The Honors Program in Mathematics

General Description

In broad terms the honors program has the following components.

  1. Three semesters of Honors courses - one semester, Math 95, at the junior level and two, Math 97 and Math 98, at the senior level. Junior Honors will serve to develop greater understanding in a selection of several mathematical topics, ultimately leading to a choice of study for the year-long Senior Honors. Senior Honors will consist of an in-depth two-semester study of a particular topic in mathematics. (See attached descriptions of each.)
  2. Outside examination - Each Senior Honors candidate must complete written and oral examinations set and administered by an outside examiner. This exam will cover the material relevant to each individual project. The work and examination for the Honors program is separate from and in addition to the collegiate Senior Exercise requirement set by the College.

Eligibility

 A student enters the honors program when in his or her Junior year. To be eligible for the program the following requirements must be satisfied.
  1. The candidate must ordinarily have a 3.33 average in mathematics courses and a 3.20 grade point average overall.
  2. The candidate must complete two upper level courses (those numbered 35 or higher) before taking the first honors course.
  3. The candidate must show unusual promise in mathematics as determined by the Mathematics Department.

Junior Honors

 The Junior Honors seminar, Math 95, is taken in the spring semester of the junior year by those students pursuing Honors in Mathematics. Seminars will be run by one or more faculty who will serve as mentors throughout the semester. Students who successfully complete Junior Honors are then eligible to continue their studies in Senior Honors the following year.

Objectives. To develop a greater understanding of selected mathematical topics, and to write a proposal to the Department for the work of Senior Honors.

Course Description. Students will work individually on short topics during the semester. The number of topics could vary depending on the nature of the topics of study. Normally, three topics is about the right number. The number, as well as the particular areas of study, must be approved by the faculty mentor. Collectively, these projects are intended to provide a breadth of study in mathematics. For each project, students will work with one (or more) faculty member(s) who will serve both as a guide and as an audience for presentations of findings. The work will usually be one-on-one. The course may include any or all of the following elements, depending on the procedures set by the instructor.

  • Literature Search and Reading. Projects will require reading in mathematical texts and journals. Instructors will help in guiding the student to relevant literature once a topic of study is chosen.
  • Class Presentations. At the end of work on each topic, each student will present their work to the rest of the students and faculty involved in Junior Honors. Presentations will be 50 minutes in length, and should be accessible to fellow students in the seminar.
  • Journal. Students are required to keep a journal for the course. The journal should contain a list of references (grouped per project), notes taken on the reading, thoughts and ideas, written exercises, conjectures, theorems, and anything else that pertains to the project. Students should develop the habit of writing about all relevant work using, dated journal entries. The portion of the journal pertaining to a particular project will be submitted for evaluation along with a summary report for that project one week after the class presentation.
  • Summary Reports. Students will complete each project with a written summary of their work. Written summaries should report the main results, and should be written at the appropriate mathematical level. The report will be read by the mentors, so that accessibility by student peers in the course is not an issue.
The Senior Honors Proposal. The final requirement for Junior Honors is the Senior Honors proposal, which will serve to lay out a course of study for the senior year of Honors. Honors candidates should be thinking about possible Senior Honors topics throughout their spring semester in Junior Honors. Allow for ample time to write a Senior Honors proposal. Proposals should contain a brief introduction to the topic, a summary of related work completed thus far, a bibliography, and a proposal of the work to be achieved in the senior year, including an estimated time-line. The proposal should also indicate who will serve as the Senior Honors faculty mentor, and this person must endorse the plan of study. Each candidate must then submit their proposal to the Chair of the Department no later than one week prior to the end of classes. The Department, as a whole, will meet to consider approval of students for admission to Senior Honors. A proposal can be approved, disapproved, or returned to the candidate for reconsideration. In the last case, a date for the revision and resubmission to the Chair will be established so that a final decision can still be made before the end of that academic year.

The candidate for Senior Honors should be sure to understand the means by which the faculty mentor for Senior Honors will evaluate work accomplished.

Senior Honors

Senior Honors consists of Math 97 and Math 98, and it carries a total of one unit of credit. The workload is substantial, particularly when considering that the reading involved is at a high level. A person admitted to Senior Honors will meet with a member of the faculty, who acts as a mentor, one or more times a week, generally. However, as with independent study, the faculty mentor is not teaching the material, but will be guiding the student and responding to questions. At the end of the first semester of Senior Honors the faculty mentor submits a grade, and recommends to the Department whether or not the student should be continued in Honors. If the recommendation is negative, the Department will meet to make a final determination. The Department normally accepts a positive recommendation.

Students are advised to keep a journal. The journal should contain a list of references, notes taken on the reading, summaries of discussions with the mentor, thoughts and ideas, written exercises, conjectures, theorems, and anything else that pertains to the work. Students should maintain the habit of writing on a regular basis about all relevant work using, dated journal entries.

At the start of Senior Honors, the faculty mentor of the student will confirm and discuss the means set for the evaluation of work.

Senior Honors concludes in the late spring with an examination set and evaluated by an examiner from a college or university other than Kenyon. The Department selects the examiner who will be informed of the mathematics courses the candidate for honors has taken, and of the studies undertaken as part of Senior Honors. The examination will cover the general area studied during the work of Senior Honors. The examination will consist of two parts: a written three hour examination, and an oral examination. Though the written exam may be administered by the Kenyon Mathematics Department, it is read and evaluated by the outside examiner. The oral examination is conducted by the outside examiner. However, members of the Department will be present

At the conclusion of the Honors Exam, the outside examiner, with the advice of the Department, determines whether Honors will be awarded or not, and if so, what the degree of Honors will be.

In order to achieve honors, honors level work is required in all parts of the Honors Program. Similarly, in order to achieve highest honors, truly exceptional performance is required in all aspects of the honors program.

This page is copyright © 1997
The Kenyon College.

Comments to: Carol S. Schumacher, Schumach@kenyon.edu
Edited: 03-19-98