Love it or loathe it, math is everywhere. From the algorithms behind shopping recommendations to the encryption that keeps data safe online, the world is driven by numbers and data. And while knowledge of mathematics can help people understand this complex world, many Americans are fearful of the subject.
This spring, the Mathematics in the Media course, taught by Jerry Kazdan, provided students with insights on how mathematics can be applied and used in everyday life. By working through examples of complicated real-world problems, students from various academic backgrounds, including math majors and minors, business students, and engineers, were able to see how math could be used to answer some of the world’s most pressing questions.
Kazdan, who has taught a number of iterations of this course since 2000, structures the class by keeping an eye on what’s happening in the news. He then asks his students questions that they “will care about the answer to” and provides them with a background of fundamental mathematics they need to approach and solve the problem.
“This course isn’t designed to build a standard machinery of mathematics,” says Kazdan. “Instead, I’m trying to focus on the problem using case studies, with specific problems and enough discussion on the topic, so that one can answer the question and have some insight into a neighboring question.”
Probability and statistics was taught in length at the beginning of course, with this cancer test problem as an example of a question that involves both serious mathematics as well as real-world consequences.
The course also discussed how online search engines use similar mathematics to return relevant results. “The hard part is to assemble the data and to have a way of searching for it, which is what Google did,” says Kazdan. He showed the class how Google broke down this problem using a simplified database and talked about how a fundamental mathematical approach was applied to solve an incredibly complex problem.
Sarah Heard, a first-year Wharton School student from Starkville, Mississippi, says that this discussion of Markov chains was one of the most interesting topics they covered in class. “It was pretty simple, but I had never learned about them before,” Heard says. “I had done matrices and probability but didn’t know that Markov chains were a thing, so it was interesting to see how formulaic [probability] could be.”
The prevalence, and power, of math
Plurality voting: The system used by most political elections, where voters choose only one candidate and the candidate with the highest number of votes wins the election. Using this system, Smith wins the election with 6 million votes.
Ranked choice: The system that is used in Australia, Ireland, and, with recent controversy, in Maine’s 2018 state elections, where voters rank candidates in order of their preference. If no candidates have more than 50 percent of first-place votes, the candidate with the least number of first-place votes is removed from consideration, and their votes go to the candidate whom that group listed as their second choice.
Using this system, since Smith’s 6 million votes only account for 40 percent of the total electorate, the candidate in last place, Jones, is removed from consideration and his 4 million votes all go to Davis. This gives Davis 9 million votes, or 60 percent of the total, and the election.
Borda count: A version of the ranked choice system that assigns a pre-determined number of points based on how the candidate is ranked. With a Borda 3,2,1, count system, for example, the first-place candidate gets 3 points per vote, second place gets 2 points per vote, and third place 1 point per vote.
Using this system, Jones has the highest number of points and wins the election.
Smith: (6 million * 3) + (5 million *1) + (4 million *1) = 27 million points
Davis: (5 million *3) + (4 million * 2) + (6 million *1) = 29 million points
Jones: (4 million * 3) + (6 million * 2) + (5 million * 2) = 34 million points
Voting was also discussed in the course as a problem where the mathematics is not complicated but where different ranking systems lead to different results. By using a mock dataset, Kazdan showed the class how elections with three or more candidates are much more complicated than simpler elections with only two candidates.
Other topics covered include modeling epidemics, data mining, and encryption. Junior Sarah Baumgarten, a logic, information, and computation major from Roslyn, New York, says she enjoyed learning about modelling how diseases spread, a relevant topic due to recent outbreaks covered in news reports. “It’s refreshing to do something with a basis in the world,” says Baumgarten. “It’s given me an awareness of how to apply what seems theoretical, to look at what’s happening in the world, and to see how things fit together.”
While each of these topics could be studied for a lifetime, the course is designed to provide a glimpse into each problem without delving too deeply into theory. “In a pure math class, a lot of time is spent grinding out problems, but this is focused on the bigger concepts,” says Heard, who appreciated the open and fluid structure of the course. “It’s a nice change because most classes have a very set syllabus, and there’s no slowing down if people are confused. Whereas with Dr. Kazdan, if we don’t understand something, we go on for another day,” she says.
Baumgarten says that the mindset of being able to apply what she knows to the world around her will be the biggest thing she takes away from the course, while Heard says that the approach of being able to understand concepts and how they might be applied, regardless of whether or not she can do the calculations yet, will be incredibly useful for her.
Kazdan hopes that this course has helped students recognize how they could use math to answer questions that haven’t even been asked yet. “They will see questions that don’t have good answers and will be brave enough to try and understand them,” he says.
This course, and others like it, might also be a way for future students to see how math can be a tool for empowerment, not a topic to be feared or ignored. “I’m happy with how the course has gone,” Kazdan says. “These students aren’t afraid of math.”
Jerry Kazdan is a professor in the Department of Mathematics in the School of Arts and Sciences at the University of Pennsylvania.
