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MATHEMATICS COLLOQUIUM

  • April 2017
    Dr. Michael A. Jones - Mathematical Reviews
    A Voting Theory Approach to Golf Scoring

     
    Abstract:
    The Professional Golfer's Association (PGA) is the only professional sports league in the U.S. that changes the method of scoring depending on the event. Even without including match play or team play, PGA tournaments can be scored under stroke play or the modifed Stableford scoring system; these two methods of scoring are equivalent to using voting vectors to tally an election. This equivalence is discussed and data from the 2004 Masters and International Tournaments are used to examine the effect of changing the scoring method on the results of the tournament.

    With as few as 3 candidates, elementary linear algebra and convexity can be used to show that changing how votes are tallied by a voting vector can result in up to 7 different election outcomes (ranking all 3 candidates and including ties) even if all of the voters do not change the way they vote! Sometimes, regardless of the voting vector the same outcome would have occurred, as in the 1992 US Presidential election. I relate this to the question: Can we design a scoring vector to defeat Tiger Woods? And answer it, retrospectively, for his record-breaking 1997 Masters performance.

  • October, 2016 - Dr. Eva Goedhart (Lebanon Valley College)
    Minding My p's and q's: Using Continued Fractions to Solve Diophantine Equations

    Abstract: After a friendly introduction to continued fractions and Diophantine equations, we show how continued fractions can be used to solve a family of Diophantine equations.

  • March 2016 - Dr. Hugh Denoncourt (CUNY)
    "Mathematical Oddities and Their Meanings"
     
    Abstract: 
    Many familiar operations have a simple interpretation. For example, Multiplication is repeated addition and exponentiation is repeated multiplication. Yet, even as early as high school algebra, we find ourselves raising numbers to negative and fractional values and somehow making sense of it. Similarly, we understand what it means to sum a collection of finite numbers. Yet, in calculus, we are tasked with making sense of assigning values to infinite sums. Is this expansion of familiar operations into unfamiliar territories just a game that mathematicians play? If so, are there rules or is it all pure invention? In this talk, we explore these questions through a tour of such oddities as complex numbers and divergent sums. We explore modern ideas that may help remove some of the mystery surrounding these objects.

  • November 2015 - Dr. Tom Concannon (King's College)
    "Understanding Gravity: Relativity, Black Holes, and Beyond"
     
    Abstract: Newton originally conceived of a universal gravitational law in a explicit mathematical form, stating that the gravitational force is an attractive force between two massive objects proportional to the product of their masses and inversely proportional to the square of the distance between them. But Einstein improved on his definition and, in the process, unified space and time into one entity, space-time. This powerful formulation gave birth to radical new ideas about how we perceive motion in space and our passage through time as well as gave validity to the idea of black holes, strongly gravitationally bound systems from which not even light, the fastest thing in the universe, can escape. In this talk, we'll explore the foundations of gravity, from Newton to Einstein and beyond, from its cosmological implications to its quantum ramifications via string theory, a possible unified description of all known physical laws.

  • April 2015 - Dr. Stanley Ryan Huddy (Fairleigh Dickinson University)
    An Introduction to Chaos Theory
     
    Abstract: If a butterfly flaps its wings in Brazil does this set off a tornado in Texas? Why are weather reports often incorrect? Join me as we answer these questions and more through a visually interactive introduction to chaos theory.

  • November 2014 -- Dr. Kathleen Ryan (DeSales University)
    "Non-Diplomatic Degrees!"
     
    Abstract: A graph is a set of vertices together with a set of edges between some pairs of vertices.  We say that the degree of a vertex in a graph G is the number of edges incident to the vertex. If we create a list of integers consisting of the degree of each vertex in G, then the resulting list of integers is called the degree sequence of G.  Given a sequence of integers d=(d_1,d_2,...,d_n), we explore the answer to the following question:  When does there exist some graph whose degree sequence is d? We then explore a generalized version of this question for edge-colored graphs within certain graph families.