Project Information
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Project Information
Part of the final grade evaluation for this course involves a group project in mathematical modeling. Groups should be formed of two or three students. The project cannot be something any fellow student (in any course at WLU or elsewhere) or group member has submitted for another course at WLU or elsewhere, including MA489.
The project should be an extension of an existing model as described by a published research paper in a journal (e.g., that can be found in the WLU library library.wlu.ca) or possibly an extension of a model from the textbook and its sources, simulating the model using Maple, Matlab (or a clone like Octave or Scilab), or other software or programming language, and reproducing results from the original source. In addition, the project should formulate a question that is not fully addressed in the original source and modify the model to study it or extend the analysis of the behavior of the model beyond that of the original source. Other options are possible upon consultation with the instructor.
Project components
The project counts for 30% of the final grade and involves a few components:
1. proposal (2%) due Monday Feb . 6
2. oral presentation (13%) Monday Apr. 3, Wednesday Apr. 5
3. written report (15%) due Monday Apr. 10
1 Project Proposal
By Monday Feb. 6, each group should submit a written (typed) proposal containing the following information:
1. the names of the students in the group
2. a clear explanation of the phenomenon to be modelled
3. ideas on the methods the group plans to use to analyze the model
4. an initial/introductory list of at least two references on which the model is based (throughout the project, the group may come across and need to use other references).
Feedback will be provided on the proposals as soon as possible, so that each group can move forward with the project. It may be that the feedback indicates that a modification of the project is needed.
2 Oral Presentation
An important aspect of this project is for each group to explain to the class and professor the phenomenon being modeled and its interpretation. This skill is invaluable in life and in the workplace.
Each member of the group should present for at least three minutes. Be sure to rehearse together, so that transitions in the presentation are as smooth as possible. Practice the presentation multiple times to ensure the time limit can be met.
2.1 Oral presentation schedule
Depending on the number and size of the groups, the oral presentation schedule may vary from the following plan and will be updated if needed.
The presentations are scheduled to occur on campus in the following lectures: Monday Apr. 3, Wednesday Apr. 5. |
2.2 Oral presentation time limits
The presentation time length may vary based on the group size:
❼ two-person group: 8– 10 minute presentation
❼ three-person group: 12– 15 minute presentation
and will be followed by a maximum 5-minute span for questions.
Part of the oral presentation weight is for attendance and participation: all students are required to attend all of the group oral presentations and take a sincere role in engaging in the question period for their classmates’ presentations. Naturally, collegial participation is encouraged, and only respectful and constructive inquiries will be welcomed. You may be offering anonymous feedback/grading information on group presentations.
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2.3 Oral presentation grading
Your presentation will be graded on content and form.
❼ Content: aim for clarity and conciseness, and a logical order that is informative and
appropriate for the audience.
❼ Form: speakers should make eye contact with the audience and speak clearly, and at
a reasonable pace and volume; ideally, a speaker is enthusiastic and interested in the topic and is able to get and keep the attention of the audience.
2.4 Oral presentation tips
❼ Keep in mind that your audience is assumed to have no prior knowledge of your topic
beyond introductory linear algebra, multivariable calculus, and introductory differential equations. What take-away message would you like the audience to have? You may need to provide some background of the topic first, before delving into the specific model and its analysis.
❼ For “slides” (e.g., PowerPoint or Beamer via LATEX), do not put too much
information on each slide. Each slide should focus on one idea. Slides should be legible by people at the back of the room.
❼ Do not plan on reading slides verbatim (“word for word”), slide upon slide. Keep in
mind what made you interested in the project. It might interest your audience, too!
❼ Try to find the comfortable zone between “too simplistic” and “too technical” .
❼ Aim for being clear and concise with the content. Present the topic in a logical way.
3 Written Report
Another invaluable workplace and life skill is the ability to express ideas in a clear and logical manner for a given target audience.
The final written report will be due Monday Apr. 10. |
One co-authored report per group should be submitted in hardcopy and emailed to the instructor as a PDF. The report should be approximately 8– 10 pages of 1.5 or
double-spaced text, to a maximum of about 15 pages, including supporting figures, data, and perhaps computer programs, but not including the cover page, table of contents (not required), or appendices (not necessarily required). Your written work will be graded on content and structure, including grammar and spelling. Use a font size of 11-12 and 1” margins.
3.1 Report components
The written report should be typed (using, e.g., LATEX, TEX, or a word processor) and have the following components:
❼ cover page: title, group member names, date, abstract
❼ title: provide a concise statement which encapsulates the project and its model
❼ abstract: a short (approximately 100-word) summary of the project giving the
reader an idea of the model being analyzed and why it is important to examine it, the methods used, and the overall findings; write it last
❼ problem description: describe what problem you are analyzing, why it’s important
to consider the model, and what questions your work aims to answer
❼ mathematical model: explain the model and what it represents; what kind of
equations are involved (e.g., difference equations, ODEs, PDEs, etc.); define all variables and explain any notation/symbols used
❼ solution of the model: explain what mathematical techniques are needed in the
analysis of your model (e.g., numerical methods, stability criteria, ODE or PDE techniques), whether they were discussed in this course or not
❼ computational work: in this section you can reproduce results from a key reference
you cite (i.e., generate graphs from the reference yourself using software), giving full details of the implementation (i.e., how you generated the results via software, not cutting and pasting the source’s graphs), giving corresponding interpretations; subsequently, your work would extend the given model or compare it to another data set from another source (the idea here is to ensure you are not just reproducing the work from a given paper or textbook reference). The output of software/programs should be included if they help back up the conclusions (see below), and not as a replacement for making conclusions/interpretations. If you write any computer programs, they should be attached in an appendix at the end of the report. Instead, you may want to cite Maple, Matlab, or other software’s built-in commands you use. Any large tables of data could be put in an appendix but small ones could be included within the main text.
❼ analysis and discussion of results: here you will discuss the interpretation of the
model and how it relates to the phenomenon it is meant to describe; what results do you obtain? What interpretations can you make from the computational output? Does the model fail in some way? Where/how is it successful?
❼ conclusions: summarize the achievements of the project in terms of its model
analysis; are there limitations of the model? How can the model or mathematical analysis of it be improved? Are there other models that may be more applicable/useful/accurate? If so, why?
❼ references: include a list of sources that you have used: books, journals, articles,
web pages, etc. If you refer to a reference, include a citation. Cite any reference that helps you learn an algorithm (computational technique), that provides data or historical or other information on the model that you reference. Information taken verbatim from a source needs to be quoted (using quotation marks) and properly acknowledged. Even if you paraphrase a source (i.e., reword an idea), you should cite
the source. In terms of citing references throughout your report, follow the method/approach in the key paper you are referencing.
3.2 WLU’s Writing Support Services
The campus has a Writing Center at your disposal: see https://wlu.ca/writing or https://students.wlu.ca/writing. The facility is located in the Teaching and Learning Commons, 2nd floor Peters Building. Look for the Writing and Learning Lab, room P226. They offer various services to help with the conventions of academic writing. And they can help with citations and referencing, paper organization and structure, sentence construction, and paragraph development.
2023-02-01