What is it?
Three credits of Senior Project are a required part of the mathematics major. In short, the Senior Project in Mathematics is an independent research project in mathematics. It satisfies two Manchester University requirements for majors: each major must include a "Senior Comprehensive Evaluation," and each major must include one or more courses, which by being designated "W" courses, indicate that they require a significant amount of writing. Expectations
- You will learn an area of mathematics on your own.
- You will write a paper explaining the mathematics you have learned.
- You will give a presentation explaining the mathematics you have learned.
Choosing a Topic and Getting an Advisor
You should start thinking about possible topics for your senior project as soon as you decide to be a math major. The requirements for topics are:
- It should be something about which you want to learn.
- It should require learning or discovering some new (to you) mathematics.
- It should require synthesizing material from several sources.
- It should be of a breadth and depth to be treated in a 15 to 40 page paper.
- It should be something on which a faculty member is willing to work with you.
As you are taking your mathematics courses and other courses with mathematical content, think about topics for your senior project. Are there some subjects on which you wish the course could spend more time? Think about what kinds of mathematics you enjoy the most. Look in the library. Talk to your professors. Get a list of past senior projects and look at copies of the papers written for them (on file in the department office). Topics may be from pure mathematics (e.g., the Riemann zeta function), applied mathematics (e.g., airline scheduling), or pedagogy (e.g., using computers to teach proof-writing in high school geometry). Do not reach the end of your junior year not knowing about the existence of any mathematics beyond the mathematics you have studied.
When you have some ideas for a topic, talk to a faculty member in the department (your adviser?) about your ideas to see if they are feasible, and if so, which faculty member might serve as your primary senior project advisor. Ask the faculty member if he/she is willing to be your project advisor. (Be advised, faculty members have many commitments and may decline.) You should do this before you register for Senior Project—at the latest, by the end of your junior year. Together, you and your primary project advisor should select a second faculty member (this need not be a department member) who will serve as a second reader. The second reader will give you feedback on drafts of your paper and serve as an additional grader.
Registration and Credit
When you do have a topic and an advisor, register for Math 499 Senior Project. The usual pattern is to register for three hours of credit spread over two consecutive semesters, one hour the first semester and two hours the second. For example, you may do one hour in the spring of your junior year and two hours in the fall of your senior year, or one hour in the fall of your senior year and two hours in the spring of your senior year. It is possible, but not recommended, to do all three hours in one semester.
If you follow this two semester pattern, at the end of the first semester you will receive a grade of R, which indicates that the permanent grade is not yet determined. At the end of the Senior Project, your course grade will be determined as explained below. This will be your grade for all three hours.
In addition to the course grade, you will receive a pass/fail evaluation from the department for the Senior Comprehensive Evaluation. This is separate from the course grade and is explained below.
Course Grade Evaluation
- Mastery (20% - evaluated by advisor)
Evaluation of your mastery of the topic will take into account the level of difficulty of the topic and your background, as well as the understanding that is demonstrated. Specifically, the degree to which the material is different from that covered in course work will be considered. In any case, depth of understanding must be demonstrated. Do you understand the nature and importance of your topic? Are you able to give an overview of the topic which identifies both the central results and, in general terms, the methods by which they are obtained? Effective use of examples gives further evidence of your grasp of the meaning of definitions and theorems.
- Written Paper (40% - evaluated jointly by advisor and second reader. Each will assign the paper a letter grade.) Does it demonstrate knowledge of the mathematics, including insight, accuracy, completeness and conciseness? Does it show originality, independence from the major source in developing the topic? Is it organized logically with introduction, overview, examples, transitions and conclusion? Does the vocabulary show correct use of mathematical terminology and symbols and sufficient use of non-technical language? Are the mechanics correct with adherence to manuscript conventions, correct spelling and sentence structure, careful editing and proofreading? The style should be that of a formal research paper, with introduction, table of contents, list of references, etc.
- Oral Presentation (20% - evaluated jointly by department faculty and the second reader. The procedure is explained below in the SCE Evaluation section.) The criteria listed for the written paper also apply here. Do you use board space and visual aids effectively and write legible and logical statements? Do you work at a suitable pace and not rely excessively on written notes? Do you have a sense of your audience and provide a sufficient introduction including a description of what was done in previous talks? Do you respond well to questions? (Questions may cover details of the paper or the presentation, examples or applications of the concepts and topics, or related mathematical topics. Even when you cannot provide a complete answer to a question, your ability to understand and reformulate the question and your approach to working toward a solution may be evaluated.)
- Professionalism (20% - evaluated by advisor) Do you meet deadlines and keep appointments? Do you meet regularly with your advisor and are you prepared for appointments with specific questions in mind? Do you follow through with your advisor's suggestions? Do you take initiative? Are you able to work independently and to organize the material on your own?
Letter grades will be assigned for each of these criteria and averaged using the usual four point grading scale to determine the letter grade for the course.
The SCE pass/fail evaluation is based solely on the paper and presentation portions. A passing grade (C- or better) is required on each of these to pass the SCE requirement.
After the presentation and a question period, all others except full-time members of the department and the second reader will be asked to leave. Department members will have some time for discussion, and then each will assign the presentation a letter grade. These grades will be averaged using the usual four point scale to arrive at the presentation grade. The student will be notified of the SCE results, and the department chair will report these results to the registrar.
Scheduling and Time Table
With the two semester pattern, the first semester, you will concentrate on defining your topic, beginning to read about it, and developing a bibliography. The second semester, you will continue your research and develop your oral and written presentations.
You should make arrangements with your project advisor to meet weekly (or perhaps less often in the first semester of the two semester arrangement). Assuming the two semester registration pattern and 14-week semesters, a recommended time table is:First semester
- Weeks 1-5: Begin to gather list of resources and begin to read. By the end of the fifth week, have a one paragraph statement in writing explaining what your topic is and what questions you hope to answer.
- Weeks 6-9: Continue reading, developing a bibliography, and clarifying your topic and questions. By the end of the ninth week, have a tentative bibliography in writing.
- Weeks 10-14: By the end of the semester, have, in writing, a revised statement of your topic and questions, a revised bibliography, an outline of your topic and a schedule for the following semester. At this point, you should have done extensive reading in the area, but you may not have begun to synthesize the material as your own.
- By week 4: Give a talk to a student group (this could be Math Club, a class, Science Seminar, or other) which gives the background for your project. This talk should not presume knowledge beyond the calculus-linear algebra sequence. The talk should be about 20 minutes.
- By week 7: Have a first draft of your paper which will be returned to you with comments by your advisor and second reader by the end of week 8.
- By week 11: Have a second draft of your paper. This draft should be essentially complete with only minor changes to be made for the final draft. This draft will be returned to you with comments by your advisor and second reader by the end of week 12. It will also be made available to department members before your final presentation.
- By week 13 (that is the week prior to the last week of classes): Give your final presentation to the Mathematics and Computer Science Department. This presentation may assume the background material presented in your preliminary talk. It will be scheduled for one hour beginning with a presentation of about 35 minutes and allowing time for questions afterwards. Questions may cover details of the paper or the presentation, examples or applications of the concepts and topics, or related mathematical topics. Often it is your method of approach to the question that is important, rather than the recall of specific facts.
- By the end of the semester: Submit two copies of the final draft of your paper. At least one should include a cover. These copies will be filed permanently in the department.
If you are doing the entire project in one semester, the above time table will need to be compressed.
If you have failed the SCE, the department will determine what further work you need to do pass. This might include revising the paper or redoing the presentation. It is expected that you will complete the remediation before the end of the semester.