By Pamela E. Harris and Alex Moon

I am always impressed by students who take the initiative to lead in their own learning. As I thought about this recently, Alex Moon, a second year graduate student at UW-Milwaukee, came to mind providing an example of how students can lead in this way. The lack of a course in enumerative combinatorics this past year was not a deterrent to learning more on the subject, and Alex found a way to create an educational opportunity to learn and explore some new mathematics with their peers. They organized a weeklong event at UW-Milwaukee, titled Students United for Faster Enumerative Reasoning (SUFFERfest), which brought together incoming and returning graduate students for collaborative reading and problem solving, with the ultimate goal of learning for the sake of learning! In this interview, Alex shares more about what motivated them and how the event took shape. They also give some advice for students who might be interested in starting their own workshops.

Pamela E. Harris (PEH): What inspired you to organize the Combinatorics SUFFERfest, and why did you choose the focus on enumerative combinatorics?

Alex Moon (AM): I’m passionate about enumerative combinatorics in all of its forms, and while I had learned a lot about it through undergraduate classes and by reading papers, I felt there were still serious gaps in my knowledge. My basic reasoning was that at some point, you need to sit down and read the textbook. Reading papers is a great way to learn about the highly specific information needed for research, but textbooks are written on purpose to give the reader the background they need to fully understand the material they’re curious about.

PEH: What specific gaps in combinatorial reasoning skills were you hoping to address with this event?

AM: The biggest gap I wanted to address was my knowledge of symmetric function theory. Symmetric functions show up all over the field of combinatorics, so understanding the elementary concepts like the five standard bases and the transformations between them is important for my future research ambitions. More than that, I know that symmetric function theory can get very technical very quickly - being able to understand them deeply will make understanding future combinatorics concepts that much easier.

PEH: Why did you select Stanley’s “Enumerative Combinatorics” as the primary text for this event?

AM: Stanley’s “Enumerative Combinatorics” Volumes 1 and 2 (EC1 and EC2, respectively) are widely regarded as the canonical texts for graduate students wishing to learn about enumerative combinatorics. While other textbooks covering symmetric function theory do exist, Stanley’s text is a great place to start due to its delicate balance between brevity and exposition.

PEH: How did you identify the target audience (graduate students and advanced undergraduates) for this event?

AM: Simply put, I wanted an audience of peers. I’m currently a second year graduate student, so I wanted to work with people who had similar backgrounds and abilities as me. More specifically, I wanted people who had a decent background in algebra and combinatorics but who weren’t such experts that anyone would feel left behind. I think the group that participated met those parameters quite nicely, and the event was a success.

PEH: What outcomes were you hoping to achieve for the participants by the end of the festival?

AM: I was hoping for two things: First, I wanted everyone to understand and have an intuition for the elementary attributes of symmetric functions. This includes their definition, the five different bases, intuitive reasons why the different bases are each important, and how to dance between the different bases in order to solve problems. Second, I wanted it to be a workout. The school year starts only 3 weeks after the end of the SUFFERfest, so hopefully by working really hard on some really difficult exercises before the start of the year, we would make it so the exercises we do for our classes seem easy in comparison.

PEH: How was the participation level during the Combinatorics SUFFERfest? Did the event meet your expectations in terms of attendance and engagement?

AM: The participation and attendance was great. Everyone who showed up on Monday was there throughout the week. We did a popcorn reading model where we would take turns reading the sections out loud and pausing whenever anyone had questions. This way, everyone was reading out loud and participating, and no one felt left behind. 

PEH: What challenges did you encounter in organizing and running the event, and how did you address them?

AM: The biggest challenge was exhaustion. The event ran Monday-Friday from 10-4 with a break for lunch at noon, so often by 2 PM our brains were starting to fog up. To fix this, we added an additional coffee break from 2:30-3. After implementing this change we found that we were much more productive in the final hour of the day than we were before.

PEH: How did the participants respond to the reading-and-discussion format? Were there any unexpected benefits or drawbacks?

AM: The participants were very engaged and they responded well to the format. The most unexpected benefit was to the people who were understanding the material faster on average than the rest of the group - by explaining the material to their classmates they not only stayed engaged despite being ahead of the group, but they felt that their understanding was improved by the discussion.

PEH: Did the group successfully complete the exercises, and did you notice an improvement in participants' combinatorial reasoning skills over the course of the festival?

AM: Initially we struggled with the exercises, since many of the standard exercises in EC1 and EC2 hope that the reader has read the entire section before attempting them. Later in the week, we found the supplementary exercises, which we felt were more appropriate for the reader who was still progressing through the section. Doing so much focused reading and so many exercises had measurable payoffs throughout the week. Our daily page rate was four times higher on Friday than on Monday, going through more difficult content as well!

PEH: What feedback did you receive from participants, and how might this influence future iterations of the event?

AM: The biggest piece of feedback was that they wished they’d had more time to work, since we didn’t quite finish the section that we had hoped to finish by the end of the week. It’s unrealistic to extend the event to two full weeks, but I hope to run a reading group in the fall to finish the section. I also hope to organize a similar event in the future that focuses on a different section, as I personally felt great benefit from both organizing and participating in the event.

PEH: What advice would you give to students who want to organize their own workshop?

AM: The biggest advice that I’d have is to trust your participants. They only signed up because they want to be there, and they know that you’re working hard to make sure everyone has the best possible experience. They’re willing to forgive you when you make mistakes. The second thing that I’d say is to ask for help. It is a lot of work to get funding and make sure that everyone is in the same place at the same time with the resources that they need to succeed, and everyone knows that! Your mentors are more than willing to help you figure out what you need to do and when to make sure that the workshop runs smoothly.

PEH: Anything else you wish to share that I might not have asked about?

AM: I’m very thankful to Katie Wehrheim and you, Pamela E. Harris, for help in organizing the workshop. It wouldn’t have happened without this support. Also, I’m very thankful to all of the participants who made the workshop a success. I’m excited for similar events in the future.

Dr. Pamela E. Harris is a Mexican-American mathematician and serves as Professor of Mathematics at the University of Wisconsin-Milwaukee. She was a 2023 recipient of the MAA Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics. For fun she lifts weights and enjoys watching bad reality tv shows.

Alex Moon is a second year graduate student studying mathematics at the University of Wisconsin - Milwaukee. When not studying, teaching, or otherwise doing math they enjoy playing the piano, running, and playing board games.