(U=Undergraduate, G = Graduate, A = Alumnus, F = Faculty)

Room 105: Time: 8:45-9:05
Mr. Joe Frye, Troy University, Troy campus (U)
Title:  Euler’s theorem

Abstract:
Euler’s theorem for graph theory states that the formula v – e + f = 2 holds true for any planar connected graph with v vertices, e edges, and f faces.  There are some basic definitions that will be covered in order to develop the basic understanding needed to understand the significance of this elegant theorem.  We then present a proof of the theorem.

Room 107: Time: 8:45-9:05
Mrs. Asuka Yuyama Norris, Troy University, Troy campus (A)
Title: Why Japanese are good at math

Abstract:
I will explain how Japanese work on basic pre-calculus math in different ways.

Room 105: Time: 9:10-9:30
Dr. Vitaly Voloshin, Troy University, Troy campus (F)
Title: Splitting-contraction as generalization of connection-contraction

Abstract:
We will show an example how introducing a new concept brings a new look at some old concepts.

Room 107: Time: 9:10-9:30
Ms. Kristine Lurwig, Troy University, Troy campus (U)
Title: Calculus, area, and volume
Abstract:
We will be deriving the area formula of a circle and the volume formula of a sphere using double and triple integrals.

Room 105: Time: 9:35-9:55
Peter Johnson, Auburn University (F), and Vitaly Voloshin, Troy University
Title: Coloring problems for mixed geometric hypergraphs

Abstract:
A hypergraph is a pair (V,E) in which V is a set, the "set of vertices", and E is a set of subsets of V, the "set of hyperedges".  Each subset of V in E has at least two elements.  There are different kinds of hypergraph coloring problems, but the most common is of this form:  How many colors do you need to color V (one color to a vertex) so that no hyperedge in E is monochromatic?

A mixed hypergraph can be thought of as two or more hypergraphs with the same vertex set, and with pairwise disjoint sets of hyperedges.  We will confine ourselves to two disjoint sets of hyperedges, E and F, and coloring problems of this form:  with what numbers of colors  can you color V so that no hyperedge in E is monochromatic, but every hyperedge in F is monochromatic?  Notice that the satisfying the first requirement becomes easier, the more colors you can use, but using more colors may make it harder to satisfy the second requirement.

Here is a problem exemplifying the problems referred to in the title:
For which d > 0 is it possible to color the real line so that points a distance 1 apart will be colored differently, while points a distance d apart will have the same color? And when such a coloring can be accomplished, with what numbers of colors can it be done? More questions and a scattering of answers will be given.

Room 107: Time: 9:35-9:55
Ms. Amanda North, Troy University (U)
Title:  Alfred Nobel and nitroglycerin
Abstract:

The lecture will cover the life of Alfred Nobel, his many accomplishments, and his studies of nitroglycerin and its properties.  It will also include a history of the Nobel prizes and its recipients. 

Room 105: Time: 10:00-10:20
Sibel Ozkan (G), Auburn University  and Chris Rodger of Auburn University
Title: Partial Hamilton decompositions of complete graphs with no 2-factor in the leave
Abstract:
A 2-factor of a graph G is a 2-regular spanning subgraph of G, and a Hamilton cycle is a connected 2-factor. Also, a partial Hamilton decomposition of a graph G is a partition of some of the edges of G into edge-disjoint Hamilton cycles. The edges of G not used in the decomposition form the "leave". Partial decompositions of complete graphs into Hamilton cycles with no Hamilton cycle in the leave, and into 2-factors with no 2-factor in the leave have been done in previous studies by D.G. Hoffman, C.A. Rodger, and A. Rosa. In this paper, by using amalgamation technique, we find necessary and sufficient conditions for the existence of partial Hamilton decompositions of complete graphs with no 2-factor in the leave.

Room 107: Time: 10:00-10:20
Mr. Ralph Wilson, Troy University (U)
Title:  Moire fringes and interactive emergences

Abstract:
An introduction to the phenomena of Moire fringes will be given, and
along with a few a priori generalizations.

Room 107: Time: 11:00-12:00
Invited Lecture by: Dr. Atif Abueida of The University of Dayton

Room 105: Time: 1:15-1:35
Mr. Michael Tiemeyer (U), Auburn University (joint work done with Elizabeth Billington of The University of Queensland (Australia) and Chris Rodger of Auburn University)
Title:  Two-factorizations of a complete multipartite graph in which each component                            is a four cycle
Abstract:
Each complete multipartite graph can be given a unique name:  K(a,p,L1,L2), where a is the number of vertices in each part; p is the number of parts; L1 is the number of edges connecting two vertices of the same part; and L2 is the number of edges connecting two vertices in different parts.  Given these four parameters, does a two-factorization exist for the given graph, where each component is a four-cycle?  Are there necessary and sufficient conditions for such a construction?

Room 107: Time: 1:15-1:35
Mrs. Diane Porter, Troy University, Troy campus (F)
Title:   AMSTI 2006
Abstract:
The Alabama Math, Science, and Technology Initiative, AMSTI, is the Alabama Department of Education's initiative to improve math and science teaching statewide.  AMSTI is research-based and incorporates best practices for math and science teaching in K-12 schools.   The initiative provides three basic services: professional development, equipment and materials, and on-site support.   Troy University was recently designated as an AMSTI site and as such will be the center for implementing the AMSTI initiatives in Southeast Alabama beginning in 2006.

