Julie Allen, Missouri Western State University

Using Geometers Sketchpad and Poincare Models to Illustrate the Parallel Postulate

In his infamous works, Elements, Euclid defined 5 axioms that would later be known as Euclidian geometry. I will be discussing the history of Euclid and his 5 axioms. I will also be showing what happens when you change the 5th axiom, also known as the parallel postulate, and will compare objects in Euclidian geometry to those in Hyperbolic geometry.

Kevin Anderson, Missouri Western State University"

Why I hate tick-tack-toe

Dale Bachman and Nicholas Baeth, University of Central Missouri

A college algebra course for honors students,

At the University of Central Missouri, the primary general education mathematics course has recently been redesigned from the ground up to meet the needs of the honors student. The goal was to design a course for the more motivated student in which the development and general viewpoint of various topics have precedence over rote memorization of procedures and formulae. Thus, an interactive, cooperative, experiment-based course was developed to guide the students

through refinement of their own problem solving skills. Though the topics of the course remain the same as the traditional college algebra course, instruction is neither lecture- nor readings-based, but relies instead on team-oriented explorations. In this presentation, the philosophy and methodology of the course will be explored, with specific examples of explorations and testing methods. A comparison between standardized test scores of students in the new course and those in a traditional college algebra course will be made.

Mathematical models for inventory

Many companies use mathematical models for inventory policies to help maximize profits and prevent unused merchandise. The models assist the business in determining the optimal times and amount of merchandise to produce or order to achieve the lowest costs. There are many components of inventory models, including the costs of ordering or manufacturing, holding or storage costs, unsatisfied demand or shortage penalty costs, revenues, salvage costs, and discount rates. We studied several models used to determine the optimal values. In this talk, we will show how inventory modeling can lower costs and, in return, save a company money. 

Nathan Bloomfield, Missouri State University

On the isomorphism classes of zero divisor graphs

To each commutative ring we can associate a graph whose vertices are zero divisors and such that two vertices are adjacent if their product is zero. The author is engaged in completing a classification of orientable genus 2 zero divisor graphs; in general this is a computationally difficult task. However, we can use some ideas from the theory of semigroups to detect isomorphisms among these graphs and reduce the amount of work we have to do. In this talk, we give an overview of this technique.

Suppose you would like to build the four walls of a right pyramid with height h and square base with sides b.  The walls will be made from sheets of material (say particle board) of a given thickness.  I will determine the exact dimensions of the four sides.  In particular, I will determine the miter angles needed to have the four sides fit together properly.  The solution is accessible to anyone who is familiar with the dot product and the equations of planes in three dimensions.

Hang Chen and Curtis Cooper, University of Central Missouri

How hard is Sudoku, part I & part II

We see Sudoku in many publications, newspapers, journals, calendars, web sites, and even Sudoku books. Each Sudoku is labeled with a difficulty level, such as very easy, easy, medium, hard, very hard, evil, diabolically hard, beware! very challenging, the ultimate challenge!, etc. We found many of these classifications do not reflect the true difficulty levels. We try to investigate the rules to solve a Sudoku and therefore better understand how difficult a Sudoku is.

Joseph Dence, University of Missouri - St. Louis

J.W.L. Glaisher and Euler's constant

Certain equations due to Euler, which were presented in a historical context by J.W.L. Glaisher and re-presented last year in Bill Dunham’s latest book on Euler, require corrections. This will be illustrated with one particular equation; its efficiency in the estimation of a value for r will also be demonstrated. 

Joseph Dence, University of Missouri - St. Louis

The sequence of generalized Euler constants,{r_k}_{k=0, .., ¥}, is important because of its connection to the Riemann zeta function. It will be shown at the level of introductory calculus how to obtain modest bounds on the particular constant r₁, whose value is approximately -0.072816.

