Office: Hobbs 314 Office Phone: (434) 544-8374 Email: peterson@lynchburg.edu

Office hours: TR 11:00-12:00 and 2:30-3:30 (email me to confirm) ·  or by appointment.

• Inquire: frame questions that address issues and uncertainties across a range of disciplines.
  The student will
  • recognize precise and complete statements of problems.
  • recognize what information is necessary in order to solve given problems.
  • ask essential questions about given problems.
  • ask questions for further study regarding problems and reading assignments.
  • develop an interesting problem to investigate as a final project.
• Explore: investigate issues in depth and detail.
  The student will
  • think creatively about possible solutions to problems.
  • employ knowledge and techniques of Mathematical problem solving to explore problems.
  • comprehend given problems, reading assignments, and the arguments of others.
  • investigate a chosen final project independently.
• Conclude: develop informed responses to issues.
  The student will
  • marshal evidence in support of a solution to a problem or conclusion in an argument.
  • articulate an appropriate conclusion based on the evidence.
• Persuade: convince others of the validity and value of conclusions.
  The student will
  • produce precise and complete statements of solutions to problems.
  • construct effective written arguments based in evidence, reason and understanding.
  • deliver effective oral arguments based in evidence, reason and understanding.
• Engage: use knowledge and abilities for the good of self and society.
  The student will
  • describe applications of problem solving techniques in other disciplines.
  • value achievements in Mathematics for their intrinsic worth.
  • work effectively with other members of a group to solve problems and present their solutions.

Attendance and Absences from Tests: Attendance at each scheduled class meeting is considered mandatory. If a student has missed 4 class meetings, they will lose all the points from the group projects (160 points). Students arriving late for class or leaving early may be counted as absent from that class.

Respectful Conduct: Everyone in the class will be respectful and considerate of others. Please observe the following policies:

Arriving late for class. Late class arrivals are disruptive and inconsiderate;

moreover, they may be regarded as absences. Students who frequently arrive late

may be asked not to return to class.

Talking in class: I encourage all students to participate in class discussions. Please keep all

discussions to the topic at hand. Personal conversations are disruptive and inconsiderate. Students

who frequently disrupt the class may be asked not to return.

Cheating and Plagiarism: Cheating and plagiarism are serious offenses and will not be tolerated. Plagiarism is the act of presenting someone else's work as your own (this someone may be another student, a tutor, a member of the faculty, or an author). Any student caught cheating or committing plagiarism will be subject to disciplinary action. See handbook for details.

Grades: Your course grade will be based on three main components.
1. Several individual projects: 40 points each

2. Many group projects : 40 points each

3. Final individual project: 80 points

Course Projects:

Students will hand in a detailed typed report for each project. In this course you should not confuse the written project with "showing your work".  Instead your written work should indicate to the reader how well you understand the mathematical concepts you have used in your solution.  A list of calculations without reasoning is not mathematics.  When writing each project your goal will be to communicate your solutions to another person rather than to show you've completed the assignment.

Students will be expected to write clearly and carefully.  There is no required length or word count.  Each project write up should be exactly as long as it needs to be to convey the required ideas.  Hence you will not feel pressure to omit required details or add padding to meet an arbitrary length requirement.

With this in mind each write up must include the following:

1. Introduction:  A brief description of the central problem. Do not simply recopy the problem.  Rather, describe the problem in enough detail that another student not in the class could understand the main problem and its importance.  Also give a brief description of how you plan on solving the problem.
   
   
2. Results: This section is comprised of 3 sub-sections:

a.       Exploration give a brief description of the explorations you performed and explain how they were used to arrive at your conjecture.  If you had a brilliant falsh of insght that revealed the conjecture to you, then include several specific examples that will help the reader understand both the problem and your conjecture.  You must describe how these examples helped you to generate a conjecture and/or understand the problem. If you used a computer program to generate examples attach a copy of the code and output (as an appendex).

b.      Conjecture: After your exploration, you will be ready to make a conjecture about the problem.  The conjectures should be clearly stated and labeled.

c.       Proof: Provide a complete and rigorous mathematical proof.  There should be no gaps in your explanation. Clearly define each mathematical term and variable in the problem.  Other than results from high school algebra, include the full statement of any theorem that was needed to solve the problem.  Results from high school algebra should be labeled HSA.

3. Conclusion:  This section has 2 sub-sections:

a.       Summary: Include brief summary of the problem, highlighting the parts that you felt were most interesting or surprising.  Compare your "gut-feeling", if you had one, to your actual solution explaining any differences.

b.      Further Work: Finally, state at least 3 new problems that are related to the original problem that you would like to investigate in the future.  These problems should be individually numbered and should be a clearly and carefully (with all the detail) stated in the same fashion as the original problem. The reader should not need to know the original problem to understand the new problems.

Grading:  All projects will be graded using the following rubric:

Course web page: Any modifications to the course policies and/or course syllabus will be announced on the course web page (URL is given above).