Loyola University Chicago

Mathematics and Statistics


Are you interested in participating in math research?

Are you interested in participating in math research?

Pictured Top Left: Dr. Aaron LauveAnthony Lazzeroni, Pragna Bhatt

Pictured Bottom Left: Andrew Ducharme, 

Pictured Bottom Right: Liz Jurkash, Anthony Lazzeroni, Dr. Emily Peters, Ariana Grymski, Madison McCallister 




    Last summer, six students spent their break conducting research alongside professors. We interviewed them to get their take on their experience and how they spent their summer.


  1. Please provide an short summary of your project and its long-term goals. Who did you work with? Did you make any new connections?
    • "I worked with Dr. Lauve and Anthony. My project consisted of working with a specific group of polynomials called r-quasisymmetric polynomials and our long term goal is to find a new basis for them." -Pragna Bhatt
    • "Ariana and I's project focused on using Thompson tree diagrams to find knots up to 6 crossings. Our goal was to find a simpler algorithm to generate knots. I'm a senior majoring in math and classes that prepared me the best for the project were number theory and abstract algebra." -Liz Jurkash
    • "I’ve been working in the field of knot theory trying to develop a program in Mathematica to compute the Jones Polynomial, a classification system which can distinguish between two non-trivial knots. The goal is to find a new knot invariant based upon how likely a knot projection will end up being a complex form of an unknot if the original projection is slightly altered and hopefully find a non-trivial knot which has a Jones Polynomial of one, proving that there exists a flaw in the Jones Polynomial itself." -Andrew Ducharme
  2. What level of college study are you currently pursuing? Which Loyola courses prepared you the most for summer experience?
    • "I am currently pursuing a B.S. in mathematics and a B.S. in physics.  Abstract Algebra I and II prepared me most for this research." -Ariana Grymski
    • "I’m an undergraduate math and physics major and a rising junior. Surprisingly enough, the class that was most helpful for my summer research was COMP170 with Dr. Honig since it taught me the basic computer programming principles that I’ve been using the length of this project. I had no coding experience in high school, so having that class made it possible for me to do this research." -Andrew Ducharme
  3. How did you get the position? Did someone offer it to you?
    • "I found this position through my math advisor after I told her that I wanted to see what it is like to research math, she told me that I should talk to Dr. Lauve because he was looking for a research assistant. After I talked to him and he explained to me what he was going to research and I was interested. I applied through LUROP and specifically to the Provost Fellowship." -Anthony Lazzeroni
    • "I got the position through the WISER (Women in Science Enabling Research) program." -Pragna Bhatt
    • "I got the position after talking to a few professors in the department about research this summer and after discussing with Dr. Peters, she was kind enough to offer me a spot working with her." -Andrew Ducharme
  4. Describe your average day on the job.
    • "An average day on the job involved drawing lots of tree diagrams and talking with Ariana about strategies." -Liz Jurkash
    • "I wake up early in the morning and test Thompson diagrams to see what knots they produced, usually slightly varying diagrams I had previously worked on.  I am a figure skater, so I would go off to skating practice, then continue my work on these diagrams at the rink during my breaks from skating. Then, I would drive to Loyola to meet up with Liz, where we would discuss what we were each working on, make suggestions, check each other’s work.  I would then go home and work on Liz’s suggestions in the evening." -Ariana Grymski
    • "My average day is basically just pulling out my computer and working on the various programs I have or trying to fix some annoying bug. The best part is when some problem I’ve been toiling away on for the last few hours just starts working after dozens of screwy results and error messages. Of course, this requires a long time of working, hoping that your slight change did what you wanted and correcting every time it doesn’t." -Andrew Ducharme
  5. What was your favorite part? Were there any difficult or challenging tasks?
    • "The most difficult part for me was the beginning when there was a lot of information to absorb and understand in order to get to the main part of my research. A lot of it was at a level beyond me and it took some time to get used to thinking in the way my research required me to think. My favorite part was when I was able to understand enough background knowledge so that I could work on the actual goal of the project." -Pragna Bhatt
    • "My favorite part was when Liz or I first discovered the Thompson diagram for a new knot. We most often got either repeat knots, unknots, or links, so a new knot was a rarity! Since we kept getting the same knots over again, we had to really think out of the box about how to get new ones." -Ariana Grymski
  6. What did you get out of it? Did you learn any skills or something about yourself?
    • "One of the big things I got from this half of the summer, was learning how to read math papers, it wasn’t really taught to me in class, and it is a good skill to learn if anyone wants to go into the math field. After that half of the summer, the rest was trying to find a new basis, one that would be helpful, we had a set of rules that we wanted this new basis to follow." -Anthony Lazzeroni
    • "I got to have the thrill of working for a long time, and finally discovering something new!  I learned how to work with a partner, and how to build off of other people’s work."  -Ariana Grymski
    • "I learned that I love coding. There’s something really rewarding about getting your program to run and give you the output you expect. Once I got my program to run for lower order Temperley-Lieb algebras, I could then use it to predict higher order Temperley-Lieb algebras that are impossible to solve by hand." -Madison McCallister
  7. Did you use any programming language(s)? If so, what language(s)? Did you already know them, or were you trained?
    • "To make these bases we used python. My MATH 215 class prepared me a lot for programming, and it was also taught by Dr. Lauve. For half of the summer, Dr. Lauve was teaching us everything about that topic and things leading up to that topic, our homework assignments were often reading math papers and coding exercises. Every week we would send him an email telling him what we learned, did, what we didn’t understand, and ask him to talk about something when we would meet again."  -Anthony Lazzeroni
    • "I also learned how to use LaTex and practiced my mathematica skills. I didn't use any other programming languages." -Liz Jurkash
    • "I’ve been using Mathematica, which I only had a little experience from previous classes at Loyola. I’ve far and away improved my ability in that language from highly inexperienced to semi-competent, which will be excellent for my life after Loyola."  -Andrew Ducharme
  8. Do you have any advice for undergraduate students when looking for a similar summer experience?
    • "For women in STEM, I definitely recommend the WISER program and for all undergraduate students, I recommend talking to your professors and getting to know about their research/other work they do outside the classroom." -Pragna Bhatt
    • "Advice I would give for other students trying to find research opportunities would be to have good relationships with professors and mention your interests. Let them know you'd like to work with them and if they don't have anything currently they could also recommend you for other ones." -Liz Jurkash


    Each summer experience was unique and geared toward certain goals. Research opportunities are not limited to these areas nor locations. If you are in the market for research opportunities or summer experiences, check out our Summer Opportunities tab. If you are interested in looking into programs like WISER, check out our Scholarships & Opportunities tab. If you don't think research is for you but still are considering other opportunities, check out our Career Resources tab.