CMSE/MTH 314: Honors Option Project Guidelines#

Overview#

In order to satisfy the honors option in this course, you must obtain a 3.0 grade in the course and earn an 80% or higher on an honors project. This honors project will consist of a deeper dive into the material we’ve been working on in the course. You will create a Jupyter notebook, slides, and a presentation to answer a research question of your choosing.

Your project can expand on anything we’ve touched on in the course. If you find yourself interested in the mathematical underpinnings of linear algebra, you can look into proving some of the more important theorems used in the course. If you are more interested in applications, you can demonstrate the use of linear algebra in a real-life setting that you find interesting.

Some examples of project types and research questions include:

  • Look into infinite dimensional vector spaces. This could involve showing that \(L^2\) is a Hilbert space, discussing examples of an orthonormal basis, etc.

  • Build up the machinery behind the proof that every matrix has a unique (up to some conditions…) singular value decomposition.

  • Find an interesting dataset to perform some data analysis on using linear algebra. This could involve things like data scaling, dimensionality reduction, regression, etc.

  • Numerically solve a differential equation using the finite difference method.

  • Demonstrate and/or implement an iterative linear solver that is commonly used in practice.

  • Or many other things!

A successful project will include all of the following components:

  • A question that you will attempt to answer or a problem you will try to solve.

  • Computational or mathematical methods that seek to answer your question. (This will vary from project to project, depending on the context).

  • An explanation of the mathematics (related to the concepts in the course) that you use to answer your question.

  • Meaningful visualizations that productively convey your results.

  • An answer to the question or an explanation as to why you were unable to answer the question.

VERY IMPORTANT NOTE: When you’re finding resources or datasets online you should make sure to record exactly where you found them and cite them in your final project notebook. Additionally, if you use any code that you find online to complete part of your project you must give credit to the original source code and cite this in your project as well. Any code you use that is found online and not properly cited will be considered plagiarism and violates the academic integrity expected of you in this course.

Timeline#

  • By January 30th, 11:59PM: Notify your section’s instructor via email that you will be doing an honors project.

  • Before February 17th: Do some preliminary research to find a project you’re interested in. If you need any help, feel free to bring rough ideas to your instructor to help brainstorm.

  • By February 17th, 11:59PM: Submit a short project proposal to your instructor via email (no more than 1 page double-spaced) for your project which includes:

    • Your main research question

    • An outline for answering your question

    • An explanation of how your project will use or expand on some part of linear algebra that we have discussed in the course

    • A description of any datasets you will use in your project

    • At least 2 citations to help you do continue your research

  • By February 24th: Your instructor will respond to your proposal either approving your idea or asking for further information (which may take the form of answering short questions, having a meeting to make sure your project will meet the requirements, etc).

  • After receiving project approval, but before Wednesday March 1st: Go to the Registrar’s website and complete the Honors Option Agreement Form located under “Student-Instructor Forms” (reg.msu.edu -> Student Resources -> Forms -> Student-Instructor Forms)

  • By April 30th, 11:59PM: Turn in your finished Jupyter notebook, slides, and presentation to your instructor via email.

Detailed Requirements#

For your honors project, you’ll be expected to turn in a Jupyter notebook, an 8-10 minute recorded presentation, and slides used in the presentation.

Jupyter Notebook#

Your Jupyter notebook should contain the following:

  • All of the code used to complete your project. The code should be documented so that the instructor can understand what you did and why you did it. This means including meaningful comments in the code itself! You should also use logical variable names to ease the reading of the code.

  • Narrative text (using Markdown cells) that explains what you did, why you did it, and how you went about it. You should break the notebook up into meaningful sections so that the instructor can follow the logical flow of your work. For example, your project should discuss all of the following (though perhaps in a different order or composition):

    • Background and Motivation: Provide some context for the problem and what question(s) you set out to answer.

    • Methodology: How did you go about answering your question(s)? Most of your code or mathematics will be contained in this section.

    • Results (optional, for a more data science focused project): What did you find when you carried out your methods? Some of your code related to presenting results/figures/data may be replicated from the methods section or may only be present in this section. All of the plots that you plan on using for your presentation should be present in this section.

