Once, years ago, I found myself at a party talking about what it would mean to divide by zero. (No wonder I was terminally single at the time!) I explained that, while we can’t divide by zero, we can think of approaching a divisor of zero, and see what happens. Think first of dividing 1 by 1, to get 1/1, or 1. Now divide 1 by 0.1, to get 10. Continue on to divide 1 by 0.01 to get 100, and 1 by 0.001 to get 1000. You can see that if you continue on like this, the smaller the divisor gets, the larger the ratio gets. While we can’t actually divide by zero, we can approach doing so, resulting in a ratio that grows larger and larger, until it approaches infinity.
I used this discussion when I applied for tenure years ago, to highlight the growth in the math department in the years since I had taken over the position of chair. When I took over the position, there were no math majors, and the number has slowly grown in the past 12 years. Since percentage change is calculated by taking the change in a value and then dividing it by the original value, this would mean that we would take the change in the number of math majors and divide it by zero, an impossible feat, of course. However, as I pointed out in my tenure dossier, using the logic outlined above, the percentage change could be thought of as approaching infinity. I guess someone agreed with me, because I am still here.
However, tonight the reverse happens, as we graduate a handful of math majors and the number shrinks. Although I will not be at graduation, as I still can’t walk in a procession, I am excited for this cohort of majors. I have taught them classes ranging from calculus to advanced statistics, and, quite frankly, I will miss them as they leave.
I think of “Nancy”, who I first met when she sat in my class to assist a student who was taking my introductory class who had practically no vision. She would put tiles with Brail writing on a board so he could follow along with my examples from the board. Along the way she came to a realization that, while the math from that class was relatively simple, she really enjoyed spending time with numbers and equations. She has taken a job for a large firm in Ohio’s capital city, where she will continue to spend time with numbers.
I also think of “Dee”, who is a single mother of a child about the same age as my own daughter. As I struggled with the day to day challenges of raising a child, I often thought of her with all the responsibilities of raising her own child, responsibilities that were combined with going to school full time and working to support her little family. As overwhelmed as I felt by motherhood, I always had the reality check of being able to see the challenges she triumphed over on a day to day basis.
“Jill’s” story is similar to that of many of Ursuline’s students. She began her college career at a large university, but came to Ursuline for its small classes and individualized attention. She says that Ursuline helped her believe in herself and to see all that she could become. After impressing her superiors at an internship at a large public utility, she took a job in another state, where she also plans to pursue a master’s in business administration. That is, unless she can find a way to return to Ursuline to earn that M.B.A.
Last week, I received a note from another graduating student who, alas, was not a math major. She told me that “Today I handed in my last undergraduate student homework assignments and am leaving behind an institution that has not only changed my life for the better, but changed my life for good.” What these students don’t realize is that they also change our lives for the better, as we share a small part of their life’s journey. We are forever changed because of each student who enters our classroom and touches our lives.
And so, to my students, math majors and not, who are graduating tonight: May God bless you on the next stage of your journey. Good things await you. Your future awaits you. Infinity awaits you.
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