The purpose of the senior capstone is to engage each senior in the exploration and communication of mathematical ideas encountered in 300+ level mathematics/statistics coursework and beyond.

### Basic Components

The student independently studies a topic of interest and creates a poster covering their topic. The student gives a 20-minute presentation of the poster to an audience of Mathematics and Statistics faculty and later participates in the Senior Mathematics & Statistics Poster Symposium, where they share their work with the wider Kenyon community.

### Requirements and Important Dates

- 1. Student selects a topic.
- 2. Student submits a formal proposal describing the proposed topic for their poster and presentation.
- 3. Student presents the background and preliminaries of their topic to peers in the Senior Seminar.
- 4. Student presents their main results and the implications of those results to peers in the Senior Seminar.
- 5. Student completes and submits an electronic version of their poster.
- 6. Student presents their poster to mathematics and statistics faculty members.
- 7. Students participate in the Senior Mathematics & Statistics Poster Symposium.

#### 1. Student selects a topic.

As this is the capstone experience for the mathematics major, we expect the work to build on earlier intermediate and advanced work in the discipline.

In choosing a topic, the student has four options:

**Survey of a Contemporary Research Problem:**The poster presents a contemporary open problem in mathematics or statistics, discusses historical approaches to the problem, and reports on progress that has been made.**Summary of Research or Internship:**The poster summarizes mathematical or statistical results stemming from the student’s experience in an undergraduate research program or in an internship involving mathematical or statistical ideas at the 300+ course level.**Introduction to a 300+ Level Math/Stat Course Topic:**he poster provides a lively presentation of a specific topic from a 300+ level mathematics or statistics course that is accessible to a junior/senior-level mathematics major who has not taken the course.**T****Presentation of a Topic Leading into Honors Study:**The poster describes material the student has learned in preparation for a spring-semester Honors project in Mathematics or Statistics.

More details about these topics can be found here.

The student's topic should be of suitable difficulty — not too easy and not too hard. If in doubt, the student should consult with faculty members about this. Once the student has a topic and a few print resources (books or articles) in mind, they should approach one or more faculty members to consult on the suitability of the proposed topic and to discuss ideas for the proposal.

Students should have topic ideas and some resources in hand no later than the first week of the fall semester. (Classes begin Thursday, August 29, 2024.) We encourage students to begin thinking about possible topics in the *spring of their junior year.*

#### 2. Student submits a formal proposal describing the proposed topic for their poster and presentation.

Even though the proposal itself is fairly short, the amount of work that goes into it is much greater. Writing a good proposal requires a reasonably good understanding of the major ideas and technical material involved in the topic. Before attempting to write the proposal:

- The student needs to understand the general motivation behind the topic.
- The student needs to identify the end-goal(s) for the senior capstone.
- The student needs to make sure they have the necessary background and appropriate resources for completing the topic.
- The student needs to be fairly sure the project is doable in the given timeline.

In other words, the student cannot write a reasonable proposal without studying their major resources enough to get a good sense of the topic, its difficulty, and its feasibility. All of this requires a substantial amount of reading and background work prior to writing the proposal. Therefore the preliminary work needs to begin several weeks in advance of this first deadline.

In addition to extensive reading, the student should be consulting with one or more faculty members who will be able to give guidance on end goals and feasibility. It will ordinarily take several discussions with faculty members to really narrow down the goals of the project.

Students should not underestimate the importance of the preparation step or the amount of work that goes into it. This is a big part of the overall senior capstone project and a big deadline.

The proposal must include:

- a description of the topic: this is more than the mere title of the topic. The description should include motivation and describe the basic ideas underlying the topic. It should also state specific end-goals and the nature of the mathematical material that is needed and will be covered. The description should also explain how the topic fits the students’ background and interests in mathematics. The student should also be careful to choose a topic that has substantial content and that is also doable in the timeline given for the senior capstone.
- an annotated bibliography saying generally what is in each source and how the student expects the source to contribute to the eventual poster, (these annotations need not be extensive; keep them general and short, but writing them will require the student to have done some reading in the source.)
- a list of courses the student has had that will support study of the topic, and
- a summary of the discussions the student has had with faculty members concerning the topic.

