Prerequisite: Senior standing and in final year

Course Description:
During their senior year, each major who has not completed a capstone experience registers for this course and is matched with a Departmental Faculty Mentor. Each student's project will begin with a lead paper or text provided by their Faculty Mentor. The project will involve two separate components:

1. Preparation of a research paper with a body of approximately 9 and no more than 14 pages.
2. Professional quality oral presentation of a (possibly small) portion of the research paper.

Course Goals:
Students will gain experience in working outside of a classroom setting, carefully reading and coming to understand literature in the mathematical sciences, organizing and writing a professional-level paper, and organizing and giving a professional-level presentation. Each lead paper is chosen mindful of the student's background, so that students will draw upon and synthesize knowledge from their previous course work. Though revision of both the paper and the oral presentation, students will hone their ability to communicate the main ideas.

Overview of the Timeline:
Each student in the Senior Seminar is paired with a faculty member who will serve as the student's assigned Faculty Mentor. As soon as possible in the term, students are to arrange a meeting with their assigned Faculty Mentor. At the first meeting with the Faculty Mentor, students arrange to get their lead paper. Next, they meet with their Faculty Mentor regularly as arranged. Students are expected to meet the deadline for the first draft of the paper to be turned in to Faculty Mentor. Then students revise the paper and continue to meet with Faculty Mentor as arranged. By the next deadline, the finished paper should be distributed to all Math Faculty and to all of the other students in the Seminar. Students may receive additional corrections from the committee and are then to make the corrections and deliver the corrected final draft of paper to the Faculty Mentor and the Director to be kept on file by the Department. After completing their paper, students in the Seminar prepare for their presentation. By the given deadline, they are to deliver their abstract and presentation title and request materials needed for their presentation to their Faculty Mentor and to the Director. They then schedule a videotaping of a practice presentation at the Learning Center (LC) and watch the video of themselves. Next they have a practice presentation session with the director and the senior seminar students which is not open to the public. Finally, students give their final presentations which is open to students, faculty, and the public. It is required that students in the Seminar attend all sessions of the final presentations.

Attendance Policy:
Students are required to meet with their Faculty Mentor on the assigned dates as well as at any other mutually arranged times, to attend and/or present at all of the presentations. Failing to meet any of these requirements may be grounds for failure of this course.

Student Responsibilities for the Seminar:

1. Read and understand the lead paper and an appropriate number of related papers, the number depending in part on the difficulty of the original paper.
2. Prepare a research paper on the topic chosen by the Faculty Mentor with body of approximately seven to eleven double spaced typewritten pages. Be sure to have a title page and bibliography appended.
3. Provide the Faculty Mentor a rough draft of the paper including the bibliography on schedule, and make all changes suggested by the Faculty Mentor.
4. Provide the Director of Senior Seminar with the title of the presentation and an abstract of fifty words or fewer on schedule.
5. Provide all Math Faculty and all of the students in the seminar with copies of the completed paper on time.
6. Prepare note cards, overhead transparencies and any other supporting materials to be used during the oral presentation. It is not acceptable to read the papers.
7. Prior to the public presentation, hold two practice sessions. Schedule a videotaping of a practice 20 to 25 minute presentation at the Learning Center (LC). Watch this video and use it as an aid to improving the final presentation. The night prior to the final presentation, meet with the director and all of the other students in the seminar for a practice session. Use the comments from this session to improve the final presentation.
8. Present the final 20 to 25 minute presentation at the scheduled time and preside over a question-discussion period of 5-10 minutes immediately following.
9. Attend and be engaged in each of the presentations and write one evaluation of another speaker of your choice.
10. In case written and/or oral work is judged by the faculty committee to be of questionable quality, complete whatever additional requirements the committee may set forth.
11. Adhere to all deadlines!

Method of Evaluation:

Evaluation of both the written paper and the oral presentation is completed by a committee composed of two or more Faculty Mentors.

Evaluation of the completed paper will be based on the following set of expectations:

1. The paper is well-organized.

   a. Include a title page and a bibliography in the standard scientific format.

   b. Limit the main body of the paper to between seven and eleven pages, using good judgment about what to include in the paper.

   c. Begin the main body of the paper with an introduction designed to capture reader's interest and to make clear the objectives and approach selected by the author.

   d. Following the introduction, have an identifiable body of the paper which focuses on main points and logical transitions between them.

   e. Make the relationships among ideas clear by developing clear transitions.

   f. End the paper with a conclusion that accentuates the structural plan and, as appropriate, identifies related questions or directions for future development.

g. Site page number references throughout paper as appropriate.

