Fall 2011

All talks begin at 4PM unless otherwise noted. To carpool to Platteville from Loras, meet outside Hennessy 210 by 3:15 on the afternoon of the talk.

If you would like to give a talk at Loras or have questions regarding the colloquium, contact Angela Kohlhaas. Titles and abstracts from previous semesters can be viewed here.

Date | Location | Speaker | Title |
---|---|---|---|

Wednesday September 14 |
Loras College Hennessy 350 |
Travis Peters Iowa State University |
Fun with Zero Forcing |

Thursday September 22 |
UW-Platteville Ottensman 222 |
Leonida Ljumanovic UWP |
The Von Neumann Ordinals |

Thursday September 29 |
UW-Platteville Ottensman 222 |
Benjamin V.C. Collins UWP |
Euler's Polyhedron Formula |

Friday October 7 |
Loras College Hennessy 350 |
Jacob Heidenreich Loras |
Von Neumann Ordinals II: To Infinity and Beyond |

Thursday October 13 |
UW-Platteville Ottensman 222 |
Pam Peters UWP |
Beyond Euclid, Euler, and Descartes: A Survey of the Women in Math |

Wednesday October 19 |
Loras College Hennessy 350 |
Mary Bohlke, Loras Katie Burke, Loras |
REU Reflections |

Thursday October 27 |
UW-Platteville Ottensman 222 |
Irfan Ul-Haq UWP |
Am I Part of the Solution, or Part of the Problem? |

Friday November 4 |
Loras College Hennessy 350 |
Matt Rissler Loras |
Stochastic Modeling: What Do We Do When Probabilities Change? |

Wednesday November 16 |
Loras College Hennessy 350 |
Mary Bohlke Loras |
Paper-folding Geometry |

Thursday November 17 |
UW-Platteville Ottensman 222 |
Mu-Ling Chang UWP |
Some Applications of Congruences |

Friday 3pm November 18 |
Loras College Hennessy 350 |
Bob Kress Loras |
A Historical Approach to Finite Groups |

Friday 4pm November 18 |
Loras College Hennessy 350 |
Steven Meyer Loras |
College Recruiting Competition: An Application of Game Theory |

Wednesday November 30 |
Loras College Hennessy 350 |
Alex Zupan University of Iowa |
Wavelets and Digital Image Compression |

**Speaker**- Travis Peters
**Title**- Fun with Zero Forcing
**Abstract**Let

*G*be a graph with each vertex colored either white or black. Vertices change color according to the color-change rule: If*u*is a black vertex and exactly one neighbor*w*of*u*is white, then change the color of*w*to black. The zero forcing number of*G*is the smallest number of vertices needed to be initially colored black so that repeated application of the color-change rule results in all vertices being black.This talk will introduce students to minimum rank/maximum nullity and zero forcing and provide an opportunity for hands-on computation of the zero forcing number of several graphs. In addition, we will discuss the positive semidefinite zero forcing number and consider a family of graphs whose (standard) zero forcing number differs from the positive semidefinite zero forcing number.

Travis Peters is a graduate student at Iowa State University.

**Speaker**- Dr. Leonida Ljumanovic
**Title**- The Von Neumann Ordinals
**Abstract**In the first part of the talk we will define natural numbers in terms of sets. In particular, we will discuss von Neumann's idea that a natural number can be represented nicely by the set of all smaller numbers. So for example by his definition the first few natural numbers would be 0 = { } = ∅, 1 = {0} = {∅}, 2 = {0,1} = {∅,{∅}}, 3 = {0,1,2} = {∅,{∅},{∅,{∅}}}. These numbers are ordinal numbers because they are well-ordered, and because of that are often called "von Neumann ordinals." Writing natural numbers in terms of sets is useful, because we can define the operations on natural numbers in terms of set-theoretic operations. In this talk we will also use properties of sets and induction to prove some of the properties of natural numbers.

Leonida Ljumanovic is an Assistant Professor of Mathematics at UW-Platteville. She graduated from the University of Iowa in 2008, under the direction of Dr. George Nelson.

