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Michigan MAA
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CMU Math Department
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Timetable
The final timetable and
full program with abstracts (~430K)
are now available. Printed copies will be available at the meeting.
Plenary Lectures
Sarah Greenwald, Appalachian State University
Good News Everyone! Mathematical Morsels from The Simpsons and Futurama
Did you know that The Simpsons and Futurama contain hundreds of humorous mathematical and scientific
references? What curious mathematical object is used as a bottle for beer in the 31st century? What happens
when Homer tries to emulate Thomas Edison? We'll explore the mathematical content and educational value
of some favorite moments along with the motivations and backgrounds of the writers during an interactive talk.
Popular culture can reveal, reflect, and even shape how society views mathematics, and with careful
consideration of the benefits and challenges, these programs can be an ideal source of fun ways to introduce
important concepts and to reduce math anxiety. For more information, check out SimpsonsMath.com and
FuturamaMath.com |  |
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Jennifer Quinn, University of Washington-Tacoma
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.
In this talk, we will investigate 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. |
Jennifer Szydlik, University of Wisconsin-Oshkosh
Teaching to Inspire Mathematical Thinking
Suppose you have twelve identical coins. However exactly one of them is counterfeit and weighs either more or less (you are not sure which) than the rest. You have your trusty balance scale. How many weighings are needed to guarantee that you will identify the counterfeit coin? What if you have n identical coins to start?
Our community, the mathematical community, holds a set of values, mathematical tools, and distinctions about language that allow us to learn new mathematics and to solve problems. We value careful definitions of objects, deductive arguments, and shared notations. We use logic, create examples and counterexamples, consider extreme or trivial cases, and make models for problems. We distinguish necessary from sufficient conditions, pay close attention to quantifiers, and are sticklers for careful language. This is our culture. I advocate for making this culture transparent to our students both in the way we speak about mathematics and in the way we do mathematics with them in class. In this presentation I will talk about ways we might do both, and I will provide samples of problems and activities that inspire mathematical thinking (and if you get bored, you can work on the problem and pretend to listen).
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Daniel Velleman, Amherst College
An Introduction to Constructive Mathematics
Almost all mathematicians agree about what methods of reasoning are acceptable in mathematics--almost all, but not quite all. A small group of mathematicians practice a kind of mathematics known as constructive mathematics. Constructive mathematicians do not accept all of the laws of logic that most mathematicians use. For example, they do not accept the Law of Excluded Middle, which says that for any statement P, either P or not-P is true. Since constructive mathematicians do not use the same laws of logic as other mathematicians, the theorems they prove are also different. In this talk, I will discuss the philosophical motivation for constructive mathematics, and then I will give some examples to illustrate the methods and theorems of constructive mathematics. |
Gerard Venema, Calvin College
Dimension, Fractals, and Wild Cantor Sets
The discovery of unexpected examples forced a reexamination of the concept of dimension in the early twentieth century. Several competing definitions of dimension emerged. They do not all give the same answer when applied to a subset of Euclidean space and do not even necessarily yield integers as answers. (Spaces whose dimension varies, depending on which definition is used, are called fractals.)
In this talk I will take a quick look at the examples mentioned above and review the definitions of topological dimension
and Hausdorff dimension from an elementary point of view. A fundamental theorem states that every compact metric space
contains a Cantor set whose Hausdorff dimension equals that of the given space, so it is natural to focus on examples of
Cantor sets. There is a simple construction that yields Cantor sets in  n of dimension s
for every s in the range 0 ≤ s ≤ n.
Antoine's necklace is a classic example of a wild Cantor set in 3;
I will explain why the Hausdorff dimension of an Antoine's necklace Cantor set must always be at least 1 and
how to construct an Antoine's necklace of Hausdorff dimension s for every s in the range
1 ≤ s ≤ 3. This is a special case of a much more general theorem that relates Hausdorff dimension to
embedding dimension and implies that every wild Cantor set is a fractal.
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Local Invited Talks
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Ryan Hutchinson, Hillsdale College
Determinantal Conditions in Coding Theory
In this talk, we begin with a brief overview of some main ideas of the theory of linear block codes, focusing on determinantal conditions characterizing codes having optimal minimum distance and looking at some constructions of such codes. We then move to convolutional codes, which may be viewed as a generalization of linear block codes, and see what the analogous determinantal conditions characterizing optimal distance properties look like in this case. This leads to the notion of so-called superregular matrices, for which there is presently no known construction. |
Christopher Moseley, Calvin College
Sub-Finsler Geometry in Dimensions Three and Four
Sub-Finsler geometry is a generalization of Riemann-Finsler geometry in which velocity vectors of curves are subject to linear constraints. Such constraints arise naturally in studies of simple mechanical systems. This talk will introduce the essential ideas of sub-Finsler geometry and geodesics of sub-Finsler three-manifolds and four-manifolds.
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Mark Pearson, Hope College
Necklaces, Symmetry, and Irreducible Representations of Wreath Products
The problem of finding the complete set of irreducible representations of wreath products of
cyclic groups can be solved using necklaces. Each necklace in the set of k -bead, n -color
necklaces that is distinct under rotation can be used to form a degree-k representation of
Ck Cn. If a k -bead, n -color necklace has
s -fold rotational symmetry, then the degree-k
representation formed from that necklace will reduce into s irreducible representations of degree
k/s. The set of distinct k -bead, n -color necklaces contains each
irreducible representation of CkCn exactly once. |
Katrina Piatek-Jimenez, Central Michigan University
Factors that Influence Career Aspirations of Women Mathematics Majors
The national trend shows that although women make up nearly 50% of undergraduate mathematics majors in the U.S., the proportion of women earning graduate degrees in mathematics or entering mathematical careers is much smaller. So why do so many women choose to major in mathematics and then leave the field? In order to address this question, I conducted a series of in-depth interviews with 12 women mathematics majors. Through these interviews I explored what motivated these women to choose mathematics as a major and what is influencing their future career plans. In this talk I will share some of my results and will discuss some implications of the findings. |
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Shelly Smith, Grand Valley State University
The Puzzling Mathematics of Sudoku
Sudoku is the latest craze in puzzles, and is played by entering digits from 1 to 9 to complete a partially filled 9 x 9 grid so that each digit appears exactly once in each row, column, and 3 x 3 subgrid. While no math is required to play the game, discrete mathematics is a useful tool for studying many aspects of Sudoku. There are numerous variations of the familiar game that have different additional requirements instead of the subgrids, and these variations make Sudoku a rich topic for a variety of investigations accessible to students. We will discuss some of the mathematics that can be used to study Sudoku, including equivalence relations, inclusion-exclusion, and rook polynomials. |
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