MATH 256 project

PCC Math 256 Group Project (Summer Term) Instructor: Jeff Pettit

The project for this term will be an independent research project/experiment applying differential equations. You may likely choose a topic that applies concepts and methods explained in class but that goes beyond the topics and methods covered in class or you may need to apply topics not covered until the very end of the course. You and your group will choose a scenario that can be represented as a differential equation such as a cascading salt-vat scenario (ideas permeating in a group of people, money distributed in an economy, deadly or non-deadly mutating or non-mutating virus permeating a society, etc.), spring-mass scenario (conservative and liberal discourse on a topic, emotional progress through tragedy, regaining financial stability after debt, etc.) or any topic that begins with the derivative defined as a set of influences (how one changes one’s mind, orbits around a star or two stars, bungee jumping, blood-alcohol level, predator-prey scenarios, etc.). Define your parameters, create your equation(s), solve for the generating equations and interpret your results. As part of the assignment, you will need to employ a “guru” who is an expert holding a degree related to the field you are exploring. If you submit a written component, I will assess your progress and correct any mistakes/fill any holes. Even without submitting a written component, groups are expected to check-in regularly with the Instructor to maintain integrity of the final product. Your grade will be assessed on your presentation of an oral component or display. The final presentation (oral or display) will describe your method, your findings and an analysis of your results.

Due dates. Submissions are due at the end of the last class day of the week listed:

1. Week 5 – Submit your group members and topic. Preferably, have at least two topics you could pursue, since other groups may have chosen a topic too similar to pursue. Also, having more than one topic early in the term allows for the possibility that your first choice of a topic may quickly turn out not to be feasible for unforeseen reasons, so your group can quickly move to a next-best choice.

2. Week 6 – Submit the name of degree-holding guru who has agreed to work with your group (or two names of people you have contacted but have not yet replied) and the date your group has scheduled to meet with the guru (this could be an in-person meeting or a virtual meeting).

3. Week 7 – Submit preliminary topic outline and/or rough draft of presentation for feedback.

4. Presentations are on the class before final exams. A sign-up will be listed on the whiteboard – include your group topic and all group members (It is important to write all group members on the board to make sure each student earns credit.). It is to your advantage to sign-up early -- in the very unlikely event that we run out of time, groups will need to make arrangements with the Instructor on how to present their project outside of class time.

Presentation:

1. Format – You are welcome to use any presentation method: strict lecture; PowerPoint-based presentation; diorama; singing and dancing… Whatever best fits your topic and presentation style. However, some form of technology should be employed in your presentation for full credit.

2. What needs to be included – At a minimum, you will need to have the following:

   1. Explanation of the topic you are exploring using differential equations

   2. Explanation of how you mathematically represented the various components

   3. The roll your guru played in the development of your project

   4. Difficulties and/or successes in how you came to your method of developing your differential equation(s) including pros and cons of your method

   5. At least one specific example including all numerical values. More than one example is preferred.

   6. An intuitive assessment of the accuracy of the mathematical application (i.e. are you satisfied with the solution(s)? Is it what you expected? Why or why not?)

Please see rubric for additional details.

Extra Credit: A group-mate assessment will be given on the day of presentations. Please see below. If a score of 2 for all categories is received from all other group-mates and specific comments are left regarding that student, additional points will be added to that student’s score unless more than one student in that group receives 2’s for all categories. If a student receives 0’s or 1’s from more than one group-mate, that student will be contacted to discuss how to proceed. All comments will be read by the Instructor and may be shared with the student if the Instructor believes it beneficial to do so.

Sample Group Interaction Rubric: