Mathematical Models, Spring 2016
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Mathematical Modeling is a unique upper-level math class since its goal is to give you the tools necessary to use mathematics outside of school. The language of mathematical modeling is the language that real-world companies and business managers understand. If you are trying to convince your boss that she or he should follow a course of action that you suggest, you will need to justify yourself; basing your reasoning on a mathematically-sound model can provide the basis for a proof that your method is justified. This project is designed to give you practice in applying modeling techniques.

You will be using the real world data published on NYC Open Data to investigate a real-world situation of your choice. What part of city life is interesting to you? Nature? People? Schools? Transportation? ... the list is endless ... (ok fine, it's finite, but you get the idea.) Once you've settled on a general area of study, explore the available data sets and come up with a real-world question or situation that the data might be able to help answer or shed some light on. From this, determine a project statement that you will be researching in depth and using the data to analyze.


You will work in a group of at least two and at most three people. It is important that you choose a group of people with whom you can work well. You will have to meet outside class with your groupmates throughout the semester. Together you will come up with a project topic (vetted by Prof. Chris), determine the mathematical model you wish to study, do the work, write up a paper, and present your results to the class. If you are having trouble finding groupmates by mid-February, discuss this with Prof. Chris.


In order to help your time management, I have broken up the project into pieces. Disregarding this timeline will negatively impact your project grade.

Just as with the other homework assignments, if you are running into trouble or you would like my input on your project, I suggest coming to see me earlier rather than later.

  • Project Statement due Wednesday, March 2: By 11:59pm on Tuesday, March 1, email Prof. Chris a written explanation of the project that you and your group will attempt. In class on Wednesday, March 2, we will meet to discuss your proposal. If you feel like your group is unable to settle on an idea, set up a meeting with Prof. Chris on Monday 2/29 or Tuesday 3/1.
  • Organizational Statement due Monday, March 21: Before class, email Prof. Chris a page-long description of your plan of attack for the project statement. This will include the following:
    • A title for your project, a list of your group members, and a revised project statement.
    • The scope of your project---what exactly will you be analyzing? Briefly mention the simplifying assumptions that you are making.
    • You must also submit an extended bibliography that includes at least two sources that have been published in print form, such as books or journals. The copy of the source you consult may be on the internet, but they must have appeared in print form at some point. An extended bibliography includes not only the author, title, and publishing information, but also a two-to-three sentence explanation of the content of the source. I expect this bibliography to include a vast majority of the works you will use to write your paper.
    If you are having trouble getting started or would like guidance, meet with me the week before.
  • Final Draft due Monday, April 11: I expect your project to be in a finished state. You should have completed all calculations and written up the entire report following the guidelines below. Prof. Chris will skim this draft, assign a provisional grade, and we will meet in class on Monday, April 18 to discuss how to improve your article.
  • Peer Review Day, Wednesday, May 4: Bring in three printed copies of your draft to class in order to discuss it in depth with your classmates. They will give feedback which will enable you to revise it one final time.
  • Final Written Project due Monday, May 15: You shall hand in a final paper version in class and submit an electronic copy via Blackboard on this date.


Content: Your report will be 14–17 pages long. I expect your report to include the following sections. Your report may include additional sections.

  • Abstract. A brief summary of the main content of your paper. 100 words at most!
  • Introduction. This should provide the reader with the necessary background information about why your project is an interesting and worthwhile project, and where the project fits into real life. Give a clear project statement.
  • Mathematical Model / Assumptions / Methodology. Explain in depth the model you are using to solve the problem. Explicitly state any assumptions that you are making in your research. Discuss how you collected data and worked to make your model as representative of real life as possible.
These next three sections will constitute over half of the paper:
  • Results / Analysis of the Model. You will use the mathematics we have learned in class to discuss what the math says and what conclusions you can draw in terms of the real-life problem.
  • Discussion. Every model makes simplifying assumptions. You need to elaborate on yours and explain what is good and what is bad about your model. Is your model precise, accurate, etc? What future research should be undertaken?
  • Conclusion. Explain briefly the take-away message of your project, especially the real-life consequences. (One to three paragraphs)
  • Bibliography. Cite the sources you use!
(See here for a more detailed description)


This project represents 35% of your grade this semester—25% for the written report and 10% for the presentation, described below. Your written report will be graded on content and structure. Yes, even in a math class, you must use proper grammar and spelling and follow conventions for good paper writing. Your paper must include a proper bibliography. I recommend that you visit the QC Writing Center to go over drafts before peer review day.

(Here is a draft of the grading rubric.)


You will need to organize a presentation highlighting your work over the semester. You will have twelve to fifteen minutes for your presentation and you should make full use of your time. In order to do so, you will need to practice giving your presentation out loud at least twice before your presentation day. You will need to summarize the content and results from your paper in a way that conveys the information well to your classmates.

This presentation will count for 10% of your grade this semester. You will be graded on clarity, organization, and how well your fellow students understand your presentation. Presentations will occur on the last two days of class and during the scheduled final exam time.

Attendance is mandatory as you will be grading your fellow classmates. You must be present each presentation day; if not, you will lose points on your own presentation.

Getting help:

Long before the peer review day, it would be good to schedule an appointment with the Queens College Writing Center with whom you can go over your writing so far. They can take a critical eye to your writing to make sure that your paper is well written and that your message is conveyed clearly. If you have questions about the mathematics in your paper, you should schedule an appointment with Professor Chris.


I ask you to submit your final draft through the SafeAssign feature of Blackboard. SafeAssign compares your paper against content from the internet and multiple large databases of past term papers. This helps detect if sources were copied directly into your project. If you have concerns about how to correctly use sources in a term paper, feel free to come and talk with me directly. Upon submission to SafeAssign, you will have the option to include your paper in Blackboard's Global Reference Database, which will allow Blackboard to keep a copy of your paper in a database for future comparison. You are not obligated to submit your paper to this database if you are worried about copyright or other issues.