Contributed Talks - MAA Intermountain Spring 2013
MAA Intermountain Section Spring Meeting
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Mathematics to DIE for: The Battle Between Counting and Matching
Positive sums count. Alternating sums match. So which is "easier" to consider mathematically? From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we know that the permanent of an n × n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties. This talk is one part performance art and three parts combinatorics. The audience will judge a combinatorial competition between the competing techniques. Be prepared to explore a variety of positive and alternating sums involving binomial coefficients, Fibonacci numbers, and other beautiful combinatorial quantities. How are the terms in each sum concretely interpreted? What is being counted? What is being matched? Do alternating sums always give simpler results? You decide.
Fibonacci's Flower Garden
It has often been said that the Fibonacci numbers frequently occur in art, architecture, music, magic, and nature. This interactive investigation looks for evidence of this claim in the spiral patterns of plants. Is it synchronicity or divine intervention? Fate or dumb luck? We will explore a simple model to explain the occurrences and wonder whether other number sequences are equally likely to occur. This talk is designed to be appreciated by mathematicians and nonmathematicians alike. So join us in a mathematical adventure through Fibonacci's garden.
Who Wrote L'Hôpital's Calculus Book?
The Marquis de l'Hôpital (1661-1704) was a French nobleman whose name is inextricably linked to the well-known rule for resolving indeterminate forms. Although credit for discovering l'Hôpital's Rule rightfully belongs to Johann Bernoulli (1667-1748), the Marquis deserves a special place in the history of the calculus, because he authored the first differential calculus textbook, Analyse des infiniment petits (1696).
In the preface to his book, the Marquis acknowledged "owing much to the illuminations" of Johann Bernoulli, but did not get into specifics about Bernoulli's contributions. In the years following the Marquis' death, Bernoulli made ever greater claims of priority over the contents of the book, once having gone so far as to claim that "Mr. de l'Hôpital had no other part in the production of this book than to have translated into French the material that I gave him, for the most part, in Latin." In the 20th century a number of original documents came to light and we now understand that l'Hôpital's textbook was essentially the collaboration of a brilliant mathematician and a talented expository writer.
In this talk, we will consider both the mathematics that was presented in the Analyse and the process by which in came into being.
Mathematics and the Life-Impaired: How Disease Theory Predicts the Zombie Apocalypse
"Here a zombie, there a zombie, everywhere a zombie, zombie..."
From movies to pop music ("If I were a zombie, I'd never eat your brain...), it seems the undead are already taking over the world. The usually staid Centers for Disease Control launched its tongue-in-cheek "Preparedness 101: Zombie Apolcalypse" public campaign in 2011 to drive home the importance of emergency preparation. Even Utah State University has been infected as evidenced by USU Housing's wildly popular, campus-wide"Humans vs. Zombies" (HvZ) war this past fall.
Anthropologist Krystal D'Costa suggests zombies capture our imagination because they represent modern society and technology gone awry and offer the perfect metaphor for an unstoppable pandemic. USU professor Jim Powell expands the zombie metaphor to illustrate the concepts and results of mathematical epidemiology. Using storylines from such movies as "Night of the Living Dead," "28 Days Later," "The Walking Dead" and "I am Legend," as well as data from the USU HvZ games, Dr. Powell will show how mathematicians model diseases. He'll talk about how scientists predict the course and impact of epidemics, discuss how "herd immunity" (vaccination levels for disease eradication) works and apply some of these modeling strategies to the understand and predict the spread of Chronic Wasting Disease (Zombie Deer) in southern Utah