**Speaker**- Dr. Benjamin V.C. Collins
**Title**- Euler's Polyhedron Formula
**Abstract**In 1750, Swiss mathematician Leonhard Euler stated his famous result that, "In any solid enclosed by planes, the sum of the number of solid angles and the number of faces exceeds the number of edges by 2." In modern notation, we say that for a polyhedron where the number of faces is

*F*, the number of edges is*E*, and the number of vertices is*V*,*F-E+V=2.*This formula is well known, and is used in classroom lessons from grade school to grad school. However, Euler's proof of the formula had a major flaw. I will present a proof that, while not perfect, comes as close as any proof for a general audience can expect to.

Ben Collins has been a member of the UW-Platteville Mathematics Department since 2000. In 11 years at UWP, he has taught 17 different courses. Among his favorites are History of Math, Discrete Math, Calc II, and Elementary Statistics. An avid crossword puzzler, he knows the name of Bambi's aunt and the sequel to

*Typee.*

**Speaker**- Dr. Jacob Heidenreich
**Title**- Von Neumann Ordinals II: To Infinity and Beyond
**Abstract**In her Sept. 22 colloquium, Leonida Ljumanovic talked about how Von Neumann constructed the natural numbers using sets. Surprisingly, this tool can get us infinite numbers as well! In this talk we will follow the road of the natural numbers out of finite town and explore the wide, infinite world beyond. We'll look at the wild and unpredictable properties these infinite numbers have, and why we might want to make such a journey. You do not need to have heard Dr. Ljumanovic's talk to follow this one.

Dr. Heidenreich is an Associate Professor of Mathematics at Loras College. He received his Ph.D. in Mathematics at the University of Notre Dame where he studied both mathematics and philosophy.

**Speaker**- Dr. Pam Peters
**Title**- Beyond Euclid, Euler, and Descartes: A Survey of the Women in Math
**Abstract**We are all familiar with Euler, Descartes, Lagrange, and many other prominent mathematicians who have given their names to theorems that we frequently use. Curiosity led me to explore the other side of the coin: the prominent women in the history of math. For this colloquium, I will present a survey of several well known and some lesser known mathematical women, their lives and times, and some of what they contributed to math as we know it.

Dr. Pam Peters earned her PhD at Colorado State University with a focus on Algebraic Topology under Dr. Jeanne Duflot. When not exploring intriguing areas of mathematics, she is an avid runner and quilter, and looks forward to again being able to ski the Rockies this winter.

**Speakers**- Mary Bohlke and Katie Burke
**Title**- REU Reflections
**Abstract**Research Experiences for Undergraduates (REUs) provide students with opportunities to perform mathematical research and consequently to view mathematics from a perspective outside of the traditional classroom setting. This past summer, the presenters were given such an opportunity at the NSF-VIGRE Heartland REU Program held at the University of Iowa. During the two-month-long program, we received valuable instruction in several comprehensive mathematical courses, worked in small research groups with dedicated University of Iowa graduate student and faculty advisors, and were given a glimpse of graduate school mathematics. The presenters will speak about their experiences and the specific topics each researched. Mary Bohlke’s research group studied the theory of τ

_{n}-factorizations with a focus on the integers. Katie Burke’s group studied irreducible representations of groups which are generalizations of the dihedral group of order 2*p*, where*p*is a prime.Mary Bohlke and Katie Burke are both senior math majors at Loras College.

**Speaker**- Dr. Irfan Ul-Haq
**Title**- Am I Part of the Problem, or Part of the Solution?
**Abstract**This is the first talk in a series of talks which I am planning to give. I want to talk about issues which math faculty face every day and talk (mostly complain) about in hallways, in their offices and in places where they can gather in groups of at least two. This talk is about student’s work submitted for grading. I will focus on just one thing which I consider is the most common problem with student’s work. I will discuss why it seems to be becoming a greater issue for me. Am I part of the problem? Is there a solution to it? Please join to learn and discuss. I am sure this talk will make you pick a side on this issue.

