We expect that our majors, after completing all the required courses in one of the tracks (pure, applied, general and statistics), and having been through the senior exercise in mathematics (which includes the completion of a thesis), will have learned how to read technical material, write mathematics clearly, and explain mathematical ideas to non-experts. We also expect our graduates to know how to learn new material independently, to have at least a vague idea of what the major areas of mathematics are about, to be able to understand and create logical arguments, and to have an appreciation of the power of mathematics in applications. Our graduates should also be able to solve non-routine and non-algorithmic problems; that is, to be able to solve problems that do not conform to a set method, and to be able to apply mathematical techniques to new contexts and areas.
Many of the learning outcomes stated in the previous paragraph are easily assessed through the senior exercise. The senior exercise involves directed research, under the supervision of a faculty member, in a topic that goes beyond the material covered in advanced courses that students take while fulfilling one of the tracts in the major. Students may work in an original research project and communicate their results in a manner analogous to an article for a research journal, or write an expository paper on an important problem or theorem. Students are trained to write up their findings in a professional manner and are coached on how to communicate their results effectively in an oral presentation. The faculty advisor assesses the quality of the work and determines whether the entire process (research, writing and communications) has been satisfactorily completed.
To help advisors and seniors in the process of completing a research project successfully, we instituted several years ago a Seminar in Mathematical Exposition (Math 190), which trains our majors on how to do a literature search in mathematics, how to read research papers in mathematics, how to write a mathematics paper, and how to present a mathematics talk. Students give oral presentations on the background material and major questions in the area of their senior research.