Department of Mathematics and Statistics
UMKC (University of Missouri - Kansas City)

Expository Talks Series, and
Video/Film Series

Semester: Spring 2009 - 22nd Year
Location: Haag Hall, Room 309 (unless otherwise indicated below)
Day & Time: Friday, 4-4:50 pm (talks), 4-5:00 pm (videos)
Campus Map for Talks (PDF Format)

Contact: Richard Delaware, delawarer@umkc.edu


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Dates, Titles, Speakers (with Abstracts & Posters as available)


  • Friday Feb. 6
    Expository Talks Series
    Counterintuitive sets
    Chuck Moore, Mathematics, Kansas State University

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    [Campus Map for Talks (PDF Format)]

    There exist bounded sets in the plane which have no area but which contain a line segment of unit length in every direction. There exists a set contained in the unit square [0,1] X [0,1] of area 1 which has the property that for every point in the set there is a line in the plane which intersects the set only in that point. I will discuss the constructions of such sets. Besides being curiosities, these sets provide useful examples in the study of differentiation of integrals (that is, the Fundamental Theorem of Calculus) in dimension 2.

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  • Friday Feb. 20
    Expository Talks Series
    Who's #1?
    Can a Simple Ranking Algorithm
    Answer College Football's Toughest Question?
    Brian Hollenbeck, Mathematics, Emporia State University

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    [Campus Map for Talks (PDF Format)]

    Almost every year multiple teams believe they have a legitimate argument to be college football’s national champion. Even with human input and complicated formulas, agreement is rare. We look at a model that is simple enough for discussion and use in the classroom, but accurate enough to provide a reasonable ranking of 120 college teams. The algorithm supplies opportunities for classroom investigation into the modeling process, convergence of iterative methods, and other topics in linear algebra. It also provides some illumination as to why the ranking problem in college football is so difficult. Variations of the algorithm will be discussed as time allows.

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  • Friday March 6
    Expository Talks Series
    Knots, Links, and the Jones Polynomial
    Chad Wiley, Mathematics, Emporia State University

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    [Campus Map for Talks (PDF Format)]

    Mathematical knots and links are abstract versions of the knots we encounter in our everyday lives (for example, the ones we tie in our shoelaces every morning). They are important in mathematical topology, but they are simple enough that they can be studied without a lot of advanced theory. In this talk, I'll give an introduction to knots and links and we'll see how to construct one of the most famous and important tools for studying them: the Jones polynomial.

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  • Friday March 13
    Expository Talks Series
    Coxeter-Dynkin Diagrams
    Liana Sega, Mathematics, UMKC

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    [Campus Map for Talks (PDF Format)]

    Coxeter-Dynkin diagrams are certain finite graphs that come up in many areas of mathematics, and reveal deep connections between apparently unrelated topics.  We discuss two such contexts. (1) One can associate to each finite graph a quadratic form (that is, a polynomial of degree 2 in several variables). We want to understand when these quadratic forms are positive definite, that is, when they take nonnegative values and only have the trivial solution.  Using some matrix theory, we will discover that the only positive definite quadratic forms occur for Coxeter-Dynkin diagrams.   (2) One can associate to a directed graph a collection of vector spaces and linear transformations, called a representation of the graph. We define a notion of indecomposability for such representations and we’ll see that the only directed graphs which have finitely many indecomposable representations are exactly those whose undirected graph is a Coxeter-Dynkin diagram.

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  • Friday April 17
    Expository Talks Series
    Two (yes two!) Short Talks by Students from Mathematics
    [Please come and support our students.]


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    [Campus Map for Talks (PDF Format)]

    (1) Cayley’s 1889 Formula Counting Trees:

    "There are nn-2 different labeled trees on n vertices.”


    Richard Harris, Mathematics Student, UMKC
    [Math 464 WI, History of Mathematics]


    (2) The 1966 Erdös-Renyi-Sós Proof of the Friendship Theorem:

    “Suppose in a group of people we have the situation that
    any pair of persons have precisely one common friend.
    Then there is always a person (the ‘politician’)
    who is everybody’s friend.”


    Cameron Buie, Mathematics Student, UMKC
    [Math 412, Advanced Analysis II]

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