Mathematical Modeling

Frequently Asked Questions
What Are the Prerequisites?

You need to know some differential equations not because at any specific point I will tell you “take out a pencil and solve these differential equations,” but simply because you will read some papers that use them, and you will not be able to read the papers if you don’t have some training on the subject. Also, some computer programming experience is necessary. I don’t care what language(s) you know, but you will need to be able to program. We assume it as a core skill in this class the same way we’d assume some familiarity with calculus, linear algebra, and so forth. While I don’t want knowledge of programming to be a harsh gatekeeping mechanism, it is also true that you won’t be able to learn the substance of mathematical modeling and the substance of programming at the same time. I want to set you up for success to learn modeling, and that means I need to assume knowledge of programming.

Let’s recognize that not everyone will know the same computer languages. Because this course is highly collaborative, sometimes you might be teaching someone else a little bit of a language you know, and sometimes you might be learning a little bit of a language that someone else knows. This is reflective of what people who do mathematical modeling academically/professionally actually experience. BTW, the languages I most often program in (and hence, the languages I am best equipped to help you with) are R and Matlab.

What Even Is Mathematical Modeling?

Un-humbly, I think Mathematical Modeling is different from every other math course in the curriculum. Linear algebra covers techniques from linear algebra. Analysis covers techniques from analysis. Mathematical modeling is not a mathematical subfield or a specific batch of techniques at all. Rather, math modeling is the art and science of translating the real world into mathematics. As mathematical modelers, we call upon specific areas of mathematics if and when we need them. So there is no particular area of mathematics that we will cover in this course, and indeed, the real focus of the course is not actually on mathematics. It’s on using mathematics to study things in the real world. Also, even though “data science” is not really “mathematical modeling,” I am taking a slightly liberal view of mathematical modeling and including data science in it. Data science is too important for us to ignore it.

How will this course happen, logistically speaking?

The course is remote, that is, completely online. We will make use of the scheduled class time but there is no moment during the entire term when the entire class will meet together. I make this choice because for me, it is not possible to have meaningful interactions with 20 students online all at once. I will be dividing students into groups for the various course activities. You’ll meet with your groups during class time and I will spend part of the time with each group. You will of course need to spend substantial time meeting with your group outside of class time as well. For the final project, you will have some say in your group choice, but this also means that you are going to need to compromise on topic selection.

What Are We Actually Going To Do In This Course?

The course has three main components:

(1) Journal club. This provides you an opportunity to read case studies of mathematical modeling. Students will take turns facilitating journal club sessions.

(2) Mini-modeling. This provides you an opportunity to practice modeling skills in a scaffolded manner, with me leading you through the process.

(3) Research project. This is an open-ended group research project where you will construct and investigate a mathematical model of interest to you. Past students in this course have modeled amazing things, ranging from surf waves to the growth of urban road networks to opinion dynamics and much more.

How Will I Be Graded?

This course is ungraded. The way I implement ungrading is that every so often, I will have you write a rather detailed self-reflection about your goals and progress in the course. None of the assignments you complete “count” towards a final grade. I focus on giving you substantial written/verbal feedback that aids your learning. At the end of the course, I will ask you to think about your self-reflections and assessment of yourself and tell me what grade to assign you. Then I will assign you that grade. The one restriction is that I will not assign an A+ grade. Please realize that if you ever ask me for a letter of recommendation, it will be based on my own assessment of your work and not on the grade you assign yourself.

What Do I Need to Ask Myself?

As you decide whether you want to follow through with taking this course, please ask yourself the following questions.

(1) Am I ok taking a class where the professor doesn’t lecture at all? I don’t lecture at all in this course. It is a research seminar.

(2) Am I ok taking a class where there is no textbook? Modeling is not something most effectively learned from a textbook.

(3) Am I ok taking a class where none of the activities are problem sets? It is impossible to realistically model anything by means of a problem set.

(4) Am I ok taking a class where, even though it is about math, the idea of a “correct answer” is extremely fuzzy? There are lots of ways to model things.

(5) Am I ok taking a math class where, even though we DO a lot of math, in a way, the FOCUS is actually not on math? In math modeling, the application, not the math, is the driver. This means you are going to learn things about biology or physics or sociology or literature or whatever else you study using mathematical tools and frameworks.

(6) Am I ok taking a class where every single assignment involves collaboration? There is no individual work in this class, which is also reflective of how most mathematical modeling research takes place. If you are the type of person who envisions saying to yourself “I don’t understand why I can’t work on this course by myself” then this is absolutely, 100% not the course for you. You will not be happy.

(7) Am I ok taking a class where communication plays a significant role? You will do a lot of recorded oral presentations in this class, we will spend time honing our presentation skills to make you excellent presenters.

(8) Am I ok taking a class where, especially during the second part of the semester when the open-ended research project is happening, there are almost no due dates? This means you need a lot of self-discipline to carry out research and keep a project moving forward until it is presented at the end of the term. This also reflects the life of a researcher.

What if I am an Economist?

Historically, this course has caught the attention of economics majors because it seems like a great way to bring together mathematical and economic interests in applied settings. WARNING: if that’s what you are after, you are going to be disappointed. Why? Econ really has its own way of approaching modeling, and I have found that it is quite different from the way many applied mathematicians (including me) approach it. Both ways (and others!) are valuable. But they are, indeed, different. So if you are an economist, you are of course 100% welcome and encouraged to take my class, but I want to be honest with you that using the course as a mechanism to apply math modeling to economics isn’t going to work out.

What Is the Point, Chad?

Please think carefully about if this is a course that’s right for you. I design it in a purposeful way to comport with my reading of the research literature in learning science. Based on that reading, I believe you will learn more if you can motivate yourself to invest in the course without the extrinsic measure of grades, and if you tackle difficult, open ended work. However, if you believe you are the type of person who will only feel comfortable if I lecture to you, or will force yourself to invest time in the course only in order to avoid the threat of a low grade from a professor, this is not the course for you.