Spring 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. Last semester's schedule can be viewed here.

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

Thursday February 10 |
UW-Platteville Ottensman 144 |
Ki-Bong Nam UW-Whitewater |
Generalized Euler φ-function |

Wednesday February 16 |
Loras College Hennessy 350 |
Joe Eichholz University of Iowa |
An Introduction to Bioluminescence Tomography |

Thursday February 24 |
UW-Platteville Ottensman 144 |
Jonas Meyer UWP |
Mathematical Truth: History and Perspectives |

Friday March 4 |
Loras College Hennessy 350 |
Megan Patnott Univ. of Notre Dame |
Symmetry, Wallpaper Patterns, and M.C. Escher |

Friday March 11 |
Loras College Hennessy 350 |
TJ Hitchman Univ. of Northern Iowa |
Counting and Dividing: m-ary partition sequences |

Thursday March 24 |
UW-Platteville Ottensman 144 |
Clem Jeske UWP |
A Theorem about Incircles |

Wednesday March 30 |
Loras College Hennessy 350 |
Erik Insko University of Iowa |
Flipping Coins, Drunken Walks, and Wallis' Formula for π |

Wednesday April 6 |
Loras College Hennessy 350 |
Chad Vidden Iowa State University |
Trading Cookies in a Gambler's Ruin Scenario |

Thursday April 14 |
UW-Platteville Ottensman 144 |
Pam Peters UWP |
Go Ask Alice: The Mathematics of Lewis Carroll |

Thursday April 28 |
UW-Platteville Ottensman 144 |
Kevin Haertzen UWP |
Polynomial Splines |

Friday May 6 |
Loras College Hennessy 350 |
Amanda Matson Clarke University |
Did She Say, "Monoid"? |

**Speaker**- Dr. Ki-Bong Nam
**Title**- Generalized Euler φ-function
**Abstract**We define a generalized Euler φ-function. We also characterize the Euler φ-function differently from the classical definition. We find some properties of the generalized Euler φ-function. We will also discuss some basic number theory which is related to the generalized Euler φ-function. The results of this work are the result of undergraduate research with my students at UW-W, so this talk will also be appropriate to general audiences.

Ki-Bong Nam earned his Ph.D. in 1998 at the University of Wisconsin-Madison, in the field of Algebra. He has taught at the University of Wisconsin-Whitewater since 1999. He has authored and co-authored over 75 papers, and has earned the Award for Outstanding Research and the research award in the College of Letters and Sciences at UW-W. He lives in Madison with his wife and two children.

**Speaker**- Joe Eichholz
**Title**- An Introduction to Bioluminescence Tomography and Associated Problems
**Abstract**Bioluminescence tomography (BLT) is an emerging medical imaging technique in which we aim to reconstruct the position of light sources inside a biological medium. The BLT has several challenging mathematical aspects, one of which is efficiently solving the radiative transfer equation. In this talk, we will introduce the BLT problem in an accessible manner, and focus on the difficulty of solving the associated RTE. We will proceed give to an efficient algorithm for solving a simplified version of the RTE developed by undergraduate students at the University of Iowa Summer REU in 2010.

Joe Eichholz is a graduate student at the University of Iowa.

**Speaker**- Dr. Jonas Meyer
**Title**- Mathematical Truth: History and Perspectives
**Abstract**A fairly informal survey will be given of some of the ideas concerning truth in mathematics, the history of the development of these ideas, and some of the diverse perspectives of mathematicians and philosophers through the ages. Topics will include a comparison between mathematical truth and truth in the physical sciences; the role of abstraction and deduction; relative versus absolute truth of foundational principles (axioms), especially in geometry and arithmetic; and independence results concerning the (set theoretic) notion of infinity.

Jonas Meyer is a mathematics lecturer at the University of Wisconsin-Platteville. He earned his Ph.D. in mathematics from the University of Iowa in 2010, working primarily in functional analysis. Reading about the history of mathematics is one of his hobbies.

**Speaker**- Megan Patnott
**Title**- Symmetry, Wallpaper Groups, and M.C. Escher
**Abstract**We often see repeating patterns used in decoration. All of these patterns remain unchanged if we shift them in the correct direction, but some of them can also be rotated or reflected over a line without the pattern changing. We call these shifts, rotations, and reflections symmetries of the pattern. If we are mainly interested in the symmetries of the patterns, then it turns out that there are only a very small number of types of patterns. We'll discuss four types of symmetry, the wallpaper patterns they lead to, and a variation on the classical wallpaper patterns.

