Spring 2013 Program


Abstracts are listed at the end of the page. (link)

Friday, April 26


6:30-9:15 Registration - Olin Hall First Floor Lobby
$\$$10; Students, first time attendees and speakers free;
$\$$5 for MAA-NCS Section NExT members.
6:30-8:00 Book Sales - Olin Hall #219
NOTE:Starting this Spring, MAA members can now receive their section meeting discount on books online! The MAA is providing a coupon code that provides 35% off book purchases and is valid one week before and one week after your section meeting.

For your section, the coupon code is NOCENSP3 and is valid from Sunday, April 21 - Saturday, May 4, 2013. This code cannot be combined with any other offers or discounts from the MAA and is only valid at the online MAA Store.
Internet Access: wireless access throughout campus
Evening Session - Olin Hall #103, Dr. Ron Rietz, Presiding
7:00-7:20 Prof. Oksana Bihun, Concordia College, Moorhead
An Isochronous $N$-body Problem and Associated Diophantine Properties
7:25-7:40 Prof. Damiano Fulghesu, Minnesota State University, Moorhead
Generalized Peano Functions
7:45-8:00 Prof. Noureddine Benchama, Minnesota State Community & Technical College
Probability Independence: Not Nature, Structure of Events That Matter
8:10-9:00 Invited Lecture

John Holte, Gustavus Adolphus College
Random Arithmetic
9:00-10:15 Reception - Beck Hall Atrium

Saturday, April 27


8:15-11:00 Registration - Olin Hall First Floor Lobby
8:15-11:00
12:00-1:30
Book Sales - Olin Hall #219
Morning Session - Olin Hall #103, Dr. Mike Hvidsten, Presiding
9:00-9:05 Welcome
Dr. Darrin Good, Associate Provost, Dean of Sciences and Education, GAC
9:05-9:25 Prof. Brandon Rowekamp, Minnesota State University, Mankato
Planar Pixelations and Shape Reconstruction
9:30-9:50 Prof. Jeff Rosoff, Gustavus Adolphus College
Arbitrarily Unfair Card Decks and a Conjecture of Artin
9:50-10:10 Break - Olin Hall First Floor Lobby
10:10-10:30 Prof. Roger B. Kirchner, Carleton College
A Generalization of the Crease Length Problem
10:35-10:55 Prof. Christopher Phan, Winona State University
Cohomology Groups on $CW$-complexes from Noncommutative Algebra
11:00-11:50 Invited Lecture - Olin #103, Dr. Dan Kemp, Presiding

Prof. David Bressoud, Macalester College
Characteristics of Successful Programs in College Calculus: Preliminary Findings
12:00-1:00 Luncheon Three Crowns Room of C. Charles Jackson Campus Center
1:00-1:30 Business Meeting Olin Hall #103, Dr. Dan Kemp, Presiding
Afternoon Session I - Olin Hall #103, Dr. San Skulrattanakulchai, Presiding
1:35-1:55 Prof. Dan Singer, Minnesota State University, Mankato
A Problem in Combinatorial Linear Algebra
2:00-2:15 Prof. Jung-Han Kimn, South Dakota State University
A Study of the Space-Time Finite Element Approaches for the Gauge-Free Dirac Equation
2:20-2:35 John Hanenburg, Cost Estimator, Amateur Mathematician
Solving for the Measure of Multidimensional Regions Using a Generalized Surveyor's Formula
2:40-2:55 Prof. Shawn Chiappetta, University of Sioux Falls
Within an Epsilon: The Evolution of a Real Analysis Course
3:00-3:20 Vic Dannon, Retired
Khintchine's Constant and Lebesgue's Measure
Afternoon Session II - Olin #220, Dr. Baili Chen, Presiding
1:35-1:55 Siqi Zheng, Macalester College
Necessary and Sufficient Conditions for Benford Sequences
2:00-2:15 Isaac Garfinkle, University of Minnesota, Minneapolis
Subdividing Wheel Graphs Towards a Unit Distance Embedding
2:20-2:35 Sammy Shaker, University of Minnesota, Minneapolis
Noninteractive Guessing Games in Coding Theory
2:40-2:55 Gregory Tanner, South Dakota State University
Approximating Geodesic Paths
3:00-3:15 Christopher M. Galbraith, South Dakota State University
Modeling the Daily Volatility of the Dow Jones Industrial Average

Abstracts

Invited Addresses

John Holte, Gustavus Adolphus College, Random Arithmetic

What happens when random numbers in a sequence are combined by operations of arithmetic? We’ll look at the probability distribution of the digits we get when computations are performed—either exactly or by finite-precision computer—using fixed point, floating point, and symmetric level index systems. Some answers are unexpected. Some questions still need answers.

