The third meeting of the Carolina Mathematics Seminar took place at the University of South Carolina Sumter, Sumter, SC. This is a list of our speakers, titles and abstracts.
Anthony Coyne (USC Sumter)
Title: Mathematics, Metaphysics, Morality.
Abstract: Reflection on what Plato says about the place of the study of mathematics in the education of the guardians provides a sharp contrast with what is happening as USC approaches revising general education. In particular, Plato does not advocate the study of mathematics because it leads to any of the learning outcomes identified by USC. USC hopes students will be able to apply the methods of mathematics, statistics, or analytical reasoning to critically evaluate data, solve problems, and effectively communicate findings verbally and graphically. Plato hopes instead for more important psychological, metaphysical, moral and political outcomes.
Wei-Tian Li (USC Columbia)
Title: Lubell Function and Forbidden Subposets.
Abstract: In 1928, Sperner proved that the size of a largest antichain in the Boolean lattice Bn is equal to n choose n/2. Since then, the results on largest sizes families not containing some specific posets were discovered gradually. The well-known inequality, the LYM-inequality, was individually used by Lubell, Yamamoto, and Meshalkin to reprove Sperner's Theorem. We will introduce the Lubell function, derived from LYM-inequality, and use it to estimate the maximal sizes of families do not contain some posets P. (This is a joint work with Jerrold R. Griggs and Lincoln Lu.)
Wei-Kai Lai (USC Salkehatchie)
Title: Banach Space, Riesz Space, and Banach Lattice.
Abstract: In many Functional Analysis books, we can find the following definitions: a Banach space is a complete normed linear space; a Riesz space is an ordered vector space with the lattice structure. Rephrasing them with earthly language, you will be able to measure the distance of two objects in a Banach space and you will be able to compare which one is bigger among two objects in a Riesz space. In this talk, I will introduce some basic examples of these two spaces, and together with their properties. Finally, I will introduce a special space with both structures, called Banach Lattice.
Andrew Yingst (USC Lancaster)
Title: Partition Polynomials And Their Uses (Part II).
Abstract: If a coin has probability x of coming up heads, and E is a set of possible outcomes of finitely many tosses of this coin, then the probability of event E is a polynomial in x, referred to as a partition polynomial. We define and characterize these polynomials, and discuss some questions of dynamics on Cantor space that this characterization can be used to answer.
Charlie Cook (USC Sumter)
Title: The “Magicness” of Powers of Some Magic Squares.
(This paper is in collaboration with Michael R. Bacon and Rebecca A. Hillman)
Abstract: Several Powers of a variety of additive magic squares are computed and conditions which guarantee that they are also magic are investigated.
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