Megan Patnott is a graduate student at the University of Notre Dame.

**Speaker**- Dr. TJ Hitchman
**Title**- Counting and Dividing: m-ary partition sequences
**Abstract**m-ary partition sequences count the number of ways to divide a set of size n into subsets whose sizes are powers of m. These things have neat divisibility properties that occur in a rich self-similar pattern. We will explore the pattern and maybe talk about a recent advance in understanding involving generating functions.

TJ Hitchman is an Assistant Professor of Mathematics at the University of Northern Iowa.

**Speaker**- Dr. Clem Jeske
**Title**- A Theorem about Incircles
**Abstract**An n-sided polygon inscribed in a circle can be triangulated using n - 2 triangles. Each of these n - 2 triangles has an incircle and an inradius. What can be said of the sum of the inradii?

Clem Jeske has been a member of the math faculty at the University of Wisconsin- Platteville since 1984. He completed his Ph.D. in mathematics from the University of Wisconsin-Madison in 1989 under the direction of Don Passman.

**Speaker**- Erik Insko
**Title**- Flipping coins, drunken walks, and a simple proof of Wallis' product formula for π.
**Abstract**We discuss the ties between the combinatorics of coin flipping problems, drunken walks, and the elementary geometric proof of Wallis' product formula for π due to Johan Wastlund. This talk is motivated by a lecture given by Donald Knuth at Bowdoin College, Wastlund's article in The American Mathematical Monthly, and a personal correspondence with aBa Mbirika.

Erik Insko is a graduate student at the University of Iowa and a Loras College alum.

**Speaker**- Chad Vidden
**Title**- Trading Cookies in a Gambler's Ruin Scenario
**Abstract**We consider several variations of a probabilistic game between a "buyer" and a "seller", whose major component is a random walk of the buyer on an interval of integers. We assume a gambler’s ruin scenario, where in contrast to the classical version the walker (buyer) has the option of consuming "cookies", which when used, increase the probability of moving in the desired direction for the next step. The cookies are supplied to the buyer by the second player ("seller"). We determine the equilibrium price policy for the seller and the optimal "cookie store" location. An initial motivation for this question is provided by the popular model of "cookie" or "excited" random walks.

Chad Vidden is a graduate student at Iowa State University.

**Speaker**- Dr. Pam Peters
**Title**- Go Ask Alice: The Mathematics of Lewis Carroll
**Abstract**While many of us are familiar with "Alice in Wonderland" as a children's story or Burton film, we aren’t quite as familiar with Charles Dodgson, Carroll’s real name, a mathematician. I will be discussing Dodgson’s more major works, specifically his algorithm for computing the day of the week and the condensation method for evaluating determinants, but also looking a bit at how he used Alice and other literary works in criticizing the more "modern" mathematicians of his time. It should be a good time to "Remember what the doormouse said, 'Feed your head'."

Pam Peters is a pure mathematician with a PhD in Algebraic Topology from Colorado State University. She has been teaching at UW-Platteville for almost 4 years now and has finally learned to find Green Bay on a map (among other Wisconsin priorities). Beyond algebra, number theory, and combinatorics, she has an interest in the history of math, as you meet such fascinating people there. And she is still in search of the winged pigs.

**Speaker**- Dr. Kevin Haertzen
**Title**- Polynomial Splines
**Abstract**What’s a spline, and why do we care about them? Wolfram Math World defines a spline as “A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary functions, and are used extensively in computer graphics.” We will explore how to produce simple splines, and see some of the advantages of this approach to approximating functions.

Kevin Haertzen has been a member of Mathematics Department since Fall 2003. He has a Ph.D. in Mathematics from Northern Illinois University, under the direction of Dr. Hongyou Wu.

**Speaker**- Dr. Amanda Matson
**Title**- Did She Say, "Monoid"?
**Abstract**If you've ever kept track of a score in a sporting event, you've used a monoid! We will be exploring some common monoids as well as the concepts of reducibility and factoring.

Amanda Matson is an Assistant Professor of Mathematics at Clarke University.