed to analyze the origins and consequences of existing policy and to play active roles in policy development for educational equity and social justice. Prerequisite: ED 7326 with a grade of "C" or better.

ED 7328. Research and Analysis in Education Policy.

This course engages students in a field-based educational policy research project using quantitative and qualitative techniques. Students will develop their skills to identify policy issues, gather and analyze data, and draw conclusions, and disseminate findings. Prerequisites: ED 7326 and ED 7327 and ED 7351 and ED 7352, all with a grade of "C" or better.

ED 7329. Field-Based Experience in Educational Policy.

This course provides fieldbased practice in policy analysis and development from a democratic and social justice perspective. With guidance from a university faculty supervisor and site mentor, the student will develop and implement a policy project related to democracy and social justice. Prerequisite: ED 7328 with a grade of "C" or better.

ED 7331. Foundations of School Improvement.

Examines school improvement efforts from philosophical, political, psychological, cultural, ethical, and technological foundations. Prerequisites: Core courses or instructor’s permission.

ED 7332. Facilitating School Improvement.

Examines school culture, schools as learning communities, the change process, and research-based school improvement models, with experiential applications. Prerequisites: Core courses or instructor’s permission.

ED 7333. Curriculum and Instructional Leadership.

Examines the relationship between curriculum, instructional improvement, and teacher development, with experiential applications. Prerequisites: Core courses or instructor’s permission.

ED 7334. Processes for Educational Evaluation and Analysis.

This course focuses on the development of the requisite knowledge and skills to facilitate the evaluation and analysis of educational programs and initiatives in complex community and school settings to inform pedagogy, leadership and community development. The course includes the assessment, evaluation, and analysis of student learning at the individual, classroom, school, and system level; teacher assessment; and program assessment. Prerequisite: Instructor approval.

ED 7341. Dissertation Proposal Development.

In this course students approaching dissertation stage meet in a seminar designed to help them clarify their research problem and develop a preliminary proposal for the dissertation. Core and concentration courses must be completed with minimum grades of "B" in each course prior to taking ED 7341. Prerequisites: ED 7351 and ED 7352, and ED 7353 or ED 7354, all with a grade of "B" or better. Departmental approval required.

ED 7345. Human Resources and Instructional Management.

This course focuses on the twin areas of human resource administration and instructional improvement. Topics addressed include legal requirements for personnel management, staff supervision, appraisal, and development, curriculum planning and alignment and student assessment. Students taking the course will complete an original research project under the instructor’s direction.

ED 7347. The Superintendency.

This course addressed issues critical to superintendents in Texas. These include leadership, leadership assessment, school board relations, and other governance issues, management strategies, the role of public education in a democratic society, and professional ethics. Students taking the course will complete an original research project under the instructor’s direction.

ED 7349. School Finance and Business Management.

This course focuses on the financing of public schools. Students will examine the school budgeting process, sources of school revenues, principals of taxation, methods of school fund accounting, and techniques of business management. Students taking the course will complete an original research project under the instructor’s direction.

ED 7351. Beginning Quantitative Research Design and Analysis.

Includes descriptive statistics; sampling techniques; statistical inference including the null hypothesis, significance tests, and confidence intervals; and causal-comparative analyses, including t-test and ANOVA. Prerequisites: Core and Concentration courses or instructor’s permission.

ED 7352. Beginning Qualitative Design and Analysis.

Introduces the qualitative paradigm. Includes distinctive features, alternative qualitative traditions, purposeful sampling, common data collection methods, inductive analysis, the role of the researcher, and evaluating qualitative research. Prerequisites: Core and Concentration courses or instructor’s permission.

ED 7353. Intermediate Quantitative Research Design and Analysis.

This course focuses on issues in the design and implementation of quantitative research. Topics include ANOVA, ANCOVA, and MANOVA, correlation analysis, regression analysis, nonparametric tests, and relationships between experimental designs and statistical analysis techniques. Prerequisite: ED 7351 with a grade of "B" or better, or instructor’s permission.

ED 7354. Intermediate Qualitative Design and Analysis.