David Bressoud, Macalester College, Characteristics of Successful Programs in College Calculus: Preliminary Findings

In the fall term of 2010, the Mathematical Association of America undertook a large-scale survey of instruction of mainstream Calculus I in two- and four-year undergraduate programs. The surveys of course coordinators, instructors, and students involved 238 colleges and universities, 660 instructors representing almost 700 Calculus I classes, and 26,000 students, 12,000 of whom answered the initial student survey. This will be a preliminary report of some of the findings.

Contributed Talks

Noureddine Benchama, Minnesota State Community & Technical College, Probability Independence: Not Nature, Structure of Events That Matters

A dynamic example where we show that the identically described events can be independent or independent to show that describing events as independent based on their nature can be misleading.

Oksana Bihun, Concordia College, Moorhead, An Isochronous $N$-body Problem and Associated Diophantine Properties

We consider $N$-body problems: systems of differential equations that describe the movement of $N$ particles, subject to some forces, in a Euclidean space. We will discuss a solvable $N$-body problem that, under some conditions, is isochronous: all its solutions are periodic with the same period. We will explain how explicit formulas for the equilibria of this system allow deriving of several interesting Diophantine relations for matrices defined in terms of these equilibria. This is a joint work with Francesco Calogero and Ge Yi.

Shawn Chiappetta, University of Sioux Falls, Within an Epsilon: The Evolution of a Real Analysis Course

This talk will present the creation and subsequent changes to an undergraduate Real Analysis course at a small, liberal arts institution over the past 10 years. Successes and challenges will be discussed from both the faculty and students’ perspective, along with future plans.

Vic Dannon, Retired, Khintchine's Constant and Lebesgue's Measure

Khintchine’s Claim about his Constant, fails to hold for even one real number. That fact is not stated plainly anywhere. Instead, the infinitely many counter-examples to Khintchine’s claim are considered exceptions to the rule. But with no one number satisfying it, Khintchine’s rule is only a conjecture. We disprove Lebesgue’s Measure argument that underlies the Conjecture’s Proof. Thus, Khintchine’s Conjecture is a falsehood that demonstrates the non-credibility of the Lebesgue Measure theory. Posted to www.gauge-institute.org.

Damiano Fulghesu, Minnesota State University, Moorhead, Generalized Peano Functions

In this talk we will present a family of functions in two variables, whose second partial derivatives are defined at every point of the real plane but they do not commute. Such functions generalize a well known example described by the Italian mathematician Giuseppe Peano. This is an undergraduate project developed together with Seth Meyer (Math).

Christopher M Galbraith, Student, South Dakota State University, Modeling the Daily Volatility of the Dow Jones Industrial Average

The variance of returns on assets tends to change over time. One way of modeling this feature of the data is to specify the variance to follow some latent stochastic process; these are referred to as stochastic volatility models whose analysis involves Markov chain Monte Carlo sampling methods. In this presentation, a single move Gibbs sampling algorithm was implemented in Matlab. Using this algorithm, the Dow Jones Industrial Average was analyzed. Two separate versions of parallel code were then written to speed up the implementation of the algorithm: one that utilizes CPU nodes and another that uses a GPU device.

Isaac Garfinkle, Student, University of Minnesota, Minneapolis, Subdividing Wheel Graphs Towards a Unit Distance Embedding

A graph $G$ is unit-distance if all the vertices of $G$ can be embedded into the plane in such a way that two vertices are exactly one unit apart if and only if they are adjacent. In 2000, Gervacio and Maehara showed that all graphs can be made unit-distance by a graph operation called subdividing and that any graph can be made unit distance by subdividing every edge. Gervacio later gave an asymptotic bound for the subdivision number of complete and complete bipartite graphs, but a precise value for any infinite family of graphs is unknown. In this project, we provide an upper bound for the subdivision number of another well-known infinite family of graphs: wheel graphs. We prove that $\lceil n/5 \rceil$ subdivisions suffice to obtain a unit-distance graph from the wheel graph on $n+1$ vertices. We conjecture that our upper bound is tight.

Jung-Han Kimn, South Dakota State University, A Study of the Space-Time Finite Element Approaches for the Gauge-Free Dirac Equation

In this talk, we present some updated numerical results of space-time finite element approaches for the gauge-free Dirac equation. Our discretization approaches avoid any modification of to the Dirac operator. The results show the origin of the errors and a newer discretization approach can produce possible stable and accurate numerical approach for the Dirac equation.

