What are you doing in the featured picture?I am using Maple, a computer algebra software program, to help us analyze the graph of a function. You can see in the picture the sine and cosine waves that make up the traces, or cross-sections, of the function.
What do you love about math?
I love how everything fits together! I love that even though we all have specialties you have to know a bit about everything in math. It is amazing how a seemingly unrelated topic sneaks in when you least expect it. There is nothing better than the moment when you figure out that problem you have been working on for a week (or a year). When you finally solve a problem and see the results and how it all fits together, it is beautiful!
What kind of research do you do?My main research interest is in noncommutative algebra. More specifically, I am interested in finding the structure of an object called an algebra associated with a directed graph. This allows us to gain a better understanding of the object and how it behaves when we move things around. I am currently working on an algebra associated with an n-dimensional hypercube.
Why should a student study math at UW -Eau Claire?The faculty members here are very encouraging and genuinely care about their students. They are approachable, dedicated, and involved with their students’ work. You can get experiences here that are usually reserved for those who are already mathematicians; in some ways, it is as if every student gets to leave here with an internship-like experience.
Can you share some memorable experiences you’ve had with students?Office hours always create a great atmosphere for learning and getting to know students. I enjoy helping students figure out problems and understand the topics we are working on in class. In return I have a “policy” that if there is more than one student who comes in to ask the same question, and the first student understands and figures it out, I ask them to try and help explain it to the other students; that way students are learning from each other. It is great to see!
What do you hope your students are getting from your courses?I hope they get an appreciation for math, that they see it as more than a formula and dry process, but rather see how they can use creativity to solve problems.
What classes/topics do you teach?
Abstract Algebra, Calculus III, Algebra for Calculus.
What is your favorite course to teach? Why?Abstract Algebra, it is my field of study and I love to teach what I am passionate about. It is a fun course to teach because we go over a lot of interesting examples in class, such as studying symmetry and cryptography.
Best advice for students?Talk with your peers and professors about your ideas and questions. Work together to get through things you are having trouble with.
I have a paper entitled “Representations of Aut(A(?)) acting on homogeneous components of A(?) and A(?)!” published in the January 2009 publication of Advances in Applied Mathematics.
Awards, presentations, published work?
I have presented at the Joint Mathematics Meeting in San Diego, a conference where several math organizations come together for one large conference. I have also given talks related to my thesis at Rutgers, where I earned my PhD.