David Ewing, University of Central Missouri

What geometry can exit on the surface of a Hubcap, a chocolate "Kiss", a cowboy's saddle, or a "Donut"?  Learn to teach (Euclidena) Geometry more effectively by having your students create their own geometries on these surfaces.  Serveral student-created, classroom-tested lessons will be demonstrated and include 'creating definitions', 'forming shapes', formulating theories, and proving/disproving theories. 

David Garth, Truman State University

Numeration system and fractal bases

It is well-known that every natural number can be written uniquely as a sum of nonconsecutive Fibonacci numbers. This gives rise to the Fibonacci representation of an integer as a string over the set f0; 1g that contains no consecutive ones. These representations can be used to construct the famous Wythoff array, from which an associated fractal sequence can be constructed. An infinite sequence in which every positive integer appears infinitely often is a fractal sequence if the sequence obtained from removing the first occurrence of each integer results in the original sequence. In this talk we consider an abstract numeration system of the integers as any subset of strings over {0; 1}. We show that every such numeration system that has a base sequence gives rise to a fractal sequence in a similar manner to the Fibonacci base. This result was obtained as part of an undergraduate research project. We also discuss other potential problems for future undergraduate research that are suggested by this work.

James Guffey, Truman State University

An Introduction to the Randomized Response Technique (or How to Ask About Sex and Get Honest Answers)     

In 1965, Stanley Warner published an approach for gathering sensitive data. That is, for a variety of reasons, respondents may become uncooperative in order to avoid some kind of stigma which may be associated with survey questions. Applications throughout the years include asking taxpayers if they cheat on their returns, students if they cheat on exams, or homeowners if they have illegal extension telephones. This talk will introduce the basic idea and discuss possible variations that have been proposed. An explanation of how the technique works will be provided for at least one variation.

William Hall, University of Central Missouri

21+3 blackjack casino game

In this talk we are evaluating a popular casino game 21+3 Blackjack. By using basic knowledge of probability the expected number of wins and what factors could affect this expected number are discussed.

Poker is a game of probability and the human element. The probability side of poker can be both hard and complex but is much easier to describe than the human element. Through the use of combinations and proper partitioning, many hand outcomes can be properly predicted.

Steve Klassen, Missouri Western State University

A student investigation of the Kolmogorov-Smirnov Test statistic

An introduction of the Kolmogorov-Smirnow test statistic for testing whether a random sample is approximately normally distributed, followed by a computational investigation of extending the test statistic to joint distributions. This work is the result of a student project using simulated random samples from a joint normal distribution to explore the distribution of the corresponding K-S test statistic.

Chad Klein, Missouri Western State University

Encryption of messages using chaotic sets of differential equations

This talk will introduce methods on how to encode messages using Chaotic waves.

Designer primes: you can have your own personal prime number!

Suppose N is an integer that has a personal meaning to someone (marriage date, telephone number, social security number, etc.). The presenter will show how the digits of N can be embedded in a prime number, thus making it a personalized prime number. A recent result on the distribution of prime numbers will be used to show that this can always be done, but the proof will involve only elementary algebra.

Aaron Lewis, Missouri Western State University

Using Geomview to illustrate 3-dimensional animation.      

This talk will focus on how you can use simple matrix algebra to make a 2-dimensional rendering program, like Geometer's Sketchpad, animate 3-dimensional shapes.

Marlgorzata Marciniak Westminster College

On the Hartogs phenomenon

We say that the Hartogs phenomenon holds in a complex manifold X if for every compact set K and for every holomorphic function f on a connected set X \ K, there exists a holomorphic extension of f on X.  I will describe the Hartogs phenomenon in Cⁿ for n ³ 2 and show some elementary examples of smooth complex manifolds and explain why the phenomenon does or does not hold in them.

Rhonda McKee* and Lianwen Wang, University of Central Missouri

Boundedness of solutions of nonlinear second order differential equations

The monotonicity and boundedness of solutions for a class of nonlinear second order differential equations are discussed. Firstly, it is proved that all solutions of differential equations are eventually monotonic and can be extended to infinity. Then, several necessary and sufficient conditions for boundedness of all solutions are established. Finally, some examples are provided to illustrate the application of the obtained results.