**Deadline for the Proposal: **Sunday, Sept. 8, 2024, by 5 p.m.**Departmental Response by: **Friday, Sept. 13, 2024

#### 3. Student presents background and preliminary information to peers in the Senior Seminar.

Students present the mathematical background information and preliminary results for their projects in 7- to 10-minute talks to a subset of the seminar class. Seminar students in the audience and the seminar instructor will provide constructive feedback based on this presentation.

**Background/Preliminary Presentations: **during seminar on the week of Monday, Sept. 16, 2024.

#### 4. Student presents main results and the implications of those results to peers in the Senior Seminar.

Students present main results and implications (with significant mathematical content) from their projects in 7- to 10-minute talks to a subset of the seminar class. Seminar students in the audience and the seminar instructor provide constructive feedback based on this presentation.

**Results/Implications Presentations:** during seminar on the week of Monday, Sept. 30, 2024.

#### 5. Student completes and submits an electronic version of their poster.

Students submit complete, electronic but print-ready, versions of their posters. Each poster should be designed to facilitate an accessible, efficient, and engaging presentation of the topic to an audience of peers. To this end, the poster should include all components necessary to tell a complete story about the student’s project. This may include, but is not limited to, definitions, examples, theorems (and their proofs), applications, and any other critical content. Visualizations should be incorporated to support the story line and to convey key concepts, when appropriate. The poster will be submitted to the Senior Seminar Moodle page.

General Poster Instructions:

- The poster will be formatted using a template provided in Senior Seminar.
- The poster should be self-contained. The necessary background, basic definitions, and useful examples must be explicitly included so that the audience can understand it without consulting other sources. The poster may, however, assume the general background covered in the core courses in mathematics and (if necessary) the material covered in other math courses the student has taken at Kenyon.
- The poster text should be written so that it is understandable to junior/senior-level mathematics majors.
- The poster should include graphics, data, and/or calculations that facilitate understanding of the topic.
- When using multiple sources for the project, the student will be expected to coordinate and systematize material from these sources. This includes standardizing the notation, which often varies from one source to another.
- Information presented on the poster should be well-organized with appropriate headings, and the student is expected to use correct English and mathematical grammar throughout.

**Deadline for Electronic Poster: **Friday, Nov. 8, 2024 by 5 p.m.

#### 6. Student presents their poster to mathematics and statistics faculty members.

Each student gives a 20-minute oral presentation of their poster to an audience of Mathematics and Statistics faculty at an assigned date and time. This will be followed by a question and answer session with the faculty members. In this presentation, the student will tell a complete story about the topic they have selected, highlighting the components of their poster.

**Poster Presentations: **Monday, Nov. 11, Wednesday, Nov. 13, and Friday, Nov. 15, 2024 at times to be specified.

General Presentation Instructions:

- Like the poster, itself, the presentation should be a self-contained story of the student’s results. Any background information necessary to understand the story should be included, beyond the core course content for the mathematics major.
- The student should practice their presentation to ensure that they meet the 18- to 20-minute time requirement.
- After the formal presentation, the student should be prepared to respond to questions posed by the Mathematics and Statistics faculty members in attendance.
- The presentation will be evaluated on the correctness, completeness, and clarity of the presented material.

#### 7. Student participates in the Senior Mathematics & Statistics Poster Symposium.

All students will participate in the Senior Mathematics & Statistics Poster Symposium. At the Symposium, students will present their work to the wider Kenyon community.

**Poster File: **Final poster files must be submitted by Friday, Nov. 22, 2024, at 4 PM

**Poster Symposium: **Tuesday, Dec. 3, 2024, from 11:10 AM - 1 PM.

#### Evaluation of the Capstone

The department will evaluate each senior capstone poster and presentation (the result being either distinction, pass, or failure) using the criteria on this rubric.

The student's work will be rated as exemplary, acceptable, marginally acceptable, or unacceptable in each category. An evaluation of "unacceptable" on any component of the senior capstone may be considered grounds for failure. To achieve distinction on the senior capstone, each component of the evaluation must be judged “exemplary.”

#### Second Chance to Pass the Capstone

College policy provides each student who fails their senior capstone the first time with a second chance. If the senior capstone poster and/or presentation was found to be unacceptable, the student will be required to construct a poster and make a presentation on a topic chosen by the department. The second poster and presentation will be due during the penultimate week of classes in the spring semester. Other (preliminary) deadlines will be imposed by the department in consultation with the student.