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MTH 325 Application Projects: Overview and initial information

Purpose and overview

The Application Project for MTH 325 will give you a chance to apply what you have learned/are learning/will learn about relations, graphs, and trees to a real-world problem. In your application project, the fundamental goal is the following:

Solve a real-world problem or provide a real-world service that uses relations, graphs, and/or trees in a significant way.

This is a very broad criterion, and it's meant to allow a wide variety of interpretations, problems, and approaches. The idea is to combine your knowledge of the course material, your creativity, and your curiosity into bringing the course content to life.

You will be working in teams of 2--3 to work through and complete the project over the course of the last 2/3 of the semester. The project itself involves two "deliverables" that will be due from your team during the last week of class:

  • A poster presentation on your project, which will be done in a public space on campus on Wednesday, April 15 during your class' normal meeting time. (The location will be announced later, but it will be on the Allendale GVSU campus.)
  • An executive summary consisting of an overview of your project and its results along with citations of any references you used.

You will also submit two team updates during the development of your project, to ensure that your work is proceeding at a reasonable pace and that you are getting your questions answered.

The Application Project will be graded on a Pass/No Pass basis. Specifications for the project are below. Passing the Application Project is required only for those working toward an A or B grade in the class. If you are aiming for a C+ or lower, you do not have to participate in the Application Project. But conversely, the highest grade one can attain in the course without Passing the Application Project is a C+.

Timeline for the Application Project

  • Wednesday January 28: Startup discussion of the Application Project in class and handout of informational overview.
  • January 28---February 9: Form working groups by interacting with other students and viewing potential projects of interest on a Google Document.
  • Monday February 9: Commit to personnel on project teams. All students must be on a team at this point.
  • Monday February 23: Submit first team update report.
  • Monday March 16: Submit second team update report.
  • Friday, April 10: Decide on schedule for presentations at the poster presentation session.
  • Wednesday, April 15: Poster presentations; executive summary due.

Specifications for the Application Project

A Pass mark on your Application Project will be awarded if the following specifications are met:

  • An official team roster is submitted on or before Monday, February 9 at class time.
  • The first and second team update reports are submitted (via email or a Markdown document) by class time on February 23 and March 16 respectively.
  • The first and second team update reports show evidence of significant progress, are between 250 and 500 words in length, and follow the guidelines for general writing in the main MTH 325 Specifications for Student Work document.
  • A schedule for who will staff your team's poster is submitted by class time on April 10.
  • You are present for the poster presentation on April 15. (An individual can receive a No Pass mark for the project by being absent, while the rest of the team receives Pass.)
  • The team's poster presentation is of acceptable quality (see below).
  • The executive summary is submitted at the time of the poster presentation on April 15; see below for specifications.

The first team update report must do the following in addition to the specifications listed above:

  • The report must demonstrate significant initial progress on at least one but no more than three potential problems or services that the team would like to investigate.
  • The problems or services being considered must be specific and detailed. For example, "cryptography" is too broad. "Writing software to implement a digital signature system using tree structures" is sufficiently specific, although additional detail would be expected in the report.
  • The report must also list the personnel in the project team.
  • The report must list between 2--4 concrete next steps that need to be taken in order to push the project forward.

The second team update report must do the following in addition to the specifications listed above:

  • The report must demonstrate significant progress on exactly one of the potential topics given in the first update. In other words, the second report should demonstrate that the team has narrowed their approach down to one topic and has made significant progress toward solving the problem or providing the service. Teams may not work on a topic that was not included in the original list in the first report.
  • The report must list between 2--4 concrete next steps that need to be taken in order to push the project forward.

The poster presentation must meet the following specifications:

  • Details on the poster include important information about the project and increase the audience's understanding of the work.
  • The poster contains visual and graphical elements that are related to the topic and none that are superfluous; these communicate information in a clear and visually appealing way.
  • The information on the poster is organized with titles and subheadings, and the information is visible and in focus from 6 feet away.
  • The poster contains no grammatical, spelling, mathematical, or coding errors.
  • The presentation given by the person staffing the poster is brief and informative, including a description of the problem or service, the methods used, and the results of the team's work. The speaker speaks clearly and confidently and demonstrates mastery of the project.
  • The presenter listens carefully to audience questions and makes a reasonable attempt to answer each one with a clear and concise response. No "BS" answers are given for questions that the presenter is unsure about.
  • The problem or service that the project addresses is interesting, significant, and more difficult than just a homework probem. The team has done a thorough job of investigating and solving the problem.

The executive summary must meet the following specifications:

  • The executive summary is to be at least two pages, but no longer than four pages in length using 11 or 12 point font, single spaced, using and ordinary margin sizes.
  • The executive summary must also include a reference page listing all references used in the project, formatted according to a professional style (you choose the style). This does not count toward the page count in the executive summary.
  • The executive summary must adhere to the writing standards in the MTH 325 Specifications for Student Work document for general writing.
  • The executive summary is to give an overview of the problem or service of the project, the methods used, and the results obtained.


  • How do I find a good problem/service for my project? -- Anything that is of interest to you personally is a good place to start. Look to problems you may have encountered in your personal experiences, other classes, from the textbook, from your jobs. You can also do some reading in popular math and computing articles and blog posts, news items, and books. Also, talk with your classmates to see what they are thinking about; perhaps a friend has a great idea, and you can work with her/him.
  • I have an idea but I am not sure if it's good. How do I tell if my project idea is good or lame? -- A good project is rooted in real life and the real world; has broad appeal not only to programmers and mathematicians but also to regular people; is focused narrowly enough to be completable within the semester; and has an "interesting" factor that makes people want to think about it.
  • Does my project topic have to be original research? -- No. This is not a "research" project; you are solving a problem or providing a service using relations, graphs, or trees. The problem can be simply a real-world problem that's been solved before, but in which you are using a unique set of real-world data for instance. The goal is not publishable research but rather a solved problem or a provided service.
  • I found a neat homework problem or example in the book that looked like a real-world application. Can that be my project? -- Probably not. The specifications state that the project must be interesting, significant, and more difficult than just a homework probem. You can possibly take something you see in your textbook and extend it, or apply it to a new real-world situation; but doing simple example- or homework-like problems is not sufficient.
  • Do I have to do any programming for the application project? -- No, but writing software to solve a problem or provide a service has been quite commonly done in past MTH 325 projects. Coding is optional.
  • We haven't covered graphs or trees yet, but I read about a problem that uses them, and I think I'd like to use for my project. What should I do? -- You can simply read ahead to get an idea of what graphs and trees are; or search on Google/YouTube for an overview; or come by the office for a consultation. If you think you'd like to do something with graphs or trees but you don't know what these are, then take the initiative to learn "just enough to be dangerous" and dive in. (This is a great way to prepare yourself for Chapters 9 and 10.)
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