John Hanenburg, Cost Estimator, amateur mathematician, Solving for the Measure of Multidimensional Regions Using a Generalized Surveyor’s Formula

In this presentation, I will show how the measure of any multidimensional polyhedra can be determined. This topic started when I was in the Math club SCSU and I took a long shot and applied a variation of the Surveyor’s Formula to determine the measure of a 4-dimensional hypertetrahedron. After I came up a solution, I realized, I could apply this concept to any multidimensional polyhedra where the coordinates of the vertices are known.

Roger B. Kirchner, Carleton College, A Generalization of The Crease Length Problem

Let $R$ be a convex region and $P_0$ a point in the plane. $R$ is “folded” so a boundary point $P$ coincides with $P_0$. If $S$ is a segment of the boundary, the crease length problem for $(R, P_0, S)$ is to find the shortest and longest creases formed when $P$ is in $S$. If $p$ parameterizes the boundary of $R$, the crease length function for $(R, P_0, p)$ is the length of the crease when $P = p(t)$. A Wolfram demonstration explores and solves crease length functions and problems when $R$ is a polygonal or elliptical region.

Christopher Phan, Winona State University, Cohomology groups on $CW$-complexes from noncommutative algebra

In 2009, Cassidy, Shelton, and the speaker introduced new cohomology groups associated with $CW$-complexes in order to test the Koszulity of some algebras introduced by Gelfand, et. al. Properties of these cohomology groups have been further explored in other papers. In my talk, I will briefly describe these groups and some of the topological insights they have provided.

Jeff Rosoff, Gustavus Adolphus College, Arbitrarily Unfair Card Decks and a Conjecture of Artin

Cheating at cards has long been a source of fascination, and has been immortalized in music, countless movies, and in other venues. A relatively subtle form of unfairness involves the actual number of cards in a deck. In this talk we give a measure of fairness of a card deck, and use a bit of abstract algebra and calculus to show that arbitrarily unfair decks sizes can be achieved. We also note how these ideas lead in a natural but surprising way to a famous conjecture in number theory.

Brandon Rowekamp, Minnesota State University, Mankato, Planar Pixelations and Shape Reconstruction

Any positive width defines a grid of square pixels on the plane. Using this grid, we can associate a set of pixels to any subset of the plane. When this happens some of the geometric information, such as lengths, may be distorted or lost. We may then ask, can we recover the original picture from its associated pixels? In this talk I will describe an algorithm which approximates the original picture in such a way that also approximates area, length, curvature and other geometric information.

Sammy Shaker, Student, University of Minnesota, Minneapolis, Noninteractive Guessing Games in Coding Theory

A common childhood activity concerns a game wherein one individual picks a number and another individual attempts to guess that number by asking yes-and-no questions. A mathematical generalization of this game is “Ulam’s game”, and one significant modification occurs when the responder lies. In this talk, a noninteractive Ulam’s game derivative is presented, where all of the questions’ answers are received simultaneously as binary vectors. These vectors make up a code, and the techniques of error-correcting codes are applied to analyze the code’s error-correction capabilities. The minimum distance of the code and its derivation are presented along with further abstractions.

Dan Singer, Minnesota State University, Mankato, A Problem in Combinatorial Linear Algebra

Given a forest of binary trees, we can construct a vector of associated binary trees. We prove that forests of binary trees of sufficient length give rise to linearly independent binary tree vectors. Our proof illustrates the acyclic digraph technique for constructing a non-singular lower-triangular matrix and reveals many interesting properties of binary trees.

Gregory Tanner, Student, South Dakota State University, Approximating Geodesic Paths

In order to find the exact geodesic path (shortest distance locally) along a curved surface requires the solution of a system of nonlinear differential equations. In all but the simplest geometries, these systems are impossible solve explicitly. In this talk, we will present methods of approximating geodesic paths using direct minimization of the arc length over families of curves. Special attention will be paid to methods of iterative refinement.

Siqi Zheng, Student, Macalester College, Necessary and Sufficient Conditions for Benford Sequences

What makes a sequence of real numbers Benford sequence? It turns out that a lot of sequences growing exponentially or faster are Benford sequences. However, being exponential is not sufficient to prove that the sequence is Benford. Therefore, more generalized sufficient conditions for Benford sequences are needed. In this paper we will explore some sufficient and necessary conditions for Benford sequences. Specifically, for any sequence $\{a_n\}$, we will explore the limit. We will show how this limit assists us in determining the Benfordness of $\{a_n\}$.

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