What you need to know:

• Pamela E. Harris (‘08, MS; ‘12, PhD Mathematical

Sciences) joined the UWM math faculty in the fall.

• She is passionate about supporting underserved and

minority students in mathematics.

• Her latest research highlights “games on graphs” that

teach computer science and statistical concepts.

Pamela E. Harris has finally come home.

Harris attended UWM for graduate school, earning her PhD in mathematics in 2012. After a decade of teaching math at West Point and then at Williams College, she returned to Milwaukee and joined the UWM faculty this fall. Harris has made a name for herself in the mathematical world, both for her research and teaching and her commitment to making math accessible to everyone, especially underserved students and racial minorities. That is a mission close to her heart, because Harris is a Dreamer – she and her family moved from

Mexico as undocumented immigrants when she was 12 years old.

Harris sat down to talk about her work, her principles, and her latest research

– a book chapter that describes “games on graphs” that teach students the

beginnings of mathematical research and some connections to computer

science and data analysis.

**What is it about math that drew you?**

I tell the story that I became an accidental mathematician. When I went to

Milwaukee Area Technical College for my undergraduate work, I started in

intermediate algebra and I worked my way up. Every end of term, one of the

teachers would say, you should take the next math class. And I just did.

I think I followed what people thought I should do, because I didn’t know what

to do. My parents didn’t graduate high school. We weren’t having conversations

about, how do you become a mathematician? The goal was to finish high school.

**You like math, though, right? **

Oh, I do! I love math. But I wasn’t envisioning that one could be a mathematician. I didn’t understand that that was a possibility for a job. But I knew that I wanted to be a teacher. From an early age, that was something that I was passionate about.

**You lived your childhood as the daughter of undocumented immigrants and you yourself were undocumented. How did that impact you growing up?**

You don’t talk about it. You have this horrible amount of shame over something you can’t control, and you can’t ask for help because you don’t know who is safe to talk to about this, or who might decide to call immigration on you and get your whole family deported. It was very isolating, especially during high school. Everybody starts asking, “What college did you apply to? Where did you get in? What scholarship did you get?” And I was silent. I couldn’t apply anywhere. I didn’t know where I was going to go or what I was going to do.

It’s still terrifying. There are still parts of family who are progressing through

the immigration system, and it’s still hard to talk about it because they’re still in danger.

**How does it work, trying to apply for college and being undocumented?**

It doesn’t. DACA (Deferred Action for Childhood Arrivals) didn’t exist when I was still in high school. There was no way to apply for college with the exception of applying as an international student. But I had an ITIN, an Individual Taxpayer Identification Number, that also has nine digits. When I went to MATC and applied there, I put my ITIN number (in place of a social security number). I thought, well, that’s an identification number for me from the IRS.

At that time, there wasn’t the robust check that exists nowadays, and I got in. But at the point that I became a green card holder, I had to go to the registrar and ask them to merge my records. I remember the registrar at the time said, “I’ll have to talk to the lawyers. People don’t have two social security numbers. You might have committed identity theft. We don’t know who you are.”

I thought, this could not be how I get my entire family deported, and all because I wanted to transfer to Marquette University and needed to get my records to match with my social security number. A week later, I got a letter in the mail saying, “We merged your records.” I’m very lucky. I was president of the student government, I had started an LGBTQ+ organization at MATC, and I was known on campus for all the work that I was doing. I don’t know how much of my visibility on campus played a role in my family not getting deported.

**You graduated with your PhD in mathematics from UWM in 2012, spent 10 years at West Point and at Williams College, and then you ended up back here at your alma mater. What’s it like to come home?**

It is amazing. My face hurts from smiling every time I drive here. I’m happy to be somewhere where, finally, the mission of the institution aligns with my values in a way that, for a long time, it hadn’t. To see students who are working so hard to improve the quality of their life and that of generations of their family – it feels so good to be here.