Irfan Ul-Haq joined UW-Platteville in 2005. He has become increasingly interested and involved with issues related to student learning and success at college level. His four-year-old son, Abdulhaq, challenges him every day to make sure that he is always thinking about the future to make it better for the next generation. Irfan enjoys spending time with his family and having small discussions with Abdulhaq.

**Speaker**- Dr. Matt Rissler
**Title**- Stochastic Modeling: What Do We Do When the Probabilities Change?
**Abstract**Stochastic Modeling deals with a system or process that changes over time in some probabilistic manner. It has applications in many fields, from Physics and Geology to Biology and Financial Mathematics. (You may have heard of such models used by "quants" in the last couple of years.) Like your first probability and statistics course, we are interested in means and standard deviations, but unlike that course we are not assuming that the probabilities of events remain constant. In this talk, we will look at a few basic examples of stochastic models and simulate or analyze them during the talk to make some conjectures about them.

Matt Rissler is an Assistant Professor of Mathematics at Loras College. He received his Ph.D. from the University of Notre Dame where he studied mathematical biology.

**Speakers**- Mary Bohlke
**Title**- Paper-folding Geometry
**Abstract**Most everyone knows origami as the Japanese art of paper folding. Recently, however, mathematicians have analyzed paper folding from an axiomatic perspective. In this talk, I will introduce you to the seven axioms of paper folding. These axioms can be used to construct objects which are impossible to create with just a ruler and compass. I will discuss my current exploration of the constructability of regular n-gons.

Mary Bohlke is a senior at Loras College. This presentation is in partial fulfillment of the Loras College mathemetics major.

**Speaker**- Dr. Mu-Ling Chang
**Title**- Some Applications of Congruences
**Abstract**This talk is ideal for students who have learned the concepts of congruences.

The language of congruences was developed in the early nineteenth century by Gauss, one of the most famous mathematicians in history. Among all applications of congruences, I will introduce to the audience three basic ones, including divisibility tests.

Mu-Ling Chang came to Platteville in 2001. She is originally from Taiwan and received her PhD from the University of Maryland at College Park. Her specialties are Algebraic Number Theory and Algebra. She also likes teaching, reading, cooking, and gardening.

**Speaker**- Bob Kress
**Title**- A Historical Approach to Finite Groups
**Abstract**My presentation deals with group theory. I will talk briefly on the work I have done in the past three semesters on a project titled, "Abstract Awakenings in Algebra: Early Group Theory in the Works of Lagrange, Cauchy, and Cayley." I will also be doing some work with groups of order 12, 14, and 16, including Abelian and Non-Abelian groups. I will also talk about the Fundamental Theorem of Finite Abelian Groups.

Bob Kress is a senior at Loras College. This presentation is in partial fulfillment of the Loras College mathemetics major.

**Speaker**- Steven Meyer
**Title**- College Recruiting Competition: an Application of Game Theory
**Abstract**Using Game Theory, I will model a theoretical annual recruitment competition between Loras College and the University of Dubuque. With the use of desirability functions and a population density function that I have posited, I will calculate the equilibrium payoffs for both colleges using a payoff matrix. I will also explore other methods of finding the equilibrium payoffs of each college to verify any solutions we find using the payoff matrix.

Steven Meyer is a senior at Loras College. This presentation is in partial fulfillment of the Loras College mathemetics major.

**Speaker**- Alex Zupan
**Title**- Wavelets and Digital Image Compression
**Abstract**Have you ever wondered how a computer compresses digital images? In this talk, we will seek to answer the following questions:

-How are digital images stored and manipulated as data?

-Why are some images more easily compressed than others, and how do we measure this mathematically?

-What is the Haar wavelet transform, and how can it be utilized in image compression?Using basic linear algebra, we will show how and why the wavelet transform provides an effective and efficient means of compressing digital grayscale images. In the process, we hope to understand a general framework of data compression that can be applied to any type of digital information.

Alex Zupan is a graduate student at the University of Iowa.