# Math Geek Mom: Limits at Infinity

In Math, we often talk of how a function behaves as a variable approaches limits at infinity.

January 26, 2012

In Math, we often talk of how a function behaves as a variable approaches limits at infinity. That is, if we let “x” take on larger and larger values, what happens to the value of “y” it creates? It is possible that this does not approach any particular value, but instead, like x, grows without bounds. However, it is also possible for the value of the function to approach a particular value way off to the right or the left, as we approach the end of the number line that actually has no end. I found myself thinking of this concept lately as I wished I could see the end result of my work as a teacher and as a parent. Of course, such results are not to be seen, as the fruit of our work will not fully materialize for a long time.

Being a parent is a lot like being a teacher. In both cases, we try to impart knowledge and skills to people less experienced than ourselves. In both cases, alas, we know we will probably not see the final result of our efforts. This past week, however, allowed me several rare glimpses into the effects of my work as a teacher from past years, and I savor them.

I recall one student who, several semesters ago, attended some class meetings of a course I teach. It was obvious from the first few days that she was not as well prepared as she needed to be. Although it meant going back and taking another course before taking my own class, I encouraged her to do that, which she did. She is now back in the class she originally tried to take, and is one of my star students there. As is often the case with star students, she sits in the front row and readily answers questions when I ask them, only occasionally asking me to repeat a line of thought, which I do, usually to the relief of the other students in the class. Although I did not want to advise her to add another class onto her list of required classes, I found that advising her to do so was in her best interest in the long run.

When I teach my class in Statistics, I always end with a promise to my students that I will be there as a resource for them, should they have any statistics questions in later classes, or in later life. This has led to some interesting requests over the years, such as the one young man from another school where I taught who called me asking about the odds of winning a particularly large payoff in the lottery. He told me that the answer would determine the winner of a bet between him and some friends, and that the payoff was a keg of beer.

I have also assisted students in Research Methods classes and in writing undergraduate theses. This past week, I received an e-mail from a former student who is now in a Ph.D. program in Psychology, who was looking for a data set that we used in our Statistics class. I was able to help her find it, and was thrilled that she was pursuing a terminal degree in a subject in which I know she excels.

I also received a visit from another former student this past week, one who is graduating from a Master’s program and applying for jobs. It was good to hear from her that she felt very well prepared as she made her way through the program, and that she was surprised at how little knowledge of Statistics some of her classmates brought to graduate school. She said that her education at Ursuline had served her well, and noted that she was a transfer student who transferred to Ursuline only when she realized that she wanted a small, student-centered college. When she left my office after visiting, I realized how proud of her I was, and I knew that her future held many great things.

I hang on to these moments, and try to relate them to my experience as a mother. I am deep in the days of being a mother to a child in grammar school, with all is duties of helping with homework and driving to sporting events and even “girl drama” that it includes. It is a rare day when I feel that my efforts will have any tangible results in the end. These events of last week remind me that even if I can’t see any result in the end, they are, in fact, there. I realize, however, that I will not be here to see exactly where they lead to, or to know exactly what happens in her life as time marches on to infinity.

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