Hamiltonicity of subgroup graphs

The subgroup structure of groups lends itself to graph representation, and an area of ongoing research is determining how group structure is related the structure of its subgroup graph. In particular we are investigating which groups have graphs with Hamiltonian circuits. We will present results for cyclic groups, dihedral groups, and certain p-groups, and discuss areas of further research.

Timothy L. Miller, Missouri Western State University

Using the TI-89 to Find Both Series Solutions to a Second Order Differential Equation at a Regular Singular Point           

TI-89 programs will be provided and demonstrated to find partial sums of Frobenius series solutions to 2nd order DE for all possible exponents of the DE.

Jeffrey Poet, Missouri Western State University

Bacterial computing: solving a Hamiltonian path problem in vivo

In 1994, Leonard Adleman began the field of DNA computing by solving a 7-node hamiltonian path problem in vitro. A team of student researchers and faculty mentors in math and biology from Missouri Western and Davidson College used synthetic biology techniques to provide a proof-of-concept for solving Adleman's hamilton path problem inside a living cell. This talk is appropriate for undergraduate students.

Jeffrey Poet, Missouri Western State University

Proofs that really count: some of my favorites

In the book Proofs that Really Count, by Art Benjamin and Jenny Quinn, many mathematical identities are proven with combinatorial arguments. The point of the book is not necessarily to bring to light proofs of new theorems but to provide a new perspective in thinking about existing theorems. To keep this on the lighter side, the examples given will be primarily binomial coefficients. This talk is appropriate for undergraduate students.

Some Finite Groups with Eulerian Subgroup Graphs (jointly with Joseph P. Bohanon) 

We investigate when the subgroup graph of a finite group is eulerian (i.e. when one can drawn it (beginning and ending at the same point) without lifting pencil from paper and without retracing an edge.

Phil Ryan, Truman State University

A mathematical model for the Battle of Trafalgar

In 1916, the English engineer, F.W. Lanchester, made the first attempt to quantify the effect of aircraft on modern warfare. His work included a mathematical analysis of how the smaller British naval fleet under Lord Nelson was able to defeat the French-Spanish forces at the Battle of Trafalgar in 1805. I will present a module that I have adapted from this for use in a Calculus I class.

Stephen Schroeppel II and Pradeep Singh*, Southeast Missouri State University

Life-stress relationship testing for a homogeneous Poisson process in reparable systems

In accelerated life testing, a greater stress is placed upon an object than an initial design stress. The relationship between the life of the object and the stress applied is known as the life-stress relationship. This study examines a simple homogeneous Poisson process with an assumed linear life-stress relationship, proposes a test, and uses the Monte Carlo method to determine if the test controls the Type-I error rate to some nominal value α.

Renee Scott, Northwest Missouri State University

Groups and subgroups through patterns       

This talk will present designs created by the author that demonstrate and illustrate the differences between the symmetry group of a pattern and the pattern type. Some of the subgroups of the symmetry groups under the different pattern types will be shown along with some interesting patterns that occur.

Jason T Shaw, Truman State University

Strictly increasing functions with derivative zero a.e.           

A strictly increasing function that has a vanishing derivative almost everywhere was constructed by Lajos Takacs in a paper published in the American Mathematical Monthly. This function will be presented and other such functions will be mentioned such as Minkowski's Question Mark Function and the Riesz-Nagy singular function. 

Mary Shepherd, Northwest Missouri State University

Triumphs and challenges in teaching a student to read mathematics

Instead of observing the reading difficulties encountered by many students reading a single passage in a mathematics textbook, this study takes one student and has the student read many passages throughout the second half of the fall 2007 semester.  Observations are made as to improvement the student made in reading and the difficulties encountered.

Teaching math history without prerequisites

Imagine teaching a liberal learnings course on the history of mathematics which is open to all students (NO math requirements)! How can this be done with such a seemingly fatal handicap? This talk presents one person’s methods, experience, and observations.

