Evaluation Standards

Your comprehensive project will consist of a formal written paper and a 20-25 minute oral presentation. It will be evaluated primarily on

1. the substance and quality of the content of the overall project,
2. the quality of presentation of the formal written paper,
3. the quality of the oral presentation, and
4. the evidence of growth in mathematical knowledge and ability.

The comprehensive project constitutes 75% of your grade in Math 400. As a guide to the evaluation of the comprehensive projects, we give the following rubric.

Content

1. The project (as presented through your written paper and oral presentation) demonstrates a clear and in-depth understanding of some area of mathematics which goes beyond your previous experiences in mathematics.
2. There is clear and logical development of the mathematics.
3. Your work is focused. In other words, the purpose and central concept(s) of your project are solidly established and you do not deviate unnecessarily from these concepts.
4. Your work shows depth. In other words, you show a deep understanding of at least one important area of mathematics rather than showing relatively shallow or limited understanding about a broad array of concepts.
5. Your work is mathematically accurate.
6. Your work demonstrates your own understanding of important concept(s). Your project must be your own presentation of your own understanding of the material, and not simply a (non-plagiarized) paraphrasing of your sources. You demonstrate a certain level of command of the topics.
7. You clearly and fully support all of your work with good examples, well-reasoned arguments or proofs, and/or references.
8. You give motivation for your project, and put its central concept(s) into context, by presenting known or potential  mathematical or non-mathematical applications, and/or background history of the subject. 

Written Paper

1. Your paper is well written and clearly conveys all of the important mathematical concepts of your project.
2. All of your work is clearly and fully supported with appropriate examples and/or well-reasoned arguments or proofs.
3. Your paper is clearly written and contains a minimum of distracting grammatical or stylistic errors.
4. Your paper has a clear introduction that focuses the reader's attention to the topic(s) and prepares the reader for the remainder of the paper.
5. Your paper flows well from one point to the next.
6. You cite your sources appropriately in the body of the paper. You have not plagiarized from any source.
7. The paper contains all of the important mathematical concepts of your project and clearly ties all of these concepts together in a meaningful and focused way.
8. Your conclusion helps the reader bring together the important ideas of the paper.
9. You have an accurate and complete bibliography.
10. Your paper "looks good." In other words, it is presented in a relatively standard format on quality paper with reasonable margins. The integration of mathematical symbolism into the text is not distracting for the reader.

Oral Presentation

1. You give a well prepared, well practiced, and well presented 20-25 minute talk which clearly conveys some or all of the important mathematical concepts of your project.
2. You have chosen a reasonable amount of content for your talk and you present it in a clear and understandable manner for the average senior mathematics major.
3. There is clear evidence that you spent the time to carefully and fully prepare your talk and to practice your talk. You do not show an over-reliance on prepared notes.
4. The talk is well organized and flows well from point to point.
5. Your voice is clear, not too loud or too soft, and the pace is not too fast or too slow.
6. You show your enthusiasm and motivation for the subject, and make the presentation interesting.
7. You engage the audience and you are responsive to the audience, demonstrating flexibility in your presentation when needed.
8. You effectively use visual aids (such as the overhead, computer projection systems, manipulatives, etc.) if and when appropriate, and have considered that members of the audience may prefer to receive information in a variety of ways (different learning styles).
9. You are able to respond appropriately to reasonable audience questions about your topic.

Growth

1. There is evidence of a great deal of personal and/or intellectual growth on your part in completing this project.
2. The content of this project clearly challenged you mathematically either because it introduced you to a completely new concept, or it required you to take a familiar concept and work with it at a higher level or approach it in a complex way.
3. Your project was creative or original in the ways you dealt with the mathematical content or in the presentation of that content.

Note for Honors Candidates: To receive departmental honors, there is the expectation that, in addition to GPA-level and coursework expectations, the candidate must produce a comprehensive project of more significant content and higher quality than the typical senior, and must give two presentation on it. However, in the grading of Mathematics 400, the comprehensive project will be evaluated using the same set of expectations as all other seniors.

Note for Distinction Candidates: To receive departmental distinction, one must receive a Comps Exam score at or above the distinction level (determined yearly by the mathematics department faculty), and receive a grade of A- or A for the Senior Colloquium course.