    • Mathematical Analysis: What concepts from linear algebra did you use to solve your problem? If your project is focused on an application, this section should include an in-depth explanation of the mathematics behind the analysis you did to show that you understand the linear algebra concepts being used.

    • Synthesis and Discussion: What did you learn? What obstacles did you run into? What is the answer to your question(s) and why?

The code, text, and visuals should be threaded together as coherent report of your work!

In addition to the notebook, you will be recording an 8-10 minute presentation using a short set of slides to share the results of your project with your instructors. Your recording should include appropriate visual aids. The presentation included in your recording should address:

  • The question(s) you set out to answer.

  • The background necessary to motivate your question and understand your workflow.

  • The computational or mathematical techniques that you used to answer your question.

  • The answer(s) you arrived at.

Presentation slides#

You can create your slides using the presentation software of your choosing (e.g. Google Slides, Powerpoint, Keynote). Once you’ve finished your slides, you should save a PDF copy that you can submit with your Jupyter notebook. You should aim for having a reasonable number of slides – a good guideline is ~1 min of time per slide. For a presentation of this length, you probably wouldn’t want to have more than 12-14 slides, but you should make sure that you have a sufficient number of slides to support your presentation.

The slides should:

  • Address the above points in a logical order.

  • Include a title slide with your project title, name, and course number (with section number).

  • Effectively communicate information through a combination of text and figures. Text and figures should be clearly legible in your recorded presentation.

  • Only include text and figures that support the presentation (avoid including content “just because”).

  • Avoid large paragraphs of text, use bullet points instead.

If you would like to try to make presentation slides using your Jupyter Notebook visit this site https://rise.readthedocs.io/en/stable/. Note that this is not a requirement, but a nice feature that some instructors have found useful and interesting.

Recording#

Once you’re finished your presentation slides, you should use Zoom to record your presentation. You should be able to “Share Screen” in Zoom to share your slides and talk through the presentation as if you were giving it live. You should make sure that your recording is no longer than 10 minutes, but it should be at least 8 minutes. You will turn in the .mp4 file that Zoom produces when your record the Zoom session.

Grading Rubric#

The presentation/project will be graded as follows (total: 100 points):

  • First project checkpoint (10 points). Is the research question clear? Are relevant datasets or resources provided? Is the scope of the project reasonable?

  • Oral presentation (25 points). Is it clear and well-structured? Does the student effectively communicate the key ideas about their results?

    • Excellent presentation: student speaks clearly and in a logical manner, and makes their key points clear. (25 points)

    • Good presentation: student speaks clearly and logically and conveys key points, but presentation is somewhat lacking (20 points)

    • Fair presentation: student’s oral presentation is substantially lacking (speaking too quietly to be heard or with little inflection, clarity/logical flow in speaking is sub-par, etc.) (10 points)

    • Poor presentation: student’s oral presentation is completely lacking (cannot be heard, there is no logical progression to the presentation) (5 points)

  • Presentation slides (25 points). Do the slides complement their oral presentation, and conform to the guidelines?

    • Excellent slides: Slides conform to specifications in final presentation document, including number of slides, adequately addressing all points, legibility. Slides complement oral presentation. (25 points)

    • Good slides: Slides deviate from specifications in some minor way: too many or too few slides, not all points addressed, some slides hard to understand (poor graphics, too much or too little text, etc.) (20 points)

    • Fair slides: Slides deviate from specifications in some substantial way: too many or too few slides, half or fewer of points addressed, most slides hard to understand (poor graphics, too much or too little text, etc.) (10 points)

    • Poor slides: Slides do not conform to specifications in any meaningful way. (5 points)

  • Final project content (40 points). This is a combination of the content in the student’s presentation and in their Jupyter notebook. Does the student clearly and concisely address all off the points listed in the final project guidelines?

    • Excellent content: All points clearly and concisely addressed. (40 points)

    • Good content: Most of the points clearly and concisely addressed, or all points nominally addressed but some are unclear. (30 points)

    • Fair content: Roughly half of the points clearly and concisely addressed, or all points nominally addressed but half are unclear.(20 points)

    • Poor content: Few of the points clearly and concisely addressed, or most/all points nominally answered but most are unclear. (10 points)

To successfully complete the honors option for this course, you must receive an honors option project grade of 80% or higher and must achieve an overall grade of 3.0 or higher in the course.