Math 601 Mathematics Capstone      Westminster College        Fall, 2003

Dr. Carolyn K. Cuff      
Abstracts of projects



The capstone course is designed to provide an opportunity for students to evaluate and assess the strengths and limitations of mathematics.  The capstone experience permits opportunity for structured reflection on the value of education in and beyond the major and provides another chance to strengthen communication and problem-solving skills.




  • To independently investigate an area of mathematics
  • To present mathematics to peers that is new to you and them
  • To write a formal mathematical paper





This course is a contracted grade course.  As such, the expectations are closely tied to a specific grade.


Regardless of the grade you are expected to

  • Attend all presentations and lectures
  • Present a theoretical mathematical paper
  • Investigate or research a mathematical problem
  • Present a poster of your work Wednesday, Dec. 10th at 3:00


Theoretical Mathematics Paper

Read and summarize a recent article of your choice and approved by me.  The article is expected to be theoretical in nature.  A fifteen-minute oral presentation to the class will be scheduled during the week of Sept. 9.  By Sept. 4, you will do the oral presentation for me at a mutually convenient time that you schedule in advance.  Unscheduled rehearsals will not be held; unrehearsed presentations will not be given.  You are expected to be well prepared for this rehearsal.  The rehearsal will be graded unprepared, not sufficiently prepared, and acceptable.  To be acceptable, the presentation will give sufficient mathematical background, explain the problem and solution in appropriate detail, and be 15 minutes long.  Handouts, overheads and/or PowerPoint presentations are expected.


Investigation or research of a mathematical problem (final project)

The chosen problem will be approved by a mathematics professor with sufficient knowledge of that area to be able to determine the contract letter grade.  In general, investigation of an area is C level work; investigation at a higher level is B level work; independent research which leads to a solution of a mathematical problem is A level work.  You will submit a written explanation of the work you expect to do for approval to the appropriate professor by Sept. 16.  (I assume you will have discussed your project with the professor prior to the 16th.)  The contract letter grade will be determined through consultation with me, the professor with sufficient knowledge of the particular area (if this is not me) and you.  Contracts are due to me by Sept. 23rd.


Additional information


  • Your final project should have broad connections.  Examples of connections include but are not limited to: other areas of mathematics, the history of the problem with complete background information, and applications of the problem to areas outside of mathematics.


Once the area specific professor has helped determine the contracted letter grade, the majority of the help required should come from me.


  • You are expected to attend weekly Tuesday meetings to discuss your progress and your problems.   A 5-10 minute presentation of the progress made during the week will be given to the class.  These will be held during the scheduled class time.


  • At least two written drafts of the final paper drafts are expected.  The first draft (which may have gaps in the research/investigation) is due on or before Nov. 11th.  The second draft is expected to be mathematically complete and is due on or before Nov. 25th.   Work on the paper is expected to continue between Nov. 11th and Nov. 25th. 


The final paper and abstract are due Dec. 8 at noon.


Brief outline of paper


The final paper will consist of four parts.


a) An abstract of the paper sent to me electronically

b) A literature review

c) A statement of the problem

d) A summary of work on this problem or a solution of the problem




To that end, and to facilitate writing the contract the following are portions of the work that should be included in the contract.


a) An annotated bibliography which describes all of the works that you have read in preparation for the contract. 


b) The statement of the problem that you will attempt to solve or the set of work which you wish to summarize.  You ought to be prepared to speak about your solutions to the problem thus far.  Dead ends always happen.  Sometimes exploring the dead end will help clarify your problem.  Sometimes, other eyes will have approaches to help find ways out of the dead end.


The approach to independent solutions of open-ended problems is not linear.  I expect you to have false starts, frustrations, find out you need other papers, and maybe not even be able to clearly state the problem until a potential solution process exists.


Avenues to explore if you are still unable to articulate an area – Consider another application of the theoretical paper you read.  Is there another data set to which the work could be applied?  Is there a related mathematical field?  If you increase or decrease the constraints on the problem considered, does the problem sufficiently change?  How do you know?




A poster of your work will be presented to the mathematics faculty and other interested people during the scheduled final for this class.  The poster should clearly describe your problem and solution.  Bibliographic citations are to be in the lower right corner in 8 pt type.  Faculty will be asked to judge your poster on clarity and presentation.  Negative comments may affect your grade.


Details of the Grading


To receive an A or B or C each of the following MUST be fulfilled.


  • Attendance at all but one class meeting
  • Adequate preparation of the theoretical mathematical paper.  Presentation of the paper to class. 
  • Completion of the project including the written and poster presentations. 


The final letter grade will be dropped one third (i.e. from A to A- to B+) for each occurrence of the following.


  • Each additional absence
  • Inadequate preparation of the theoretical paper
  • Missed due date (grade continues to drop with each additional 24 hour period)




The following statement will be signed at the class meeting on Thursday, August 28th.  Students not attending class on Thursday will be dropped from the roster.




I have read and understood the syllabus and expectations for MTH 601.


I understand that if I do not fulfill the expectations for C level work, I will receive an F for this course and thus will not graduate as expected.



Signature of student.







Contract (electronic version is on the R: drive)


I am contracting for a XX in Math 601, Fall, 2003 as described in the syllabus.


Attached is the annotated bibliography which I have used to explore my topic.


Below is a description of the problem I am investigating/researching…


I expect to show the following …


I understand that this contract is renegotiable prior to Nov 1st.  I also understand that if I fail to meet the specifics for the contract, I will not pass the course.



______________________          _________________________

Signature of Student                   Date



______________________          _________________________

Carolyn K. Cuff, instructor           Date





After discussion, I concur that completion of the work described above is a XX contract.




______________________                          _________________________

Warren D. Hickman,                                    Date

acting department chair