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.

# Rosemarie Emanuele

## "Math Geek Mom"

Although she holds a Ph.D. in economics from Boston College, **Rosemarie Emanuele** is a professor and the chair of the Department of Mathematics at Ursuline College in Pepper Pike, Ohio, just outside of Cleveland. She loves to teach math but also pursues research related to the economics of nonprofit organizations and volunteer labor, and has published in both economics and interdisciplinary journals — as well as in the book that inspired this blog. She is the proud mother of a wonderful daughter.

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## Most Recent Articles

May 13, 2010

Imagine a number line, extending in both directions infinitely. Above this line we might graph bars that represent the proportion of observations of something that fall within any given interval on the number line. We can do this for much of the data sets that show up in nature, such as the length of a leaf on a tree, the height of a grown woman, the average body temperature or even the length of a human life. When we start graphing these data that show up in nature, we notice that they tend to all look slightly similar.

May 6, 2010

The idea of a tangent line is central to many aspects of mathematics. In geometry, we study when a line rests on another figure at just one point, the point of tangency. In calculus, the slope of the line tangent to a curve at a point becomes the “derivative” of that curve at that point. One can even think of tangencies in more than one dimension. Imagine an (x,y) plane drawn on a table with a three dimensional object resting on it. One can therefore find a point of tangency in the x direction, and also one in the y direction.

April 29, 2010

I remember my comprehensive exams in graduate school as the low point of that experience. Classes were fun, and I did relatively well, and writing my dissertation was actually a joy most of the time. But in the one week dedicated to my comprehensive exams that turned into months as I ended up re-taking some of them, I was expected to know everything from my years there and to prove it on paper to what seemed like merciless graders. I don’t know if I had felt so vulnerable at any point in my life up until then, and have only felt so vulnerable a few times since then.

April 22, 2010

A colleague in the Biology department recently told me about a book that applies game theory to altruism in the animal world. Since I study altruism, and game theory is central to modern economics, I was particularly interested. Of course, I had to read about it myself, and found it fascinating.

April 15, 2010

Once, when I was in high school, I must have said something that particularly exasperated one of my teachers. She took a deep breath and looked out at me in the classroom (middle seat, second row) and said “Rosemarie, do you know what you are? You are in intellectual iconoclast.”

April 8, 2010

I have written before about my philosophy of learning math. I tell my students that one needs to do math wrong first, before one can figure out how to do it right. This, after all, is the logic of doing homework. Homework gives students a chance to mull over problems and possibly go down blind alleys, only to eventually learn how to solve a problem in a way that works. I have also seen such a theory applied to many areas in life. It is often the case that we need to make our own mistakes so as to learn how not to make those same mistakes again.

March 25, 2010

A central tenet of economics is the assumption of non-satiation. This concept says that people will always want more of a good, that there is no such thing as “enough” fancy cars or chocolate cake. Of course, there can be more than enough of a bad thing, such as garbage. This assumption might be summarized by the phrase “more (or a good thing) is better.” Anyone who has been a parent to a young child knows this almost reflexive reaction to something they want. I recall times when my then two year old daughter was delighted with something and simply proclaimed “more.”

March 18, 2010

If you took Geometry in High School, you almost definitely learned it as a subject based on rules and axioms discovered by the ancient Greeks. The details of this subject, which I must admit was probably my favorite class in High School (what a geek!), reflected the world view of the ancient Greeks, including the perception of the world as a flat surface. On this flat surface, triangles have exactly 180 degrees, and parallel lines go on forever and never intersect. This is called “Euclidean Geometry.”

March 11, 2010

Before finding my job at Ursuline College, I taught economics or statistics at several different colleges. I taught as part of my graduate assistantship on the way to my Ph.D., as an adjunct at several colleges in the Boston area as a graduate student, and at my first job out of grad school, and the one that brought me here to Cleveland. I was recently reminded of a lecture I tried to teach at one of those schools many years ago. As part of a class in macroeconomics, I tried to have a discussion about how the United States could help people in poorer countries.