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Makkah Davis ‘18

“Analyzing Partisan Combinatorial Games”

Major & Minor: Mathematics and Secondary Education
Hometown: Bethlehem, PA
Project Advisor(s): Dr. Nate Shank


Tell us about your research. 

My research was conducted at the 2017 Muhlenberg College Mathematics and Computer Science Summer Research Experience for Undergraduates Program in conjunction with its participants. I worked on two fairly unrelated research projects, one exploring properties of Factor Pair Latin Squares and one exploring Game Theory. Additionally,  I worked with my advisor, Dr. Shank, on the game theory project, in which we created a partisan variant of the popular combinatorial game, Nim, in which the game is played on a colored cycle graph. The bulk of our research was devoted to analyzing and solving our game. 

How did it materialize? (E.g., did you pitch the idea and choose a
faculty member, or did they come to you with an idea?)

After Dr. Shank had proposed doing a SOAR project (along with the REU), and I learned more about the great opportunity that SOAR afforded, we discussed projects we might take on to research that would fit well with proposed projects at the REU program.

What was the best part about working with your faculty advisor? What valuable insights did they bring to the research process?

The best part about working with Dr. Shank was having him as a resource for guidance throughout my research; he was able to propose new directions for the project as well as add new insight for ideas that I or my research colleagues proposed. Having an experienced and supportive professional to work alongside allowed me more freedom to study and explore the project fully. 

What was your biggest obstacle?

The biggest obstacle during my research was coming across mathematical topics of which I was unfamiliar, however would prove useful to solving/understanding an aspect of my project. Thankfully, doing the appropriate research and taking the time to gain some background knowledge on related topics was both helpful in remedying that as well as in developing a methodology for exploring new mathematics. 

What was your biggest takeaway from this experience?

My biggest takeaway from this experience was the ability to take agency over an academic interest, namely mathematics, which can sometimes get lost in undergraduate studies. 

What was the result of your research? 

The result of my research was that we were able to discover and prove various interested properties for our Partisan Cycle Nim game, we submitted a new sequence which we discovered in our research to the OEIS (Online Encyclopedia for Integer Sequences), considered relations between our game and the original Nim, as well as consider other implications of playing and solving our game.

Now that SOAR is over, do you plan to expand upon your research? If so, where would you like to see it go? 

I would love to expand on my research. In particular, I would like to continue working to completely solve our game and continue relating previous and new discoveries from our game to the field of game theory and other fields of mathematics. 

In your own words, how do you feel about being rewarded this opportunity? Why should other students take advantage of the SOAR program? 

Being awarded this opportunity has been a great privilege. To take part in undergraduate research and experience math research has allowed me greater insight into the goals, uses, and wonders of mathematics. In many ways, this research opportunity has put my pursuit of mathematics in a new focus. Other students should take advantage of the SOAR program because it promotes discovery and scholarship in your field of interest.