# Mathematics Senior Comprehensive Project

## The Advanced Writing Requirement in Mathematics

### Section 3: The Senior Comprehensive Paper

The student prepares her paper under the direction of her project advisor. When it is complete and acceptable to the advisor, she prepares three copies for her examining committee.

Following the Senior Comprehensive oral examination, the student will meet with her advisor or all members of the committee (the advisor will choose the most practical route) to find out if the paper requires revision. If it does, the student will make the revisions and give a revised copy to her advisor. The advisor will monitor the revision process and notify the student when her paper is acceptable.

### The Senior Comprehensive Project

*A. General description*

The college requirement for a Senior Comprehensive Examination is met by mathematics majors through completion of the Senior Comprehensive Project, which is an extended independent study project on a topic new to the student, undertaken under the guidance of a faculty advisor. The project culminates in a formal written paper and a formal public oral presentation of the results of the study followed by questioning by a faculty committee including the faculty advisor and the seminar instructor. This paper and presentation comprise the Senior Comprehensive Examination. The paper also serves as the final submission for the Advanced Writing portfolio.

*B. Mechanics*

- Paper
The paper is a summary of the student's work. It will contain a summary of the seminar talks on the comprehensive project (see Part I) and a detailed discussion of the material for the formal comprehensive presentation. There is a specified format for the paper; for details on the format and on the preparation of the paper, see "Guidelines for the Senior Comprehensive Paper " in Part III of this handbook.

The paper must be approved by the advisor before it is submitted to the committee and must be accepted by the committee (which may require some further revision) for the examination to be complete. Three copies of the paper in its final form must be given to the committee (the readers) at least a week before the talk is to be given. Specific due dates will be given at the beginning of the semester. Failure to meet deadlines will usually be reflected in the Proseminar grade, but may (in extreme cases) prevent the student from completing the examination in time to graduate.

- Talk
The talk is a formal presentation of the results. It should be clear, concise, and complete, and include an introduction to the topic as well as the presentation of the final results. One hour will be scheduled for the talk, with 30-40 minutes for an uninterrupted presentation and the remainder of the time for response to questions asked by the members of the committee. 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 the student's method of approach to the question that is important, rather than recall of specific facts. After the hour, the students (both audience and presenter) leave and the committee deliberates on the talk and the paper. The presenter contacts her advisor the next day, or at another prearranged time, to learn the results (pass or fail and/or what further work may be required - honors are not awarded by the committee).

*C. Grading*

The possible grades (recorded on the final transcript) for the Comprehensive Examination are unsatisfactory(U), satisfactory(S), and honors(H). A grade of S or H is required for graduation. The committee determines whether the paper and presentation are satisfactory, but honors are assigned by the whole department meeting together. If the committee identifies deficiencies in the comprehensive examination (paper or talk) the student will be told what is needed to make the work satisfactory, and this work must be done before a grade can be assigned. The Senior Comprehensive Examination must be completed (paper and talk both acceptable) before the end of the semester in which the student is to graduate.

*Criteria for evaluation of the Comprehensive Project*

- Mastery
Depth of understanding must be demonstrated. The student who has mastered her topic understands its nature and importance in a global sense. She is 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. Her grasp of the meaning of definitions and theorems is further evidenced by the effective use of examples. Evaluation of the student's mastery of her topic will take into account the level of difficulty of the topic and the background of the student as well as the level of understanding that is demonstrated. Specifically, the degree to which the material is different from that covered in her course work will be considered.

- Written paper
The written paper is evaluated using the following criteria from the Guidelines for Advanced Writing Proficiency in Mathematics The paper must follow the format described in "Guidelines for the Senior Comprehensive Paper " and in the Guidelines for writing a Mathematical Paper

Knowledge - insight, accuracy, completeness, conciseness

Originality - independence from major source in developing topic

Organization - logical flow with introduction, overview, examples, transitions, and conclusion

Vocabulary - correct use of mathematical terminology and symbols, sufficient use of non-technical language

Mechanics - adherence to manuscript conventions, correct spelling and sentence structure, careful editing and proofreading

- Oral presentation
The criteria listed above, under knowledge, originality, organization, and vocabulary, also apply here. The presenter must use board space and visual aids effectively and write legible and logical statements. She is expected to be poised and purposeful, work at a suitable pace, and not rely excessively on written notes. She must have a sense of her audience and provide a sufficient introduction including a description of what was done in previous talks.

- Responses to questions
The responses to questions are expected to be relevant and complete. The difficulty of the question is a factor in determining the completeness of the response. If a student cannot answer a question, her ability to reformulate the question or to work with the questioner towards a solution can be evaluated.

- Work with the advisor (evaluated only by the advisor)
The most important factor in evaluating the student's work with the advisor is the degree of independence. The independent student works through routine details and organizes the material on her own, working from the advisor's general outline. She meets regularly with her advisor, and is prepared for appointments, with specific questions in mind. She is able to discuss the topic with the advisor and does not need to be led through the material. For a comprehensive to be awarded honors, the work must be rated good to excellent in all areas and excellent in most.

*D. Scheduling*

The agreement with the advisor is for a four-month period for work on the project; there are three time blocks available: September 15 - February 15, October 15 - March 15, and December 12- April 15. If the project is not completed by the end of this time, the student may have to seek another advisor and project, which will almost certainly prevent her from graduating on schedule.

Students who are intending student teaching in the Spring semester must present both preliminary talks on the comprehensive topic before the end of the first semester.

*Fall semester deadlines*

- Week 2: Advisors, topics and dates for senior comprehensive must be determined
- Week 4: Schedule for Comprehensive presentations will be set
- Week 5: First (seminar) talks on comprehensive topics for First group
- Week 11: Second (seminar) talks on comprehensive topic for First group, First (seminar) talks on somprehensive topic for Second group
- Week 14: Monday - Complete draft of comprehesive paper due to advisor (First group)

*Spring Semester deadlines*

- Week 1: Second (seminar) talks on comprehensive topic Second group
- Week 2: First (seminar) talks on comprhensive topic Third group: [Beginning] Second group papers due to readers
- Week 4:Monday - Final paper due to readers ( First group) Friday - Complete draft of paper due to advisor (Second group)
- Weeks 5-6: Final presentations for First group, Second (seminar) talks by Second group
- Week 7: Monday - Final paper due to readers (Second group) Friday - Complete draft of paper due to advisor (Third group)
- Week 8: Final presentations by Second group
- Week10: Monday - Final paper due to readers (Third group)