Advanced topics in the area of algebra that are not covered in the regularly offered courses. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisite: MTH 623; permission of instructor. Recommended: MTH 525, 625.

Advanced topics in the area of applied mathematics that are not covered in the regularly offered courses. Specific topics are determined by the instructor. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisites: MTH 534 or 632 or 634; permission of instructor. Recommended: MTH 534, 632, 634, 638.

Fundamentals of topological vector spaces, normed spaces, Banach and Hilbert spaces, functionals on such spaces, operators on Banach and Hilbert spaces, spectral theorems, Banach algebras. Prerequisites: MTH 632, 636.

Solutions of partial differential equations by analytic and numerical techniques using standard methods, including Fourier series and Laplace transforms, perturbation, finite elements and finite differences. Prerequisites: MTH 334 and MTH 636.

Topics in the area of analysis that are not covered in the regularly offered courses. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisites: MTH 632 or 636; permission of instructor. Recommended: MTH 533, 632, 636, 732.

Advanced topics in the area of geometry that are not covered in the regularly offered courses. To be taken as a three-credit course and may be repeated for a maximum of nine credit hours. Prerequisites: MTH 644; permission of instructor. Recommended: MTH 533, 645.

Methods in teaching undergraduate mathematics including technology use, cooperative learning, inquiry, and guided discovery. Students will create activities and discuss issues surrounding undergraduate instruction. Prerequisite: Completion of 12 hours of graduate level mathematics at CMU and admission to one of the graduate programs in the Department of Mathematics.

Introduction to understanding and interpreting mathematics education research at the undergraduate level. Prerequisite: MTH 761.

Advanced perspectives in collegiate mathematics education as it relates to the areas of teaching, learning, and curriculum. Prerequisites: MTH 762 and EDU 614.

Introduction to the methods of qualitative research in mathematics education including research design, development of protocols, fieldwork, collecting and analyzing data, and techniques of interviewing. Prerequisite: MTH 763.

Teaching of approved undergraduate mathematics or statistics courses. Students will conduct their teaching internship under the supervision of a graduate faculty member. CR/NC only. Prerequisites: MTH 761; successful completion of all qualifying examinations.

Use of a review of literature to focus research questions and to develop a research proposal. Each student develops a proposal for his/her dissertation research. Prerequisites: MTH 764.

Conduct a pilot study to collect and analyze data. The students will then develop conclusions and implications of the study. Prerequisites: MTH 767. Pre/Co-requisite: PSY 611.

Advanced topics in the area of combinatorics that are not covered in the regularly offered courses. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisite: MTH 578; permission of instructor. Recommended: MTH 525, 623, 678.

In-depth doctoral practicum project supervised by a faculty member or internship experience in an external agency supervised by a faculty member and a professional supervisor. CR/NR only. Prerequisites: Successful completion of all required Ph.D. qualifying examinations; permission of the faculty supervisor.

Consideration of subject matter not included in regular courses. May be taken for credit more than once; total credit not to exceed 6 hours. Prerequisite: completion of 30 hours of coursework required for the Doctoral program.

Open to doctoral students in mathematics. May be taken for credit more than once; total credit not to exceed 9 hours. Prerequisites: 30 hours of coursework toward the doctoral program; permission of the instructor.

Master's thesis research. CR/NC only. Prerequisites: Graduate status and permission of thesis advisor.