# Ph.D. Courses

**Education (ED)**

**ED 7352** Beginning Qualitative Design and Analysis. (3-0) 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.

**Mathematics (MATH)**

**MATH 7111** Seminar in Teaching. (1-0) Seminar on individual study projects concerned with selected problems in the teaching of mathematics. This course does not earn graduate degree credit. Graded on a credit (CR), no-credit (F) basis.

**MATH 7187** Seminar in Mathematics. (1-0) Students are required to attend weekly research seminars in mathematics and to give at least one research presentation in the seminar during the term.

This course is repeatable for credit.

**MATH 7188** Seminar in Mathematics Education. (1-0) Students are required to attend weekly research seminars in Mathematics Education and to give at least one research presentation in the seminar during the term. This course is repeatable for credit.

**MATH 7199A** Dissertation in Mathematics Education. (1-0) 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 term.

Graded on a credit (CR), no-credit (F) basis.

**MATH 7299A** Dissertation in Mathematics Education. (2-0) 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 term.

Graded on a credit (CR), no-credit (F) basis.

**MATH 7301** Studies in Mathematics. (3-0) This course provides basic foundations in Mathematics for students entering the doctoral program in Mathematics Education. This course may be repeated, but does not earn graduate degree credit.

**MATH 7302** History of Mathematics. (3-0) A study of the development of mathematics and of the accomplishments of men and women who contributed to its progress.

**MATH 7303** Analysis I. (3-0) 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. (3-0) 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. (3-0) 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. (3-0) A course in point-set topology emphasizing topological spaces, continuous functions, connectedness, compactness, countability, separability, metrizability, CW- complexes, simplicial complexes, nerves, and dimension theory. Prerequisite: MATH 4330.

**MATH 7313** Analysis II. (3-0) 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. (3-0) 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. (3-0) 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. (3-0) 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 7324** Curriculum Design & Analysis. (3-0) 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 I. (3-0) 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, Math 3305

**MATH 7328** Instructional Techniques & Assessments. (3-0) 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. (3-0) 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. (3-0) 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. (3-0) 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 7356** Advanced Topics in Research. (3-0) This course encompasses investigation, development, and demonstration of competence, design, and execution for Mathematics Education problems. Repeatable with different emphasis.

**MATH 7356A** Advanced Quantitative Research. (3-0) This course encompasses investigation, development, and demonstration of competence, design, and execution for mathematics education problems in quantitative research. Prerequisite: MATH 7346.

**MATH 7356B** Advanced Qualitative Research. (3-0) This course encompasses investigation, development, and demonstration of competence, design, and execution for mathematics education problems in qualitative research. Prerequisite: ED 7352.

**MATH 7356C** Action Research in Mathematics Education. (3-0) 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 7361** Seminar in Advanced Mathematics. (3-0) 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 7366** Topics in Teaching. (3-0) This course examines how to develop and teach specialized student-groups. Repeatable with different emphasis.

**MATH 7366A** Teaching Post-Secondary Students (Developmental Math, Service Courses, and Majors). (3-0) 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). (3-0) 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). (3-0) 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. (3-0) 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. (3-0) 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. Prerequisite: MATH 7306

**MATH 7371** Topics in Discrete Mathematics. (3-0) In depth study of advanced topics in discrete mathematics, including advanced graph theory, advanced combinatorics, combinatorial number theory, discrete optimization, algorithms and complexity, and probabilistic methods. Repeatable with different emphasis.

**MATH 7371A** Advanced Graph Theory. (3-0) 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. (3-0) 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. (3-0) 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. (3-0) 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. (3-0) 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. (3-0) 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. (3-0) 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 with a grade of “C” or higher, or with departmental approval.

**MATH 7371H** Combinatorial Networks. (3-0) 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 7378** Topics in Standards. (3-0) This course examines the basic principles involved in Mathematics Education. Fundamental themes will be reviewed, researched, and discussed. Repeatable with different emphasis.

**MATH 7378A** Problem Solving, Reasoning, and Proof. (3-0) 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. (3-0) 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). (3-0) 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. (3-0) 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. (3-0) 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 also be addressed. Prerequisite: MATH 7306

**MATH 7385** Independent Study in Mathematics. (3-0) 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. (3-0) 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. (3-0) Students will work under the supervision of a faculty member to gain practical knowledge in Mathematics Education. Student experience can come from industry, government agencies, or other sources but must directly apply to furthering knowledge of mathematics education or its application.

**MATH 7396** Mathematics Education Research Seminar (3-0) 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 papers. Prerequisite: MATH 7346 OR ED 7352, AND MATH 7356h.

**MATH 7399A** Dissertation in Mathematics Education. (3-0) 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 7599A** Dissertation in Mathematics Education. (5-0) 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 term.

Graded on a credit (CR), no-credit (F) basis.

**MATH 7699A** Dissertation in Mathematics Education. (6-0) 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 term.

Graded on a credit (CR), no-credit (F) basis.

**MATH 7999A** Dissertation in Mathematics Education. (9-0) 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 term.

Graded on a credit (CR), no-credit (F) basis.