What is a Senior Project in Mathematics?
The senior project is a significant piece of mathematical research and is the capstone experience for the major in mathematics. The senior project may consist of 1) solving a research problem, 2) giving an expository account of a mathematical topic, 3) describing the results of an independent study project, or 4) discussing some aspect of the history of mathematics. For any of these kinds of projects, drawing connections between mathematics and other disciplines, such as mathematics education, physics, chemistry, computer science, economics, etc., is allowed and welcomed.
Regardless of the kind of senior project undertaken, it must demonstrate that the student has confronted, interacted with, or done some substantial mathematics. The mathematics may consist of proving original theorems, solving research problems, verifying nontrivial details in published proofs, devising original examples to illustrate concepts, or similar activities. The senior project may not consist only of reproducing class notes from a course taken by the student, copying mathematics in an essentially verbatim fashion from sources, merely describing mathematical procedures without explaining their derivation, or some combination of these. No doubt some of the preceding will occur in some senior projects (in some cases it may be appropriate), but the project can not consist entirely of this kind of material. To help insure that the student is doing appropriate work and is maintaining progress in completing the project, the student and project advisor must meet regularly at mutually agreed upon times.
A senior math major must demonstrate the ability to do and effectively communicate mathematics. The grade for the senior project is largely a reflection of how well this has been demonstrated and to what degree the above guidelines have been met.
Approval of the Senior Project Topic
Primary responsibility for approving the senior project topic rests with the project advisor. If there is a question or concern about the appropriateness of the topic selected, the student and project advisor should consult with other members of the department. If the second reader has been selected, then that person must be consulted.
Registering for the Senior Project
A student registers for the senior project with the faculty member who will serve as project advisor.
The Second Reader
The second reader should be chosen by the end of the fifth week of the semester during which the senior project is done, and at this time the second reader should be apprised of the topic and the plan for completing the project. Throughout the semester the student must keep the second reader informed about progress on the project and give the second reader any drafts of work done for the project.
Joint Senior Projects
Students who double major in mathematics and some other subject may elect to do a joint project on an interdisciplinary topic that bridges mathematics and the other subject. The project must meet the academic standards of both major departments, and in particular it must demonstrate that the student has done some significant mathematics as described above. For this reason the student is cautioned that appropriate topics are often difficult to find, and the student is strongly encouraged to consult extensively with faculty in both departments before making a commitment to a joint senior project.
The readers from the mathematics faculty consist of the mathematics project advisor and one other faculty member. The due date, draft deadlines, the number of credits earned, and the number of semesters required to finish the joint senior project follow the rules of the first-named department when the student registers for the project. (E.g., if a student registers for a joint CompSci/Math senior project, the rules for the Computer Science Department are followed; if a student registers for a Math/CompSci senior project, the rules for the Mathematics Department are followed.)
Due Dates for the Senior Project
The due date for senior projects for fall semester is the Monday following the Thanksgiving Break. The due date for the spring semester is the day falling two weeks before the last day of classes.
Preparing the Finished Product
The finished project must be prepared using either appropriate word processing or mathematical typesetting software. The finished project must include title page, acknowledgements (if the student chooses to include them), an abstract of at most 200 words summarizing the project, table of contents, body of the project, and bibliography.
Turning in the Senior Project
On the due date the student turns in two copies of the finished project to the chair of the mathematics department, who distributes these to the project advisor and second reader. The grade for the project is based on the quality of the copies turned in on the due date and on the oral exam.
The Oral Exam and Assigning the Grade
Soon after the senior project is handed in, the student, project advisor, and second reader set a time for the oral exam, which should occur by the last day of classes in that semester. Attendance at the oral exam is not restricted to the student, project advisor, and second reader. Others who want to attend should get permission from the student and the project advisor prior to the exam.
The oral exam begins with the student giving an introductory talk of no more than 15 minutes on the content of the project. This should include a statement of purpose and appropriate definitions, mathematical results, and other material fundamental to the project. Then follows a period of questioning by the project advisor and the second reader, and if agreed upon ahead of time, by other faculty present. The exam lasts until the second reader and project advisor are satisfied that the project and the student’s knowledge of it have been properly reviewed.
After the questioning has ended, the oral exam is over except for assigning the grade, which is done jointly by the project advisor and the second reader. Before they begin discussing the grade, all other persons in attendance must leave the room. The written project counts approximately two-thirds to three-fourths of the grade and the oral exam counts the remainder. The project advisor and second reader choose two grades that are 1/3 of a whole grade apart. After agreeing on these, the project advisor and second reader tell the student whether or not the student passed. They are not to give the actual grade, unless it is an F.
After the oral exam the student makes corrections and/or revisions to the project and has the project advisor approve them. Then the student has two spiral bound copies of the corrected project made at the Printing Department and gives these to the project advisor by the last day of finals. The project advisor selects and files with the Registrar’s Office one of the two grades described above for the project; if corrections and revisions have been made as expected, then the higher of the two grades is given. By 5 pm on the day after the last day of finals, the two spiral bound copies are given to the chair of the mathematics department, who places them in the department’s permanent collection of senior projects. If the student receives a failing grade for the project, then the student may revise the project and turn it in before the end of the semester for a maximum grade of C.
Elements considered when evaluating the written portion of the senior project
1. Creativity, quality of analysis, or overall sophistication;
2. Clarity and correctness of the writing.
Elements considered when evaluating the oral exam
1. Clarity of presentation;
2. Understanding of concepts;
3. Ability to answer questions about material in and relating to the project.