The graduate program in Mathematics and Statistics assesses its Learning Objectives using the following methods:
Evaluation and Placement of Entering Students
Applicants to all graduate programs must have successfully completed prior coursework in mathematics and statistics to properly prepare them for their intended specializations, and are additionally required to pass the GRE with a score on the quantitative portion that places them in at least the 70th percentile. Incoming students take a seminar during their first semester to introduce them to active research areas in the department, allowing students to align with a faculty mentor.
Coursework, Including Examinations, Homework, Papers, Projects, Presentations, and Reports
This assesses the Foundational Skills learning outcome. The required graduate coursework depends on the emphasis area and research topic. Coursework is typically completed in the first two years, and is selected and coordinated to provide a sound foundation in the fundamentals of theory and practice. Small class sizes (typically between about 5 and 20) and extensive homework and testing in graduate classes give the instructor detailed information on the student's assimilation and mastery of the material.
Comprehensive Examinations and Essential Courses
These assess the Foundational Skills, Research Skills, and Communication and Professional Preparation learning outcomes.
- Each Master’s students across all specializations must pass an exam or course series specific to their degree. MS Students in Mathematics are required to pass a comprehensive exam in advanced calculus during their second semester. MS students in the Industrial Math program can either take the Advanced Calculus exam or a comprehensive exam for a required course in applied mathematics. MS students in Statistics must pass the foundational probability and mathematical statistics course series with at least a B grade. All MS students must also pass an oral examination – conducted by their mentor and committee – following the completion of their Plan B project or Plan A thesis. The Plan B project for students in Industrial Math is based on work done during an internship, either with a company or possibly with another department on campus. The project includes a technical write-up suitable to the industry/field, with a presentation and subsequent oral examination by faculty and students in the program. MMath students must successfully completeeither the Advanced Calculus or the Mathematics Teaching exam by the end of their first year of matriculation.
- All PhD candidates must successfully pass three exams: (1) A comprehensive exam, designed by the faculty mentor in consultation with the student and committee to effectively prepare the student for their research project. This exam may use a combination of written and oral components, and typically requires between 4-12 hours for completion. (2) The proposal defense, which requires a written document or report that describes the student’s thesis topic and intended research approach. The exam culminates with an oral presentation and examination by the student’s committee. (3) The dissertation defense, which involves a presentation an examination by the mentor and committee, following the completion of the dissertation.
Major Professor Mentorship
This assesses all learning outcomes. Through continuous interactions over the course of their program, the major professor is the primary mentor who assesses the progress of the student in his/her development of foundational knowledge, understanding and execution of original research, ability to contribute to the writing of manuscripts describing their findings, and, eventually, compilation of research findings in the thesis or dissertation. The major professor provides expertise in the specialization chosen by the student, and has the leadership role in determining whether the learning outcomes have been met in the context of the research specialization chosen.
Student Meetings With Their Research Supervisory Committee
This assesses Research Skills and Communication and Professional Preparation learning outcomes. Every graduate student has a supervisory committee, consisting of the student's major professor along with additional experts from the faculty: two for MS, and four for PhD. This committee advises on the suitability of the courses chosen for the student’s Program of Study; determines the feasibility and strengths of the thesis/dissertation topic; and advises in the development and evaluation of the thesis/dissertation. Graduate students meet with their supervisory committee to report on progress in course work, research, and other areas pertinent to their degree program. This provides a venue for the committee to provide feedback about the student’s progress on their research project, to clarify expectations for the successful completion of the degree, and for constructive criticism to be given when necessary. Specific benchmarks expected by the committee are provided in Graduate Handbook. In addition, this committee administers the oral examination part of the PhD candidacy examination, and evaluates the thesis/dissertation defense.