Room: 105: Time: 1:40-2:00
Mr. Carl S. Pettis (Major Professor: Dr. Charles C. Lindner), Auburn University (G)
Title:  The triangle intersect problem for hexagon triple systems

Abstract:
A hexagon triple is the graph

and a hexagon triple system is an edge disjoint decomposition of 3kn into hexagon triples.  Note that a hexagon triple is the union of 3 triangles (= triples).  The intersection problem for 3-fold triple systems has been solved for some time now.  The purpose of this paper is to give a complete solution of the intersection problem for 3-fold triple systems each of which can be organized into hexagon triple systems.

Room 107: Time: 1:40-2:00
Ms. Leann Sanders, Troy University, Troy campus (G)
Title: The relationship between music and mathematics in selected examples

Abstract:
This presentation will provide an introduction to several areas in which the fields of music and mathematics intersect, with special emphasis given to selected composers and works of the modern period of music history (c. 1900 - present). 

Room 105: Time: 2:05-2:25
Wenjing Li, The University of South Alabama (G)
Title:  Quasigroups and Steiner triple systems

Abstract:
Quasigroups are non-associative binary algebraic structures. Quandle is an idempotent right distributive right quasigroup.  Several combinatorial structures such as Steiner triple systems, Latin squares give rise to non-associative binary algebraic structures. We will discuss some of their properties and give several examples illustrating this.

Room 107: Time: 2:05-2:25
Ms. Amber De More (joint work with Scott Bachman), Austin Peay State University (U)
Title:  An interrelation between statistics, derivatives, and orthogonal polynomials

Abstract:
There are many definitions of a derivative; we will explore a generalized version of the Lanczos derivative, researched by Paul Fishback and Nathan Burch, which we call the least-squares derivative. We will show how least-squares derivatives can be written in statistical terms as well as in terms of orthogonal polynomials. We will also explore the relationship between orthogonal polynomials and statistics. While this talk is infused with statistics, it is still appropriate for those who have not taken a statistics course.

  Room 105: Time 2:50-3:10
Dr. John Boncek, Troy University, Montgomery campus (F)
Title: Having fun with the witch of Agnesi

Abstract:
The Witch of Agnesi is a plane curve studied by the Italian mathematician Maria Agnesi in the mid-18th century.  In this presentation, we will show how the Witch can be used as a starting point for developing lessons in analytic geometry, parametric equations, trigonometry, and elementary calculus.

Room 107: Time: 2:50-3:10
Dr. Ken Howell, The University of Alabama in Huntsville (F)
Title:  The UAH graduate program in mathematics
Abstract:
Information about the graduate program in mathematics at The University of Alabama in Huntsville (UAH) will be given for students.

Room 105: Time: 3:15-3:35
Dr. Jun Zhang, Troy University, Troy campus (F)
Title:  An automatic proof of Euler’s formula

Abstract:
In this information age, everything is digitalized. The encoding of functions and the automatic proof of functions are important. We will discuss the automatic calculation for
Taylor expansion coefficients, as an example, it can be applied to prove Euler's formula automatically.

Room 107: Time: 3:15-3:35
Dr. Sergey Belyi, Troy University, Troy campus (F)
Title:  Teaching and learning mathematics with MERLOT

Abstract:
The Multimedia Educational Resource for Learning and On-Line Teaching (MERLOT) is a high quality collection of interactive learning materials, assignments, reviews, and people. MERLOT is also a national network of online discipline communities that selects and peer-reviews learning materials in their specific disciplines. Today MERLOT serves as a national gateway to web-based peer-reviewed learning materials. MERLOT Mathematics is a free and open resource designed primarily for faculty and students in higher education. Most mathematics faculty do not have the time to develop electronic content yet are looking for ways to enhance and improve their teaching. MERLOT provides faculty with a way of easily and cheaply incorporating material into their course and syllabus. Whether it's using MERLOT learning materials with students, creating MERLOT-related student assignments, or creating Personal Collections of materials for you or your department, MERLOT has much to offer in the way of helpful resources.

Room 105: Time: 3:40-4:00
Ms. Kim Harris, Troy University (U)
Title: Paul Erdos: the life, the legacy

Room 107: Time: 3:40-4:00
Dr. Cornelius Pillen, The University of South Alabama
Title: Graduate program in mathematics at The University of South Alabama

Abstract:
This is a short introduction of the graduate program in mathematics and statistics at the University of  South Alabama with ample opportunity to ask question concerning the program.

Room 105: Time: 4:05-4:25
Ms. Erin Beutjer, Troy University, Troy campus (U)
Title: Puzzles and number tricks

Abstract:
Basic arithmetical tricks including casting out nines, multiplication tricks,  and sine & cosine of special angles. Puzzles including "the extra square," Tangrams, Tessellations, and Sudoku.

Room 105: Time: 4:05-4:25
Mr. Charles Thompson, Troy University, Troy campus (U)
Title: Matrix multiplication
Abstract:
Essentially I am going to discuss in detail what exactly it took too explain to a computer how matrix multiplication is done. Hopefully, this will be a way to make us all more aware of what exactly goes into the process, all the things our mind handles with ease and with such speed. To have to break it down into the simplest of steps is actually quite challenging.

Room 105: Time: 4:30-4:50
Dr. Pat Rossi, Troy University, Troy campus (F)
Title: A Musical Application of Graph Theory
Abstract:
In “up tempo” Jazz Standards, the style of bass line is called a walking bass line. The speaker presents a graph-theoretic model for constructing an optimal walking Bass Line.

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