Iona College Professor Published in the American Mathematical Monthly
Co-written by Dr. Benjamin Gaines, “The Game of Cycles” is featured in the journal’s December issue
NEW ROCHELLE, N.Y. (December 20, 2021) — Dr. Benjamin Gaines, associate professor of mathematics at Iona College, was featured in the December issue of the American Mathematical Monthly— highlighting an article he co-wrote, “The Game of Cycles.”
In the Game of Cycles, players take turns drawing arrows on the edges of a graph. The goal is to be the player to draw an arrow that completes a “cycle” — that is, completely encloses a two-dimensional cell of the graph with arrows all going the same direction around it. However, there's a catch: neither player is allowed to create sinks (where all arrows point inwards at a point) or sources (where all arrows point outwards at a point). This sink-source rule leads to some interesting mathematics, both while playing the game and from a broader topological perspective.
In the article, Gaines describes how to play the Game of Cycles, how to see which player has the winning strategy and observe that the sink-source rule guarantees that if every edge on a (finite, connected) board is marked, there must be a cycle cell somewhere on the board.
The article was also mentioned in a tweet from the Mathematical Association of America, the world’s largest community of mathematicians, students and enthusiasts.
ABOUT IONA
Founded in 1940, Iona University is a master's-granting private, Catholic, coeducational institution of learning in the tradition of the Edmund Rice Christian Brothers. Iona's 45-acre New Rochelle campus and 28-acre Bronxville campus are just 20 miles north of Midtown Manhattan. With a total enrollment of nearly 4,000 students and an alumni base of more than 50,000 around the world, Iona is a diverse community of learners and scholars dedicated to academic excellence and the values of justice, peace and service. Iona is highly accredited, offering undergraduate degrees in liberal arts, science and business administration, as well as Master of Arts, Master of Science and Master of Business Administration degrees and numerous advanced certificate programs. Iona students enjoy small class sizes, engaged professors and a wide array of academic programs across the School of Arts & Science; LaPenta School of Business; NewYork-Presbyterian Iona School of Health Sciences; and Hynes Institute for Entrepreneurship & Innovation. Iona is widely recognized in prestigious rankings, including The Princeton Review’s 2024 national list of “The Best 389 Colleges” and The Wall Street Journal/College Pulse’s “2024 Best Colleges in America,” which ranked Iona at #66 in the nation overall and #8 in the nation among Catholic schools. Iona’s LaPenta School of Business is also accredited by AACSB International, a recognition awarded to just six percent of business schools worldwide. In addition, The Princeton Review recognized Iona’s on-campus MBA program as a “Best Business School for 2023.” Iona also offers a fully online MBA program for even greater flexibility. In July 2021, Iona announced the establishment of the NewYork-Presbyterian Iona School of Health Sciences, which is now principally located on Iona’s Bronxville campus in collaboration with NewYork-Presbyterian. Connecting to its Irish heritage, the University also recently announced it is expanding abroad with a new campus in County Mayo, Ireland. A school on the rise, Iona officially changed its status from College to University on July 1, 2022, reflecting the growth of its academic programs and the prestige of an Iona education.