Departmental Seminars and Professional Presentations
This assesses the Communication and Professional Preparation learning outcome. Graduate students (MS and PhD) generally present their research in regular departmental seminars and professional meetings. Intra- and Inter-departmental seminar series for this purpose are held by various research groups, including Discrete Mathematics; Mathematics Education; Mathematical Biology; Differential Geometry, Computational Algebra, and Mathematical Physics; and Epidemiology and Biostatistics. Students are able to respond to questions and receive feedback from the faculty and peers.
Data-Based Decision Making
The Department of Mathematics and Statistics conducted a comprehensive self-study of their graduate programs in 2013. The primary recommendations – as a part of a five-year plan – are summarized below.
Credit and Coursework Requirements: Reduce the number of required credit hours for PhD programs, to 45 for candidates with a prior MS, and 72 for candidates with a BS, only; provide 1-credit and 2-credit courses for greater flexibility and breadth; eliminate compulsory courses, for greater flexibility in preparing for dissertation and thesis projects.
Rapid Engagement of Graduate Students in Research Projects: Offer a fall seminar for incoming graduate students to introduce them to active research areas in the department; organize a thesis-oriented seminar in spring, culminating in a two-day research symposium for students to present their work.
Recruitment and Extension: Actively recruit from our own group of promising undergraduate students; recruit well-qualified students directly from Bachelor’s programs into the PhD track; provide a more flexible MMath program across the State of Utah.
Program Management: Place more emphasis on student presentations and publications; seek additional funding sources to increase number and quality of teaching assistants; track student outcomes more comprehensively, including time to completion and post-graduate employment.
Read an assessment of this self-study and five-year plan that was carried out in 2015
Program Learning Objectives
Each student will achieve a mastery of fundamental mathematical and statistical theory and practice, along with current knowledge at a level required for their chosen degree program. Students build this knowledge base by completing a set of required and elective courses, as outlined in a Program of Study agreed upon by a given student and their faculty mentor, and approved by the student’s committee. Appropriate courses in Mathematics and Statistics can be found in USU’s General Catalog. A Program of Study may often include directed readings or independent study courses that help students to focus on their thesis topics, and to better understand current research trends. Advanced courses in other departments may also be approved by the supervisory committee, if such courses provide additional training or insights that support the candidate’s research goals. One important outcome of graduate coursework is that students learn to independently build on their knowledge in their chosen area from the literature and other sources, as needed, for their continued education and professional activities.
Each student will pursue a research project in their chosen field of specialization, acquiring professional-level knowledge and expertise within the corresponding area. An appropriate research topic and the appropriate level of accomplishment are determined in collaboration with a faculty mentor, or major professor. A supervisory committee, chaired by the major professor, meets with each MS and PhD student to assess progress in coursework and the research project, and provide guidance and support in setting future goals.
Communication and Professional Preparation
Each student will develop professional competence in presenting scientific results and conclusions, in both written and oral form. This is accomplished through (i) presentations to faculty and peers in seminars and at other scientific meetings, (ii) the documentation and dissemination of the results of original research via a written thesis or dissertation, (iii) the submission and publication of these results in scientific journals or other appropriate venues, and (iv) the teaching and administration of departmental courses and recitations for undergraduate students.
Comparative Levels of Compentency
The Master’s and PhD degrees both lead to professional expertise and involve a student contributing new knowledge via the thesis or dissertation, and through original scientific publications. The distinction between MS and PhD degrees is principally the level of professional proficiency obtained, and the breadth and significance of the original research.
We have been able to track 78 of 81 students who completed a graduate degree within our department between 2011-16. Of these, 96% have obtained a job related to their training, or have advanced to another degree program. The distribution of occupational categories among those 78 students is given below:
14% – Faculty/University Position
17% – Secondary Ed Teaching
19% – Industry/Corporate
12% – PhD or other Doctoral Program
3% – Federal Research Agencies
Another measure of our graduate program success is the number of published manuscripts either authored or coauthored by our students. The number of student-authored publications since 2011 have appeared by year as follows:
2011 – 1
2012 – 6
2013 – 7
2014 – 7
2015 – 0
2016 – 5