Focuses on issues in design and implementation of qualitative research. Topics include influence of alternative traditions, literature in qualitative research, access to the field and ethical issues, researcher-participant relationships, purposeful sampling strategies, inductive analysis procedures, developing theory, and reporting research. Prerequisite: ED 7352 with a minimum grade of "B", or instructor’s permission.

ED 7357. Advanced Study in Action Research.

This course examines underlying theory, practice, skills, and issues in action research. Conducting research in the area of action research is also addressed. This course is an appropriate elective for majors in School Improvement or Adult, Professional and Community Education.

ED 7359. Seminar in Quantitative Research.

This course is a small group seminar that focuses on analytic strategies specific to the doctoral student’s dissertation topic. Examples include structural equation modeling, hierarchical linear modeling, log linear modeling, non-parametric analyses, factor analysis, factorial analysis of variance, and other multivariate statistical methods. Prerequisites: 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.

ED 7371. Anthropology and Education.

This course introduces the student to the basic concepts in anthropology and education and sketches the application of these concepts. It explores the research in anthropology and education with relevance to both K-12 schools and other, more general educational settings. The course is an appropriate elective for Education Ph.D. majors.

ED 7378. Problems in Education.

Individual problems or topics will be designed and completed to emphasize selected areas of study. May be repeated for additional credit at the discretion of the program coordinator.

ED 7379. Independent Study.

Individual problems or topics will be designed and completed to emphasize selected areas of study in the Counseling, Leadership, Adult Education & School Psychology Department. May be repeated for additional credit at the discretion of the program coordinator.

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 7389E. Mexican Perspectives on Mexico - U.S. Immigration.

The course gives U.S. educators an understanding of Mexican to U.S. immigration from Mexican women’s perspectives. Students will read background information and visit Mexico where through lectures, field interviews, and field visits, they will view immigration from the “other side”. They will analyze and write up data when they return. (MULT).

ED 7389H. Oracy and Language Expression for Educators.

This course focuses on the theory and practice of language expression. It emphasizes the relationship between audience analysis, speaker goals, organized outlines, delivery and development of personal style of presentation skills. The course offers direct experience writing, delivering, and constructively evaluating public speeches in a variety of educational contexts.

ED 7389I. Comparative Studies in International Adult Education.

This course compares a model of adult learning, communities of practice (CoP) today with its practice in pre-historical times. It will involve international travel and working with scholars to contrast theory and practice in the United States with the new setting. Students from both contexts will be encouraged to present their work in a conference format.

ED 7389L. Writing for Publication.

Students will hone their writing skills. Students will work individually and in groups, getting feedback from other students and the instructor. Topics include APA style, getting started, first drafts, polishing and tightening, re-writing, submitting a manuscript, responding to feedback/reviews and more. Restricted to masters' and doctoral students.

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 7389O. Educational Privatization: Policies, Actors, and Effects.

This course interrogates the origins and outcomes of educational privatization. In this course, students will review the foundations of education as a public good, study frameworks and theories of privatization, trace public policies promoting privatization, delineate types of educational privatization over time, and examine the actors involved in educational privatization.

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

This course develops theoretical knowledge, methodological skills, and scholarly capacity for educational research. It focuses on comparative adult, higher, and socio-cultural education within the complex educational environment of Italy, involving seminar components held at the university and research fieldwork and presentation in Italy. 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: Anatomy of Engaged Scholarship.

Successful leadership in school settings requires an understanding of human behavior. This understanding begins with knowledge of self and leads to the understanding of others at the micro and macro levels. The focus of this course is on you, the learner, and your surroundings. The goal is to enhance the student’s self-awareness of values, beliefs, attitudes and the ecological context informing and impacting their school leadership experience. This understanding will inform the past, but also begin to inform your future as you matriculate through your course work. We will employ interdisciplinary literature to inform this work.

ED 7389S. Feminist and Critical Thought in Education.

