Students taking differential equations spend a lot of time learning how to solve them. The Student Challenge Using Differential Equations Modeling (SCUDEM) gives them an opportunity to see what happens when they have to decide how to use them.

SCUDEM is an undergraduate team challenge built around open-ended problems. Instead of starting with an equation and a set of instructions, students start with a situation they need to understand. From there, they have some decisions to make.

A Different Way to Use Differential Equations

SCUDEM problems usually fall into one of three areas: physics and engineering, chemistry and life sciences, or the social sciences. Teams choose a problem and develop a model using differential or difference equations.

Students who participate in the challenge have to decide what matters before they even begin modeling. They also have to figure out what they can simplify and what kind of model makes sense. Sometimes the first idea does not work once they really get into the problem. That is part of what makes SCUDEM different from a typical assignment, where students usually have a pretty good idea what method they are expected to use.

That's where the math starts to feel more useful, too. They are not just practicing differential equations for class. They are using them to make sense of a problem.

Students Can Use What They Are Learning Right Now

Students can participate in SCUDEM while they are still taking differential equations, so they can use what they are learning in class right away.

That makes it pretty easy to work SCUDEM into a course. Faculty do not have to create a whole separate semester-long project, and students still get the experience of working through a problem that is much more open-ended than a typical assignment.

We talked about this more in Why Two-Year Colleges Should Consider SCUDEM. Students just need enough math to get started and the patience to work through a problem that may not have an obvious answer.

Working Through the Problem Together

SCUDEM teams can include up to three students, and the team piece is important. Students are not only working through the mathematics. They are comparing ideas, questioning each other's assumptions, dividing up the work, and trying to get several pieces of a model to fit together.

There can be some back-and-forth. Someone may see a problem with the model that the others missed. A result may send the team back to an earlier assumption. They may have two reasonable approaches and need to decide which one to pursue.

SCUDEM teams prepare a 10-minute video presenting their work. That means students have to talk about more than the final result. And this presentation piece matters! Students are practicing mathematical communication at the same time they are working on the math, and faculty get to see how well they actually understand the model they built.

A Modeling-First Approach

SCUDEM began through the Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE), which integrated into COMAP in 2026.

SIMIODE has always focused on teaching differential equations through modeling and real applications. You can also see that approach in the textbook, Differential Equations: A Toolbox for Modeling the World.

SCUDEM is a simple way for faculty to bring more applied work into a differential equations course without creating a whole project. For students, it is a chance to take the math they are learning and actually use it.

Learn More About SCUDEM

SCUDEM is open to undergraduate or high school students, with teams of up to three students participating with a coach.

Challenge dates and registration information change each year, so visit the SCUDEM page for current details, resources, and information about getting a team involved.