Assessment of Learning Outcomes

MasterŐs Degree Program in Mathematics.

The Department of Mathematics and Statistics offers a flexible masterŐs degree program to meet the needs of a diverse population of students with varied interests and career goals. Not all students enter the program with an undergraduate degree in mathematics or statistics, so that the first learning objective may be to rectify deficiencies through advanced undergraduate coursework. On completing the degree, students may go on to a doctoral program in the mathematical sciences, or take a job in industry, government or teaching.

New graduate students are required to meet with the Graduate Coordinator to determine appropriate educational objectives and devise a projected plan of study that will accomplish them. These objectives combine core program objectives with personalized goals. The Graduate Coordinator continues to meet with students on a regular basis to update the plan of study, assess the studentŐs progress toward the objectives and assure that appropriate courses or directed study will be available.

Student achievement of specific objectives is assessed:

(1) In the context of courses, through written assignments, presentations and exams. Most graduate courses require students to submit extensive written work that is carefully evaluated for both content and clarity of presentation. Exams are given in most courses, but a final project may be required instead.

(2) By a comprehensive written exam. This is normally taken in the studentŐs final semester. The examination covers real analysis and two other subjects chosen by the student subject to approval of the Graduate Coordinator. It is graded by a committee of graduate faculty. A passing grade on each section is required for graduation. Students who do not pass the exam on the first attempt may be given a second opportunity if their coursework is satisfactory.

(3) Thorough evaluation by faculty of research done for a thesis or other directed study. Completion of a thesis is an option that is encouraged, particularly for stronger students and those planning to pursue an advanced degree.

The department regularly assesses the program requirements and department activities such as colloquia and seminars to see if they are consistent with learning objectives. This is chiefly the responsibility of the Graduate Committee but also falls under the purview of the departmentŐs annual self-assessment.

Specific objectives are listed below with the courses or activities that address them.

(1) *Core knowledge of subject
matter: analysis, algebra.* Students with
a deficient undergraduate mathematics background may be required to take one or
more of MA 316 (Linear Algebra II), MA 413-4 (Algebra), MA 334-335 (Advanced
Calculus). MA 535-536 (Real Analysis) is required for all students, and is a
mandatory topic on the comprehensive exam. Mastery of core material is
essential to success in subsequent courses, where it is evaluated and
strengthened.

(2) *In-depth knowledge of
several areas of modern mathematics and statistics. *Elective coursework including at least one additional
2-course sequence. Comprehensive exam (exam topics must include an additional
2-course sequence).

(3) *Ability to formulate
conjectures and construct proofs or counterexamples.* Covered throughout the curriculum and in the comprehensive exam. A
masterŐs thesis usually includes the formulation and proof of new results.

(4) *Ability to conduct
research in the mathematical sciences by finding, understanding and applying
relevant source material. *Students
preparing for a career in research are encouraged to write a thesis. Students
may serve as research assistants in faculty research projects. Smaller
research projects are assigned in some advanced courses. The Graduate Seminar
also requires students to locate and assimilate source material.

(5) *Ability to communicate
advanced material in oral and written presentations at an expository or
technical level. * Oral presentation is
addressed particularly in the Graduate Seminar (MA 592), which students must
take in at least two semesters. Written communication is a major part of the
thesis option and is also addressed throughout the curriculum, especially in
project-oriented advanced courses. Faculty colloquia and seminars provide
additional models of presentation, and there are opportunities for students to
present their research in seminars and conferences.

(6) *Ability to teach or tutor
mathematics at the undergraduate level.*
This is important for students preparing for academic employment or a teaching
assistantship in a Ph.D. program. Most students on assistantship work as
teaching assistants for undergraduate courses and/or tutors in the department
tutoring lab. Acquisition of teaching skills is assessed by the faculty
members the students are assisting.