Feminist and Critical thought provides a means to examine and understand how issues of power shape and impact cultures, societies, and their associated policies and practices. In this seminar, students will engage with varying feminist and critical perspectives, frameworks, theories, epistemologies and methodologies to consider their application in examining their own educational journeys as well as current and systemic issues in education. Course readings and materials will primarily draw from the work of seminal and minoritized feminist and critical scholars, while providing students an opportunity to identify and explore course readings and materials of their choice as well.

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 7399A. Dissertation.

Original research and writing in Adult, Professional, and Community Education, to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled each semester (including summer) for at least three dissertation hours.

ED 7399B. Dissertation.

Original research and writing in School Improvement, to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled each semester (including summer) for at least three dissertation hours.

ED 7599A. Dissertation.

Original research and writing in Education-Adult, Professional and Community Education, to be accomplished under direct supervision on the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7599B. Dissertation.

Original research and writing in Education-School improvement, to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7699A. Dissertation.

The student conducts original research and writing in Adult, Professional, and Community Education, guided by the direct supervision of the dissertation chair. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7699B. Dissertation.

Students produce a dissertation under direct supervision of dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled. Prerequisites: Core, Concentration, and Methodology courses or instructor’s permission.

ED 7999A. Dissertation.

Original research and writing in Education-Adult, Professional and Community Education, to be accomplished under direct supervision on the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7999B. Dissertation.

Original research and writing in Education-School Improvement, to be accomplished under direct supervision of the dissertation advisor. 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.

Students are required to attend weekly research seminars in Mathematics Education and to give at least one research presentation in the seminar during the semester. This course is repeatable for credit.

MATH 7199A. Dissertation.

Original research and writing in Mathematics Education to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled each long semester.

MATH 7299A. Dissertation.

This course represents a Mathematics Education student's dissertation enrollments. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: completion of the core and required concentration courses, or approval of student's dissertation advisor.

MATH 7301. Studies in Mathematics.

This course provides basic foundations in Mathematics for students entering the doctoral program in Mathematics or Mathematics Education. This course may be repeated. This course does not earn graduate degree credit.

MATH 7302. History of Mathematics.

A study of the development of mathematics and of the accomplishments of men and women who contributed to its progress.

MATH 7303. Analysis I.

This course covers foundations of modern analysis. Topics include: sequences, LimSup, LimInf, Sigma Algebras of sets that include open and closed sets, sequences of functions, pointwise and uniform convergence, lower and upper semi-continuity, Borel sets, outer measure, and Lebesgue measure. Prerequisite: MATH 4315.

MATH 7306. Current Research in Math Education.

This course surveys the various current social, political, and economic trends in local, state, national, and international settings that are related to research in Mathematics Education.

MATH 7307. Algebra I.

Applications of Algebra and topics in modern algebra, including permutation groups, symmetry groups, Sylow theorems, and select topics from Ring Theory. Prerequisite: MATH 4307.

MATH 7309. Topology I.

A course in point-set topology emphasizing topological spaces, continuous functions, connectedness, compactness, countability, separability, metrizability, CWcomplexes, simplicial complexes, nerves, and dimension theory. Prerequisite: MATH 4330.

MATH 7313. Analysis II.

This course covers the theory of integration with special emphasis on Lebesgue integrals. Topics include: Lebesgue integral, Bounded Convergence theorem, differentiation and integration, absolute continuity, and Lp spaces. Prerequisite: Math 7303.

MATH 7317. Algebra II.

A study of the important algebraic structures of rings and fields. Topics covered include rings, ideals, modules, polynomial rings, Euclidean algorithm, finite fields, and field extensions. Topics also include an introduction to Galois Theory with an emphasis on the geometric applications. Prerequisite: MATH 7307.

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. Prerequisite: MATH 7307 and MATH 7309.

MATH 7321. Graph Theory.

Topics in this course include trees, connectivity of graphs, Eulerian graphs, Hamiltonian graphs, planar graphs, graph coloring, matchings, factorizations, digraphs, networks, and network flow problems. Prerequisite: MATH 3398.

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. These theories include behaviorism, constructivism, sociocultural theories, situated cognition, and others.

MATH 7324. Curriculum Design & Analysis.