Laura Smith, Northwest Missouri State University

Beads on a Necklace: An Exploration of Cyclic Sum Sets    

In the September 2007 issue of the College Mathematics Journal, Roger Zarnowski posed a series of problems relating to the relatively new mathematical concept of a cyclic sum set. This presentation will introduce the definition of a cyclic sum set and then include a variety of proofs as answers to Zarnowski’s problems. In addition, extensions to the original problems will be made as we examine whether it is possible to have a cyclic sum set of order greater than 2.

Some properties of semi-closure spaces

Let X be a nonempty set and P(X) the power set of X. A single-valued function c of P(X) into P(X) is called a semi-closure operator on X if it satisfies the following conditions:

C3. for each A, B Î P(X), A Ì B implies c(A) Ì c(B), and

C4. c(A) = c(c(A)) for each A Î P(X).

The pair (X; c) or simply X is called a semi-closure space. In this paper, we will discuss some properties of semi-closure spaces.

Jarod Stockton, University of Central Missouri

On infinitely nested fractions

Some properties of infinitely nested fractions are discussed. Using convergence of sequences from Calculus we prove that most infinitely nested fractions are well defined and we also are able to evaluate these well-defined infinitely nested fractions. Furthermore, we show that all transcendental numbers such as e cannot be the value of any infinitely nested fractions.

Brandon Turner, Missouri State University

The mathematical process of classification

The paper will focus on one of the most computationally intensive types of problems in industrial-organizational psychology: classification of individuals among groups. The paper will look at the bivariate case as well as the p-variate case. The paper also covers the probabilitydistribution function for particular scores and ranges of scores. The last section will explore the probabilities behind classification as well as the probabilities of misclassification

Haohao Wang, Southeast Missouri State University

Axial moving planes and singularities of rational space curves

We derive an one-to-one correspondence between the singular points of rational space curves and the axial moving planes that follow these curves. We also provide a method of detecting singularities by $\mu$-basis.

Lianwen Wang, University of Central Missouri

What's the chance to win a game - a statistical model of scoring some sporting events

The element of chance plays an important role in many sporting events. In this talk we examine the winning chance of some sporting events including long jump, discus, shot put, and other games. Both the best-of-three-attempts and the sum-of-three-attempts scoring systems are discussed.

This is a fun little talk that will highlight how differential equations can be used to improve your life in unusual places. Only a brief understanding of calculus will be needed. The presenter will show you how to set up a mathematical model and explain the benefits of bifurcations.

Carrie A. Whittle, Missouri State University

Bourbaki Ideals: A Worked Example

Bourbaki’s theorem states that if M is a finitely generated torsion-free module of rank n over a Noetherian integrally closed domain, then M has a free submodule F of rank n – 1 such that the quotient M/F is isomorphic to an ideal. In this talk we compute several examples of Bourbaki ideals for specific modules over the polynomial ring in two variables with rational coefficients.

12 squares = 1 stellated octahedron

Participants will be provided 12 squares of paper and instructed to fold and assemble the paper to create a stellated octahedron. The same folds of squares can be used to create cubes and stellated icosahedra, all of which make attractive, intriguing objects.

Aaron Yeager, Missouri State University

On the radio antipodal chromatic number of C_4k

Radio antipodal labeling is a variation of Hale's channel assignment problem, in which one seeks to assign positive integers to the vertices of a graph G subject to certain constraints involving the distances between the vertices. Specifically, a radio antipodal labeling of a connected graph G is an assignment of colors (positive integers) to the vertices of G, with x Î V(G) assigned c(x), such that d(u, v) + ïc(u) - c(v) ï ³ diam(G) for every two distinct vertices u and v of G. The span of a radio antipodal labeling, ac(c), is the maximum integer assigned to a vertex. The radio antipodal chromatic number, ac(G), of a graph G is the minimum span, taken over all radio antipodal labelings c of G. This paper establishes the bounds for the radio antipodal chromatic number of the cycle graphs of order 4k for k ³ 3 (i.e. of C_4k).