First and foremost, the students should learn how messy real-world data can be. Working with data that is generated very rarely provides you with exactly what you need, so hopefully messing with the data allows them to develop a deeper sense of understanding. Also, students should be able to take the abstract concepts we learned in class and apply it to this problem via MATLAB. This is done by loading the data matrix into MATLAB, which will be a 15 x 15 sparse matrix. This will then need to be inverted to find the long run behavior of the process. Because these students might not (and are not expected to) have a MATLAB background, specifically doing more serious numerical linear algebra computations, the functions they need are provided (in the lecture notes), which they are allowed to use freely. Additionally, MATLAB's Econometrics Add-on allows for the visualization and characterization of Markov chains, which will compliment what was performed in class for easier examples. The skills students will need to use are data analysis and model development to see if the MARTA extension is feasible. The outcome of should the MARTA extension happen, "yes" or "no" is clear, but additionally students should be able to break down this complicated problem into smaller, tractable models and combine them to solve the overall problem. Lastly, their technical communication will be tested in two different ways; first, they will write a more technical document in their proposal prospectus, and they will need to make the same information more palatable to an unfamiliar and not technical Board of Trustees.

The following activity will be taking place in Math 190: First Year Seminar, which is available to any student who needs a quantitative reasoning seminar. The type of institution is a small research institution, with a strong focus on mentorship and teaching. The class is capped at 18 students, which will make the groups between 3-4 students.
This is a module project and should be based of material covered in the last third of the 15 week semester. That makes this a longer project, where they will have 4 weeks during the semester and until their final period to work on the project, report, and presentation. I don't think the project will take that much time, especially given all the information and code that is provided to them.
Throughout the class, the students will be learning MATLAB through the homeworks and other module projects. In fact, the lecture notes are provided in MATLAB live scripts, so the notes, examples, and code are in the same document. For this module project in particular, the code that they need to solve over half of the project is given to them; they just must input the data into MATLAB. This class assumes no knowledge of coding or MATLAB in general, so it should be very amenable to first year students with a broad background.
While there is an expectation of including game theory analysis (the first module) or linear programming (the second module) in the presentation and report, the way the current project is written doesn't rely on any prior exposure to those topics, just that the students are familiar to Markov chains.
This is currently assigned as the "final" project but is based on only the last module of the course. It would be very easy to modify this to a homework assignment, or a smaller project along the course. If a full course on stochastic processes is taught, this would most likely go near the beginning of the semester.

MATLAB is used in this activity through my teaching notes, which are provided by MATLAB live scripts. While many numerical softwares can be used to form the stochastic matrix and manipulate it to get the desired results, MATLAB was chosen for its ease of use, Econometrics Add-on- which aids in visualizing Markov Chains, and its fast, numerically stable matrix algorithms.

The documents uploaded are the Markov Chain lecture notes, they will have access to at this point, as well as the project pdf. It is also LaTeX'ed so the raw .tex file is also available to download to make editing and adopting easier for other educators.

math190p3.pdf (Acrobat (PDF) 120kB Oct28 25)
math190p3.tex ( 20kB Oct28 25)
Lecture Notes for Markov Chains (MATLAB Live Script 137kB Oct7 25)

This project hasn't been used in the classroom as of the creation of the teaching activity, so I don't have much guidance for educators. I would say students will get comfortable with MATLAB throughout the course by using MATLAB on-ramps and using MATLAB in previous assignments and projects. I would say the hardest part is probably getting the real world data into a form that is similar to the examples that we did in class.

Students will submit a technical prospectus (3-5 pages), which will show their detailed work on this assignment. This will show matrices and overall profit models. This will be 65% of their final grade, broken down to 50% content, 10% clarity, and 5% formatting. The other 25% will be based on their presentation -- 13% delivery, and 12% content-- which will be more general and pictorial in nature. There will also be 10% based in peer reviews to ensure that all students are pulling their weight and the work is being done equitably. A detailed rubric, which the professor will grade and the peer review rubric are both in the assignment pdf.

While some of the data in this project is fictitious, there are some real world data sets used, specifically real world on-time data and passenger transit data from MARTA, which is available upon request.