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The Capstone Course

Here is what we have to work with (Krug's emphasis), based on

The Capstone proposal from April 2007


The goals for a Capstone:

  • The student will be able to learn the mathematical sciences independently
  • The student will display communications skills, in both written and oral presentations.
  • The student will demonstrate breadth of knowledge in the mathematical sciences
  • The student will demonstrate the ability to learn beyond regular course work


Honors theses, undergraduate research projects and other such projects could fulfill the Capstone requirement, provided they meet the goals. A process for approving these and assessing them will be needed. This could either be left to the Chair, to a committee, or to the entire department

Another way to achieve these goals would be completion of a Capstone course proposed below.

Catalog information: MAT497 or STA497

MAT/ST 497, Mathematical Sciences Capstone (3,0,3) Directed projects in the mathematical sciences designed to broaden, deepen and extend the students’ knowledge.

Prerequisite: 30 semester hours of courses for the major completed.

In many ways this is analogous to a topics course. The syllabus for the course will be developed by the instructor. An approval process and assessment will be necessary. The sample below is just to give an idea of what might be done. The number of papers, the nature of the projects, and so on, would be up to the person developing the particular version of the course.

A sample proposal for the course

The course will begin with some common reading of appropriate articles from journals and other sources in MAT, STA, and related areas. Students will write 3-4 page reports and discuss the works in class. The instructor will direct the students in approaching these tasks.

The students will select semester projects from suggestions provided by the instructor. It is likely the interests and expertise of the instructor will affect the choice of topics. These may be individual or small group projects, as appropriate. Ultimately students will present oral reports on their work to the class (and perhaps to more junior students), and a written report on the order of ten pages for the instructor to evaluate. Students will also write brief reaction papers on their fellow students' presentations.

Assessment: initial assessment can be evaluation of the quality of the student projects. This could involve faculty members who are not the instructor for the course. Ideally follow-up assessment would be done as part of alumni surveys. In particular, we should ask if the course, as well as other parts of the major, were helpful to the student in making oral and written presentations in their later life.

Conclusions following from above:

  • The capstone can be either a course, or an approved project.
  • It must consist of each of the following:
    • Independent Learning Experience
    • An oral presentation
    • A written report
  • We need an approval process
  • We probably need a set of guidelines for approving projects
    • The capstone experience should be flexible enough to allow independent workers to explore areas of mathematics of their choice, yet structured enough to provide appropriate direction for those students who need it.
    • The guidelines should be an expansion of the goals
    • How much independent learning?
    • How much writing?
    • What is acceptable for an oral presentation - must it be at NKU
    • Should we count REU's and other off-campus activities? How?
  • What should the course be?
    • One suggestion is an alternative for those students unable to work a true individual project
    • Another suggestion is that the course help students to find faculty mentors with whom to do research or reading projects

More on the approval process

  • A project must be approved by a committee of faculty, including at least one faculty member from pure and applied math, one from math ed, and one from statistics.
  • The student and adviser should create and follow a set of guidelines.
  • The committee will require a one-page proposal (a semester before completion) which will include a project title, project goals, and the name (and signature) of the supervising faculty member, as well as the projected date of completion.
  • A review of project will occur at the end (including written materials and evidence of an acceptable oral presentation.)
  • Guidelines
    • Students must do at least one of the following:
      • Read and learn independently or in a supervised independent- study some mathematics which is new to them and equivalent to four weeks of a 300+ level mathematics course
      • Do an independent research project and obtain results (new to them.)
      • Work on another project or be involved in an activity where they participate in creating or learning mathematics which is new to them.
    • Write up an N page results paper.
    • Give an X minute talk.

Examples of Independent Projects

  • A student works in the Burkardt Center on a substantial project.
  • A student undertakes the modeling contest, and then refines the solution to make it their own.
  • The student works on (and solves) a journal problem, or solves a Putnam problem; then looks into the ideas further on their own.
  • The student reads some new-to-them mathematics (say, Fractional Differentiation) and writes it up in a way that undergraduates can understand.
  • The student finds and implements a mathematical model for a practical problem.
  • A student uses a CAS to do some experimental mathematics and then verify the results.


  • Faculty Compensation
  • Credits? Those taking/not taking the course?
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