The University of Redlands Department of Mathematics has required a "capstone" course of its senior mathematics majors for over 40 years. Entitled "Senior Research Seminar," the course currently has as its objectives for students:

€ Improving proficiency in communicating mathematics, both orally and in writing;

€ Engaging in increasingly independent review, study and exploration of mathematical ideas and problems;

€ Meeting the departmental requirements of (1) passing a comprehensive examination, and (2) writing a research paper and presenting it to fellow seminarians and to mathematics faculty; and

€ Investigating career opportunities in mathematics and mathematics-related fields.

An unwritten objective of the course is to provide peer support for students as they prepare to make the transition from their small, friendly college environment to graduate school, a job, a job search, etc.

Primary emphasis is placed on improving students' independent study, problem-solving, research, reading, writing and oral presentation skills. Early in the course, preparation for the comprehensive examination is used to help students improve these skills (see the first writing assignment and the first two oral assignments listed below). The assignment that best helps them improve these skills, however, is the major assignment for the course, a (usually expository) research project in an area of mathematics selected by the student.

Our students' research topics seem to become more interesting each year. Recent papers include "Bending Without Breaking: A Study of the Behavior of Palm Trees," "Mathematical Modeling of the U.S. Cattle Market," and "The Algorithm Behind the Curtain: Rubik's Magic Cube."

In preparation for the formal research paper, the course's writing assignments become increasingly demanding and increasingly formal as the semester progresses. They include:

€ Mini-research paper, usually involving an interesting (and entertaining) application of calculus or linear algebra;

€ Reaction papers on readings such as Paul Halmos's "Mathematics as a Creative Art";

€ Formal research proposal;

€ At least 3 preliminary research reports of 3-5 pages each;

€ Abstract for the formal research presentation; and

€ At least 2 drafts of the research paper (usually 3 drafts, about 25 pages each).

Students also progress from making informal presentations and presentations in groups to making their formal presentations of their research projects. Student presentations given during the course include:

€ Explanations of topics students are reviewing for the comprehensive examination;

€ Presentation of the mini-research paper listed above;

€ Presentation of research proposal;

€ 3 or more preliminary research reports;

€ Practice presentation of the research paper; and

€ Formal presentation of the research paper to mathematics faculty, students, etc.

Beery: 9/92; rev. 1/93, 5/96


Advantages of offering Senior Research Seminar as a class rather than as independent study:

€ Students give one another a tremendous amount of constructive criticism as well as encouragement, especially during the oral presentations.

€ The combination of being expected to present findings to peers on certain dates and of having one's course grade depend on one's preparedness to do so seems to motivate students to keep up with their projects.

€ Because the research seminar is part of the student's regular course load, faculty are less worried about overburdening students than they might otherwise be.

€ At least one faculty member may count the research seminar as part of her regular course load!

Short-term goals:

€ Separate comprehensive examination from research seminar.

€ Develop students' reading, writing, and speaking skills more fully earlier in their careers.