College of Science
Department of Mathematics and Statistics
MATHEMATICAL SCIENCES PHD – General Requirements
The Department of Mathematics and Statistics teaches advanced quantitative and analytic skills for professionals in education, industry and research. At the Ph.D. level this mission is realized through four doctoral specializations within the Mathematical Sciences PhD. Common requirements are described after the specializations.
The Pure and Applied Mathematics specialization, a traditional doctoral program, provides training in the foundations of modern mathematics and specialized areas of mathematical research. Graduates are employed as tenured faculty at universities and colleges as well as governmental and industrial research centers. Students work with faculty researchers in differential geometry, computer-algebra and mathematical physics, dynamical systems, mathematical ecology, graph theory and low-dimensional topology. The dissertation should be a publishable, significant contribution to research in an area of mathematics or its applications. Students in this Pure and Applied Mathematics specialization must obtain a minimum grade of “B” or better in at least two of the 6000-level topic tracks listed below the specialization descriptions.
The Statistics PhD specialization offers training in theoretical and applied statistics for students seeking careers in academe, industry, or government. This is the only PhD program in the region allowing students to specialize in theoretical or applied statistics under the guidance of faculty dedicated to advancing statistical methodology for important and timely real-world problems. Students work with faculty mentors in areas such as Big Data, time series, statistical genetics, bioinformatics, computational statistics, data visualization, experimental design and biostatistics. Nearly all Statistics dissertations involve collaboration with researchers in other fields, including ecology, agriculture, genetics, cancer, finance, public health, nutrition, education and engineering. Dissertations constitute publishable, significant contributions to statistical research.
The Interdisciplinary Studies PhD specialization combines training in mathematics or statistics, significant interaction with other fields that use advanced methodology from mathematics or statistics, and training in an area of application outside math/statistics, with program direction by scholars in math/statistics and in an external discipline. The dissertation should constitute a body of work on significant application or relationship of mathematics or statistics to other disciplines, with the goal of publication in either mathematics, statistics or the field of impact.
The Interdisciplinary Studies Specialization requires at least 9 credits of coursework in the student’s chosen interdisciplinary area (outside both Mathematics and Statistics). Recent students have taken external courses in the College of Education, from the Departments of Biology and Physics, or as part of the Program in Climate Adaptation Science. The student’s PhD supervisory committee should include two persons in the student’s selected interdisciplinary area, and the comprehensive examination (see below) should have a significant interdisciplinary component.
Students in this Interdisciplinary Studies specialization must obtain a minimum grade of “B” or better in at least two of the 6000-level topic tracks listed below the specialization descriptions.
Topic tracks for Pure and Applied and Interdisciplinary Studies specializations:
| |
Recommended |
|
| 6000-level Topic Track |
Courses |
|
Pure |
Applied |
Credits |
| Real Analysis |
6210 /6220 |
X |
X |
6 |
| Algebra & Linear Algebra |
6310 /6340 |
X |
|
6 |
| Geometry & Topology |
6110 /6510 |
X |
|
6 |
| Differential Equations |
6410 /6440 /6420 /6450 |
X |
X |
7 |
| Applied Mathematics |
6470 /6810 |
|
X |
5 |
| Numerical Methods |
6610 /6620 |
|
X |
4 |
All doctoral programs of study (after a Masters) require 45 or more credits, at least 30 credits numbered 6000 or higher, including research credits but excluding MATH/STAT 6990 and 7990 (Continuing Graduate Advisement). No more than 15 credits numbered 5000-5999 may be taken toward a PhD. At least 12 credits must be 7970 (Dissertation Research) for PhD students starting with a Masters. For students entering the doctoral program directly from a bachelor’s degree 72 total credits are required, with at least 18 credits of Dissertation Research (and still only 15 credits of coursework allowed at 5000 level).
The core requirements for departmental doctoral degrees include the following:
- Choose an advisor and a supervisory committee, with whom the student defines a program of study. The committee must have at least one ‘outside’ member, a USU faculty member from outside Mathematics and Statistics.
- Pass a comprehensive examination that is constructed specifically for the student by his or her supervisory committee. The form of the examination may be written or oral, or may include a combination of written and oral components. The length and content of the exam are determined by the student’s supervisory committee, but is expected to take at least eight hours of direct effort from the student (e.g. three two-hour written exams followed by a two hour oral exam).
- Write and successfully defend a dissertation research proposal.
- Complete a dissertation.
- Write and successfully defend a dissertation.
- Successful defense and submission of the dissertation to the library is required. Approval of academic forms required for doctoral students by the School of Graduate Studies.
General Graduate Program Requirements
Degree Verification
A bachelor’s degree from an accredited U.S. college or university or a similarly recognized international university is required for admission to and completion of a graduate program.
Overall Graduate GPA at least 3.0 and no grades of C- or lower;
Graduate students are required to maintain at least a 3.0 GPA for degree-program courses. Grades of C- or lower will not be accepted for a graduate degree.
Course Number Acceptability
The Program of Study for a master’s degree or a doctoral degree, if the student has a master’s degree, must include at least 15 semester credits at the level of 6000 or above.
For a doctoral degree, if the student does not have a master’s degree, the Program of Study must include at least 30 credits at the level of 6000 or above.
Credits in the following areas are not acceptable in a degree program: foreign languages (unless included in an approved Program of Study), continuing graduate advisement, individual home study, military science, and courses numbered below 3000.
Matriculation Start Semester
A doctorate must be completed within eight years of entering the degree program. Additional time may be requested by the student’s committee and submitted to the Vice Provost of Graduate Studies for review.
Coursework Validity
Coursework over eight years old at the time of degree completion may not be used for a graduate degree unless it is revalidated.
USU Residency Requirement
At least 33 semester credits for a doctoral (Ph.D.) or audiology (AUD) degree must be taken from Utah State University and be part of an approved Program of Study. At least three semesters, two of which must be consecutive, of full-time registration in residence at Utah State University, is required.
