Franklin & Marshall College Franklin & Marshall College

    • math-header-image-2
    • math-header-image-1
    • quadresidues3

Additional Course Information

Majors, Minors, Independent Studies, and Honors

Majoring or minoring in mathematics:

 The College Catalog is the definitive resource for information about requirements for the math major and minor. We have also prepared some pamphlets for our students with departmental advice and course planning information:

Independent Studies and Honors in Mathematics

Independent Studies in Mathematics:

By definition, an independent study is exactly that - a chance for a student to independently study problems or topics that are of interest. The role of the advisor changes from independent study to independent study, but in general, it is to help students when they run into difficulty and to direct the studies of the students in "promising" directions.
During the first two weeks of the semester (or, preferably during the previous semester), the student wishing to pursue an independent study should approach a faculty member and express interest in doing an independent study. If the faculty member is willing, then both the faculty member and the student together should determine a direction for the independent study and write a short description of the planned study. The faculty member will then discuss the independent study with the rest of the department and must receive the permission of the department to advise the independent study.

Honors Projects in Mathematics:

The designation of Honors applies to a student who has completed an outstanding independent study project and is in good standing in the department. Formally, a student receiving Honors in Mathematics typically satisfies the following list of requirements (as stated in the catalog):

  1. The student reads and understands the regulations for departmental honors as stated in the College Catalog.
  2. The student has taken at least four courses beyond Mat111 with a departmental grade point average of at least pi (3.14159265...).
  3. The student is in good standing in his or her current departmental courses.
  4. The student completes an outstanding independent study project and successfully defends this project in an oral defense.

An outstanding independent study project is usually at the 400-level and lasts two semesters. Furthermore, in order for an independent study project to be considered outstanding, it generally must fall in one of the three categories:

  1. The project consists of new results in an area of research.
  2. The project consists of a new interpretation of well-known mathematics.
  3. The project shows a deep understanding of an advanced mathematical topic.

The following is a rough timeline of the steps for granting Honors in Mathematics for a typical student. The advisor and the department must approve any deviations from these steps.

  • At the beginning of the first semester, the student and advisor discuss an independent study project. The student writes a short description of the project and any planned results if applicable. The department then approves the independent study.
  • At the beginning of the second semester, the department discusses the projects that appear to be eligible for honors. The department may raise concerns regarding the work of the student in mathematics courses at this time.
  • Early in the second semester, by the end of February, the advisor and the student determine whether the project is "outstanding" and whether the student should apply for departmental honors. The student writes a brief summary of the project. This summary should include any results obtained by this point.
  • By the middle of March, the student and the advisor determine which faculty members to invite to be on the oral defense board. At that time the student should ask the faculty members personally. When the student asks the faculty members, he/she should provide a description of his/her project. For further information regarding the defense board, see the comments below.
  • The advisor and student, in consultation with the defense board, should set a date for the oral defense. In the past, the oral defenses have occurred during the last two weeks of class.
  • Approximately four weeks before the date of the defense, the student should distribute a polished draft of the thesis to each member of the board and to the advisor.
  • Approximately two weeks before the defense, the student should provide each board member with a final copy of the thesis. The student should encourage the board members to return comments on the thesis before the defense.
  • The student should post announcements for the oral defense at least one week before the scheduled defense.
  • Near the end of the semester, if the members of the department have any concerns regarding the student attempting honors, then they will discuss the concerns at a department meeting.
  • Prior to the start of the reading days, the department must inform the Registrar of the students who are attempting Honors in Mathematics. (For spring 2008, the deadline would be May 2.)
  • The student defends his/her thesis successfully. See the comments below.
  • After receiving corrections from the committee members, the student supplies a final version of the thesis to the members of the department on the committee for their final approval of the thesis.
  • The department grants/denies final approval of Honors and informs the Registrar by the end of finals week. (For Spring 2008, May 9, 2008)
  • The student submits final print and electronic versions of the thesis, along with an Honors Thesis Consent Form to the department chair. The chair forwards them to the College Archives. See comments regarding the written thesis below.
The Oral Defense Board:

According to the catalog, an oral defense board consists of three to five members. At most one of the members may be from outside of the department. The advisor and the student together should decide the faculty members to be on the board. The student personally asks the particular faculty members to be board members. At the time of this request, the student should give the prospective board members an outline or a draft of their thesis describing the project and all results obtained.
The department highly recommends that one member of the board be from outside the department. If this outside member is from another school, the advisor may ask that person to be a board member.

The Defense:

Any oral defense should be open to the general Franklin & Marshall community. Announcements, including the title, the location, the name of the person defending, and a short abstract, should be posted at least one week before the scheduled date of the defense. Additionally, the student and the advisor should agree on the level of the sophistication required by of the audience. A good method is to suggest that the talk should be accessible to the audience members who have taken up to through a given mathematics course.
A typical defense consists of three parts. After an introduction by the advisor, the student gives a presentation lasting approximately 50 minutes on his/her project. This presentation should include any required definitions and the main results from the project. After the formal presentation, the audience is allowed/encouraged to ask questions for at most 15 minutes. After the general question period finishes, everyone leaves except for the board, the student, and the advisor. The board members then ask the students questions regarding the thesis for as long as necessary. (Note that according to the catalog, the entire process can take at most two hours.) During the defense, the advisor is not allowed to say anything unless personally addressed.
After the question period is over, the board asks the student to leave, and then take the opportunity to ask questions of the advisor. After this, the advisor leaves the room and the board determines whether the thesis and the defense deserve departmental honors. The board informs the advisor who then tells the student the board’s recommendation.

Note: Although a successful thesis and defense are required for departmental honors, they are not the only requirements. If, at any time, the department has concerns regarding the performance of the student in his/her classes, the department may decide not to grant honors to the student independently of the decision of the oral defense board.

The Written Thesis:

In addition to the oral defense, the student is required to write a detailed thesis describing the project and any results obtained. This thesis should include definitions and proofs where applicable. This thesis will be included in the College Archives.
Two final print copies and an electronic copy of the thesis must be submitted to the department chair prior to the end of finals week. It should be include a title page with the following information:

    • Full name of student,
    • Department (Mathematics or Computer Science) to which the paper is submitted,
    • Name of course,
    • Student’s anticipated date of graduation,
    • Date paper was submitted.

The electronic copy should be burnt onto a compact disk. The CD should have the name of the student and the department on it.

Revised 3/6/08