This course examines, analyzes, and evaluates the various concepts, topics, methods, and techniques that are related to curriculum design in Mathematics Education for grade levels P-16.

MATH 7325. Statistics 1.

A study of the mathematical and probabilistic underpinnings of the techniques used in statistical inference. Topics covered include sampling, sampling distributions, confidence intervals, and hypothesis testing with an emphasis on both simulations and derivations. Prerequisite: Math 2321 and Math 3305.

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 each for grade levels P-20.

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 Polya theory of counting. Prerequisite: MATH 3398.

MATH 7335. Statistics II: Linear Modeling.

A study of the formulation and statistical methodologies for fitting linear models. Topics include the general linear hypothesis, least-squares estimation, Gauss-Markov theorem, assessment of model fit, effects of departures from assumptions, model design, and criteria for selection of optimal regression models. Prerequisite: MATH 3377 and MATH 7325.

MATH 7346. Quantitative Research Analysis in Mathematics Education.

This course surveys the various research techniques used in quantitative analysis for mathematics education and covers topics such as experimental design, statistical analysis, and use of appropriate design methodologies to achieve the strongest possible evidence to support or refute a knowledge claim. Prerequisite: MATH 7306 and MATH 7325.

MATH 7354. Advanced Qualitative Research.

This course encompasses the techniques and tools needed for the development, investigation, and demonstration of competence in conducting qualitative research in mathematics education. Principles of qualitative data analysis are a significant focus of the course, with particular attention given to specific methods used to code and analyze data. Prerequisite: ED 7352 with a grade of "B" or better.

MATH 7356B. Advanced Qualitative Research.

This course encompasses investigation, development, and demonstration of competence, design, and execution for mathematics education problems in qualitative research. Prerequisite: ED 7352 or CI 7352.

MATH 7356C. Action Research in Mathematics Education.

This course examines underlying theory and issues in action research model and the development of action research projects. Prerequisites: MATH 7346 or ED 7352.

MATH 7358. Advanced Quantitative Research in Mathematics Education.

This course surveys the various research techniques used in quantitative analysis for mathematics education and covers topics such as experimental design, statistical analysis, and the use of appropriate design methodologies to achieve the most substantial evidence to support or refute a knowledge claim. Prerequisite: MATH 7346 with a grade of "B" or better or permission of instructor.

MATH 7361. Seminar in Advanced Mathematics.

Material in course will vary with the interest of students and faculty. A detailed study of subject matter may be chosen from advanced areas of analysis; algebra; topology and geometry; applied mathematics; and probability and statistics. This course is repeatable for credit when subject matter varies.

MATH 7363A. COMPLEX ANALYSIS.

This course is a brief introduction to the complex number system and basic point-set topology of the complex plane, followed by a proof-based and rigorous study of the principal results of the analysis of functions of a single complex variable. Prerequisite: MATH 4315 with a grade of "D" or better.

MATH 7363B. NUMERICAL ANALYSIS.

This course will involve the analysis of algorithms from science and mathematics, and the implementation of these algorithms using computer algebra systems. Symbolic, numerical, and graphical techniques will be studies. Applications will be drawn from the sciences, engineering, and mathematics. Prerequisite: MATH 3323 with a grade of "D" or better or instructor approval.

MATH 7363C. FUNCTNL ANALYSIS.

This course presents the three basic fundamentals theorems of functional analysis: the Hanh-Banach theorem, the uniform boundedness theorem, and the open mapping theorem. Prerequisite: MATH 7303 with a "C" or better.

MATH 7363E. Numerical Analysis II.

This course will involve the analysis and numerical implementation of algorithms to solve partial differential equations. Applications will be drawn from science, engineering, and mathematics. Topics include the numerical solution of linear partial differential equations and the related linear systems of equations. Prerequisite: MATH 7363B with a letter grade of a "C" or better.

MATH 7363F. Functional Analysis II.

This course will involve the analysis of infinite dimensional vector spaces including spaces of functions, measures, and distributions. Topics include Fourier transforms, theory of Banach spaces, and operator theory. Prerequisite: MATH 7363C with a grade of "C" or better.