**You are a huge advocate for ****mathematical accessibility and ****you even have a podcast. What do ****you do to put math in reach for e****veryone?**

One of the things that I cofounded a few years ago was an organization for Latinx and Hispanic American students in math, Lathisms. The goal was to bring visibility to the contributions of Latinxs in mathematics. I think part of that was motivated by the fact that, for a long time, I didn’t see people who had my same heritage and history and background. I and my cofounders wanted to dispel this myth that Latinx folks don’t do math. We finally have a scholarship, and we had a book out with stories of Latinxs and Hispanics in math.

I also work to make mathematics accessible because it is something that I value. I think I have honed in on being able to explain a problem very simply. I love the field of combinatorics, because all I do is count. Being able to bring students very early on into those problems has been so fruitful. They have ended up publishing research math articles on all of these topics. For me, that fits with who I am and the access mission of UWM.

**In December, you had a book ****chapter published on “Games ****on Graphs: Cop and Robber, ****Hungry Spiders, and Broadcast ****Domination.” What are some of **

**these games?**

Imagine you have a graph, which is just a set of dots and some lines connecting the dots. The dots are called vertices and the lines are called edges. Now I give you some pebbles and say, you can put a pebble on a vertex. Once the pebble is on a vertex, we call that vertex “covered,” but we’re also going to say that anything connected to that vertex is also covered. What is the smallest number of pebbles that you can put on the vertices of the graph so that the entire graph is covered?

Say you have four vertices and they’re connected as a square. If you put one pebble on any of the vertices, it covers itself and the two adjacent, but you’ll be missing that last vertex. So, you need two pebbles to cover the graph.

But what if the graph is much more complicated and bigger? These problems are bread-and-butter to graph theory. These are called “domination problems.” There are a lot of generalizations of this problem for which the answer is not known. Proving that you have the smallest number of pebbles that you need is very difficult. If I say you need 10 pebbles, then you need to check that there is no way that I could arrange nine pebbles to dominate the graph. Those problems get really difficult really fast, but in the small scale, they’re very nice for students to do some work and get some constructions to determine the number of pebbles needed.

**How does gamification add to education?**

For me gamification means we get to be playful with mathematics. I think this makes math accessible. I just literally gave you a research problem in mathematics that people can get PhDs in by finding the solutions to the problem, and it took us just a few minutes. In this short time, you understand the question. That’s really it; we all have this innate desire to play, and mathematics is one way that we can do that. We don’t often think about mathematics that way.

**What do these games teach and why is it important to ****have this kind of knowledge?**

I think a lot of it is building a sheer love and curiosity for research mathematics, but there are also applications. Sometimes people want to figure out how you move data across some network. On the internet, you want to move from webpage to webpage by clicking on links.

In one of the games we describe, (coauthor) Eric Insko found a cellphone game where we think of the graph as a spider’s web. In this game, you’re trying to make sure a spider doesn’t eat a little fly on the graph, so you want to remove some of the edges of the graph to disconnect the web in such a way that the spider can’t travel to the fly along the edges of the web. (The analog is that) if you delete a webpage, now you might have lost the only way to get to another webpage. There are computer science applications that show up in this work. These games on graphs lead naturally to students building some intuition that they can carry on when they go to do higher level mathematics, computer science, and statistics courses.

**Is there anything that you want people to know ****about you?**

I do research, I do outreach, I teach, and I commit time to initiatives focused on diversity, equity, and inclusion. In people’s minds, they might imagine my work fitting

into separate buckets. That’s not at all how I see my work. For me, they are all completely intertwined. When I think about research and research opportunities, I think about making problems accessible that are still going to lead to original research, and I also think about who I work with and who needs access and opportunities.

All of those pieces go together. That’s what I love the most about being a mathematics professor and the place where I thrive: A place where I can be my full, authentic self and get to do math and get to think about how to make math accessible and where everyone feels included and can experience mathematical joy. That is the place in math that I call home.

**By Sarah Vickery, College of Letters & Science**