When we think about a continuous variable, that is, one that can take on any value along the number line, we note that the chance that it will take on any pre-determined value is equal to zero. For example, if we want to know whether the variable takes on a value of two, would we be willing to accept a value of 1.9 instead? How about 1.99? Or 1.999? Or 1.999 with a sequence of 9s going on into the next county but, presumably, never actually equaling two? Since it is clear that one can get infinitesimally close to any arbitrary value without actually equaling that value, we say that the probability of a continuous variable actually equaling some predetermined value is zero.

# 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

January 17, 2013

In Economics we talk about maximizing “utility” subject to a given constraint. For example, a shopper wants to choose the best combination of groceries that can be purchased given their present budget. I thought of this recently, as I recalled a class I fell into in my last days of college. Realizing that tuition had been paid that allowed me to take up to eighteen credits my last semester, and also assuming that I would never again have access to courses in Theology or Philosophy, I decided to take as many of those classes as I could before graduating.

January 10, 2013

When I first tried to teach my daughter division, I taught her to ask how many objects she could allocate evenly among a given number of piles of that object. For example, if you wanted to make six piles of marbles, how many marbles would end up in each pile if you began with twenty four marbles? I found myself thinking of this recently, as I remembered frequent carpools for teenage excursions, often heading towards the Southern part of my home state, Connecticut. I would meet up with friends to allocate those of us without cars among a set number of cars driven by friends.

January 3, 2013

When I was in grammar school, I used to say that I wanted to grow up to be an archeologist. Having not yet discovered Economics, I could not think of any other way to combine my love of social studies, math and science all at once. Had I pursued that line of study, I hope that I would have had some intelligent things to say about the idea that the Mayan calendar predicted the end of the world on December 21, as did others. Since that day has come and gone, I think it is safe to say that any predictions based on those calendars foretelling the end of the world as we know it were incorrect. Now that we know that the world is not ending quite yet, I want to share some thoughts on what we did not lose on December 21, 2012, as the New Year unfolds.

December 20, 2012

When I teach Calculus, I often begin by comparing the difference between Calculus and Discrete Math to the difference between the individual frames of an old-fashioned movie tape and the movie when shown on a projector. I tell them that, while algebra and all of discrete math looks at individual situations, or “frames”, Calculus can study a world of continuous motion. This analogy has been on my mind lately as I find myself recalling scenes from past holidays with my daughter. Individually interesting, they run together into a “movie” of emotions that grabs me at this time of the year.

December 13, 2012

Several years ago, I found myself at Cleveland, Ohio’s own Rock and Roll Hall of Fame. One of my fellow visitors pointed out an exhibit that showed a report card from John Lennon. It seems that John Lennon had a difficult time with math, which surprised us. We had both always thought that math and music went hand in hand, that learning music would help one excel in math, and that mathematical talent would help one learn a musical instrument. I thought of this recently when I observed my daughter’s Christmas concert, performed by all the students at her school who are taking lessons to learn to play a band instrument.

December 6, 2012

There is a concept in economics called a "leading economic indicator," in which certain economic outcomes are seen as providing information about the direction the economy is taking. For example, sales of cars or of new homes may be seen as leading economic indicators, since such sales tell us a lot of information about the willingness of consumers to purchase items that are expensive and which need to be paid off over the course of several years. I thought of this recently as I drove around our neighborhood with my husband and daughter, playing Christmas music on the car radio and admiring the different decorations that have sprung up on the homes in our neighborhood.

November 29, 2012

When I think of the “equals” sign in algebra, I think of it as a statement that something is true. For example, if an equation says that something is equal to a number, adding or subtracting a value to or from both sides leads to a statement that is equally true. This concept of “truth” has been on my mind recently as we approach Christmas, and I find myself in discussions with fellow mothers about the idea of “Santa Claus”.

November 16, 2012

The last time I taught a class called “History of Math”, a class I rarely teach at Ursuline College, my daughter was a young child in pre-school and was perfecting her knowledge of numbers. I was struck at the time by the similarities between the way my daughter learned about numbers and the way humankind developed knowledge of numbers, and I wondered if history was repeating itself in each child, as they learned to count.

November 8, 2012

When I teach statistics, I often point out that some values we calculate have different notation depending on whether they are calculated from the entire population or a from a sample taken from that population, even if the calculations are identical in the different situations. I explain this to my students by telling them a woman’s name, and asking them if they know who that woman is. They almost always have no idea who she is.