MATH 7366A. Teaching Post-Secondary Students (Developmental Math, Service Courses, and Majors).

This course examines how to develop and teach post-secondary students. The course references the recommendations of government agencies and professional organizations and allows for the investigation of research-based models. Prerequisites: MATH 7306.

MATH 7366B. Teaching K-12 Students (Elementary, Middle School, and High School).

This course examines how to develop and teach K-12 students. The course references the recommendations of government agencies and professional organizations and allows for the investigation of research-based models. Prerequisite: MATH 7306.

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

This course examines how to prepare teachers of mathematics. The course references the recommendations of government agencies and professional organizations and allows for the investigation of research-based models. Prerequisite: MATH 7306.

MATH 7366D. Teaching Specialized Content.

This course will be an in-depth study of a specialized content area in mathematics with an emphasis on teaching. The specific content area will vary by instructor. Examples include Euclidean Simplex Geometry and Discrete Probability Spaces with Implications for Public School Curriculum.

MATH 7366E. Developmental Mathematics Curriculum.

This course surveys the research, development, and evaluation of the scope and sequence of developmental mathematics curriculum. The course references the recommendations of government agencies and professional organizations and allows for the investigation of research-based models.

MATH 7366F. Research in Undergraduate Mathematics Education I.

Students will develop the requisite knowledge to become a good consumer of Research in Undergraduate Mathematics Education (RUME) research. The course will cover the theoretical underpinnings of current and historic RUME research. Students will develop the knowledge to understand relevant theoretical stances and the role they play in research. Prerequisite: Math 7306 or permission from the instructor.

MATH 7366G. Research in Undergraduate Mathematics Education II.

In this course, students will develop necessary knowledge to design/conduct RUME research via a topic-driven look at current RUME research. Core topics include proof, analysis/calculus, abstract algebra, linear algebra, and differential equations. Students will develop a depth of knowledge related to these topics and engage in research design and development. Prerequisite: MATH7306 and MATH7366F.

MATH 7367B. ADV GROUP THEORY.

This course covers topics including properties of 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. Prerequisite: MATH 7307 with a grade of "C" or better.

MATH 7369C. Low-dimensional topology.

This course is an introduction to low-dimensional topology. Topics include surfaces, 3-manifolds, knots, and 4-manifolds. Prerequisite: MATH 7307 and MATH 7309 both with grades of "C" or better.

MATH 7369D. Characteristic Classes.

This course is an introduction to vector bundles and characteristic classes. Topics covered include Stiefel-Whitney classes, Chern classes, Euler class, Pontrjagin classes, and their computation. Additional topics may include manifold immersion problems. Prerequisite: MATH 7317 and MATH 7319 both with grades of a "C" or better.

MATH 7369E. Differential Geometry.

This course is an introduction to modern tools of differential geometry. Topics covered include manifolds, Riemannian metrics, connections, covariant derivatives, geodesics, curvatures, extrinsic and intrinsic computations. Other possible topics include hyperbolic geometry, Lie groups, Chern-Weil theory, surfaces of prescribed mean curvature, the Gauss-Bonnet theorem, and the Cartan-Hadamard theorem. Prerequisite: MATH 7307 and MATH 7309 both with grades of "C" or better.

MATH 7371A. Advanced Graph Theory.

Topics in this course include Turan's problems, Ramsey theory, random graph theory, extremal graph theory, algebraic graph theory, domination of graphs, distance problems, and applications. Prerequisite: MATH 7321.

MATH 7371B. Advanced Combinatorics.

Topics in this course include Block designs, Latin squares, combinatorial optimization problems, coding theory, matroids, difference sets, and finite geometry. Prerequisite: MATH 7331.

MATH 7371C. Combinatorial Number Theory.

A study of fundamental techniques in combinatorial number theory. Topics will include Waring's problem, additive number theory, and probabilistic methods in number theory. Prerequisite: MATH 7331.

MATH 7371D. Discrete Optimization.