2. The author exhibits an acceptable level of understanding of the material.

   a. If a part of the paper emphasizes the formal statement of definitions and theorems and standards of proof, then it is anticipated that the paper should communicate key definitions and results accurately and should include appropriate examples to illustrate them. The paper should also demonstrate understanding of the way definitions and prior results are applied in the development of a proof.

b. If the paper is to communicate an overview of the entire topic through a careful selection of definitions, theorem statements and examples with central concepts and results being stated formally and illustrated, then the paper should explain key definitions and results accurately and include appropriate examples to illustrate them.

3. The paper is readable at a level appropriate for the intended audience.

   a. Assume the reader has solid reasoning skills and has been exposed to the ideas of calculus and the fundamentals of sets and proving, but do not assume any additional background.

   b. Be aware of the readership. Use good judgment in distinguishing between concepts and results known to readers versus those which require review or introduction and development.

   c. Be free of the kind of grammar, word usage, and mathematical notation errors that interfere with the clarity of communication.

d. Use standard notation, lay-out, and style appropriate for the intended audience.

Evaluation of the oral presentation will be based on the following set of expectations:

1. The presenter exhibits a clear structural plan for the presentation.

   a. Begin with an introduction designed to capture audience interest and to make clear the objectives and approach selected by the presenter.

   b. Following the introduction, have an identifiable body of the presentation which focuses on main points and logical transitions between them.

   c. Make the relationships among ideas clear by developing clear transitions.

d. End the presentation with a conclusion that accentuates the structural plan and, as appropriate, identifies related questions or directions for future development.

e. Adhere to the 20-25 minute time limit.

2. The presenter exhibits awareness of the audience.

   a. Prepare the presentation in such a way as to assure the understanding of the audience.

   b. Assume the listener has solid reasoning skills and has been exposed to the ideas of calculus and the fundamentals of sets and proving, but do not assume any additional background.

   c. Use good judgment in distinguishing between concepts and results known to audience members versus those which require some degree of review or introduction and development.

   d. Using note cards, overhead transparencies and other forms of support as appropriate, and speak to members of the audience as opposed to reading the paper.

   e. Maintain eye contact during the presentation making an effort to include everyone in the audience.

   f. Dress appropriately.

   g. During the question and answer period:

   i. Seek feedback when responding to a question by maintaining eye contact and inviting follow-up questions or comments;

ii. Treat all questions and questioners with respect.

3. The presenter exhibits an acceptable level of understanding of the material.

   
   a. If a part of the presentation emphasizes the formal statement of definitions and theorems and standards of proof, the presentation should communicate key definitions and results accurately and use appropriate examples to illustrate them. The speaker should demonstrate understanding of the way definitions and prior results are applied in the development of a proof.

   b. If the presentation is to communicate an overview of the entire topic through a careful selection of definitions, theorem statements and examples with central concepts and results being stated formally and illustrated, then the speaker should explain key definitions and results accurately and select appropriate examples to illustrate them.

   c. If the presentation is to communicate an overview of the whole topic, but the treatment is more informal, then the speaker should introduce central concepts and results through examples and informal statements designed to stimulate intuitive understanding.

d. Respond appropriately to questions during the question and answer period.

4. The presenter delivers the presentation with sufficient clarity and professionalism that main points can be understood by most audience members.

   a. It is crucial that the audience understand the main points of the presentation. This is far, far more important than coverage of a large amount of material from the paper. Use good judgment in narrowing the scope of the paper for the presentation to achieve this purpose. The guideline should be this question: Can the audience go home and complete a reasonable homework assignment--at the level you would be able to do after a class lecture?

   b. Use good judgment in deciding how to best present the ideas inherent in the presentation, and use forms of media support, including projected computer output, as appropriate. Weigh the advantages and disadvantages of using an overhead slide, a physical model, a computer presentation, etc.

   c. Use of the chalkboard, while not prohibited, should be kept to an absolute minimum.

   d. Prepare overhead transparencies or computer presentations slides that are:

   i. easily read from any place in the seminar room;

   ii. simple, uncluttered and designed to help communicate, review and relate main points.

e. Be free of the kind of serious grammar, pronunciation, word usage and mathematical notation errors that interfere with the clarity of communication.