A study of some fundamental techniques in discrete optimization. Topics include discrete optimization, linear programming, integer programming, integer nonlinear programming, dynamic programming, location problem, scheduling problem, transportation problem, postman problem, traveling salesman problem, matroids, and NP-completeness. Prerequisites: MATH 7321 and 7331.

MATH 7371E. Algorithms and Complexity.

A study of some fundamental concepts of computability and complexity. Topics include polynomially bounded problems, NP-complete problems, exponentially hard problems, undecidable problems, and reducibility. Prerequisite: MATH 7331.

MATH 7371F. Probabilistic Methods in Discrete Mathematics.

A study of some fundamental probabilistic techniques used to solve problems in graph theory, combinatorics, combinatorial number theory, combinatorial geometry, and algorithm. Topics include linearity of expectation, alterations, second moment, local lemma, correlation inequalities, martingales, Poisson paradigm, and pseudo-randomness. Prerequisites: MATH 7321 and 7331.

MATH 7371G. Applied Discrete Mathematics.

This course introduces fundamental concepts in logic, Boolean algebra, and binomial coefficients; and applications in different fields such as complexity of algorithms and network theory. Prerequisites: MATH 2472 and MATH 4307, all with a grade of “C” or better, or with departmental approval.

MATH 7371H. Combinatorial Networks.

Combinatorial Networks is an area of study of certain types of networks using combinatorial methods extensively. This course introduces fundamental basics as well as the latest development in this area of research. Prerequisite: MATH 5307/7307 with a grade of "C" or higher.

MATH 7373B. Partial Differential Equations I.

This course covers the theory and application of partial deferential equations, typical equations of mathematical physics, Cauchy problem for equations of the first order, classification of second-order equations, Cauchy problem for second-order hyperbolic equations, Duhamel's principle, potential theory and elliptic equations, maximum principle, and parabolic equations. Prerequisite: MATH 3323, 3373 and 3380 with grades of "C" or better.

MATH 7373C. Partial Differential Equations II.

This course covers the existence and uniqueness theory for boundary value problems of partial differential equations (PDE) including the topics linear evolution equations, variational techniques, non-variational techniques, Hamilton-Jacobi equations, conservation laws. Prerequisite: MATH 7373B with a grade of "C" or better.

MATH 7373G. Spectral Methods.

This course covers the essentials of spectral collocation methods with an emphasis on numerically implementing algorithms. The problems studied will include ordinary and partial differential equations connected with fluid mechanics, quantum mechanics, waves, and other fields. The techniques used will include both Fourier and Chebychev methods. Prerequisite: MATH 7363E with a grade of "C" or better.

MATH 7375C. Time Series Analysis.

A study of the theory of time-dependent data. The analysis includes modeling, estimation, and testing; alternating between the time domain; using autoregressive and moving average models and the frequency domain; and using spectral analysis. Prerequisite: MATH 7335.

MATH 7375D. Advanced linear Modeling.

The course provides an extension of regression methodology to more general settings where standard assumptions for ordinary least squares are violated. Topics include generalized least squares, robust regression, bootstrap, regression in the presence of autocorrelated errors, generalized linear models, and logistic and Poisson regression. Prerequisite: MATH 7335.

MATH 7375E. Computational Statistics.

This course focuses on commonly used sampling and optimization algorithms in statistics. Topics include accept-reject method, importance sampling, Markov Chain Monte Carlo algorithms, Fisher scoring algorithm, expectation-maximization algorithm, and minorization-maximization algorithm. Prerequisite: MATH 5305 or equivalent with a grade of "C" or better.

MATH 7375F. Multivariate Data Analysis.

This course focuses on statistical methodologies based on multivariate analysis. Topics include multivariate normal distribution, tests of hypothesis on means, multivariate analysis of variance, discriminant analysis, principal component analysis, factor analysis and canonical correlation analysis. Prerequisite: MATH 5305 and (MATH 3376 or MATH 3377) with a grade of "C" or better.

MATH 7375G. Bayesian Methods.

This course focuses on Bayesian statistical analysis and associated theories. Topics include one-parameter and multi-parameter Bayesian models, choices of priors, formulation of regression models in the Bayesian framework, and related data analysis. Prerequisite: MATH 5305 or equivalent with a grade of "C" or better.

MATH 7375I. Advanced Statistical Learning.

This course covers the theoretical foundations in statistical learning and deep learning. Topics include the framework of empirical risk minimization, metric entropy, Vapnik-Chervonenkis dimension, Rademacher and Gaussian complexity, symmetrization and chaining techniques, contraction principle, uniform law of large numbers, sample complexity, and neural networks. Prerequisite: MATH 7337 with a grade of "C" or better.

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

A study of the fundamental concepts of problem solving, logic, set theory, and mathematical proof and applications of these concepts in mathematics curriculum for grades P-20. Prerequisite: MATH 7306.

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. Representing Fundamental Math Ideas (Function, Data Analysis, and Enumeration).

This course examines the basic principles involved in mathematics education. The process of representing fundamental mathematical ideas will be reviewed, researched, and discussed. Prerequisite: MATH 7306.

MATH 7378D. Math Technologies.

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

MATH 7378E. Developmental Mathematics Perspectives.

This course examines developmental mathematics-specific strands including technological course support and placement tools/decisions. Issues related to the first mathematics core course required of undergraduates will aslo be addressed.

MATH 7378F. Research on Mathematical Problem Solving in Secondary Schools.

In this course a careful study is made of elementary techniques for problem solving in a variety of domains, including algebra, number theory, combinatorics, geometry, and logic puzzles. Students will learn these techniques by actually working on a collection of problems in each of these areas. Students will read and examine research about various aspects of problem solving and research in math education that includes both teacher training and student learning.

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

Discourse and discourse analysis have been used to answer research questions across disciplines throughout the humanities and social sciences. This course will focus on theory and methods for the analysis of discourse in mathematical settings. We will learn how different approaches to discourse are used to understand mathematics learning. Prerequisite: MATH 7306.

MATH 7378H. Equity in Mathematics Education.

Equity in Mathematics Education is a course examining research on equity issues in mathematics education. These equity issues will range from race, culture, class, and gender as they relate to the teaching, learning, and schooling of mathematics education. We will look at how equity is framed within the field of mathematics education, what has been addressed, and what has not been conceptualized. The course will help students understand the literature in the field, critique the extant research literature, design research, and consider important facets of teaching for various student groups. Prerequisite: MATH 7306 with a grade of "C" or better.

MATH 7385. Independent Study in Mathematics.

Student will work directly with a faculty member and develop in-depth knowledge in a specific topic area of mathematics. Topics vary according to student’s needs and demands. Repeatable with different emphasis.

MATH 7386. Independent Study in Mathematics Education.

Student will work directly with a faculty member and develop in-depth knowledge in a specific topic area of Mathematics Education. Topics vary according to student's needs and demands. Repeatable with different emphasis.

MATH 7389. Internship.

In this course, students will work under the supervision of a faculty member to gain practical knowledge in their field. Student experience can come from industry, government agencies, or other sources but must directly apply to furthering knowledge of applications of mathematics or mathematics education.

MATH 7396. Mathematics Education Research Seminar.

Collaborative research projects with faculty through identifying an educational issue, reviewing literature, creating a research question, designing a methodology, analyzing data, drawing conclusions, implications, and creating a draft of a publishable paper. Prerequisite: MATH 7356, and ED 7352 or MATH 7346, all with a grade of "B" or better.

MATH 7399A. Dissertation.

This course represents a Mathematics or Mathematics Education student's dissertation enrollments. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: completion of the core and required concentration courses, or approval of student's dissertation advisor.

MATH 7599A. Dissertation.

This course represents a Mathematics Education student's dissertation enrollments. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: completion of the core and required concentration courses, or approval of student's dissertation advisor.

MATH 7699A. Dissertation.

This course represents a Mathematics Education student's dissertation enrollments. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: completion of the core and required concentration courses, or approval of student's dissertation advisor.

MATH 7999A. Dissertation.

This course represents a Mathematics Education student's dissertation enrollments. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: completion of the core and required concentration courses, or approval of student's dissertation advisor.