Spring 2012

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 |
---|---|---|---|

Thursday February 9 |
UW-Platteville Ottensman 144 |
Rob Calcaterra UWP |
Some Problems from Mathematics Magazine |

Friday February 17 |
Loras College Hennessy 250 |
Angela Kohlhaas Loras |
Origami Mathematics |

Thursday February 23 |
UW-Platteville Ottensman 144 |
Clem Jeske UWP |
Fun with Conics |

Thursday March 8 |
UW-Platteville Ottensman 144 |
Susan Hollingsworth Edgewood College |
Packing Trees into Complete Graphs |

3pm Friday March 23 |
Loras College Hennessy 270 |
Lisa Hefel Loras |
Price Leaders and Their Effect on Profit |

4pm Friday March 23 |
Loras College Hennessy 250 |
Om Gurung Loras |
Finite Element Analysis |

Thursday March 29 |
UW-Platteville Ottensman 144 |
James Swenson UWP |
The Geometry of Cubic Polynomials |

3:30pm Friday March 30 |
Loras College Hennessy 250 |
Nicole Jess Loras |
Exploring Patterns in Fibonacci Numbers |

4:30pm Friday March 30 |
Loras College Hennessy 250 |
Kyle Riegel Loras |
Investigations in Electromagnetic Field Theory |

Thursday April 12 |
UW-Platteville Ottensman 144 |
Chris Frayer UWP |
Alpha Regular Stick Knots |

3pm Friday April 20 |
Loras College Hennessy 250 |
Jacob Heidenreich Loras |
Gaming the System: How to Engage Students |

4pm Friday April 20 |
Loras College Hennessy 250 |
Dan Willis Loras |
Autonomous Differential Equations |

Thursday April 26 |
UW-Platteville Ottensman 144 |
Jonas Meyer Loras |
Divergent Series |

**Speaker**- Dr. Rob Calcaterra
**Title**- Some Problems from Mathematics Magazine
**Abstract**Mathematics Magazine is published five times a year by the Mathematical Association of America (MAA). Each issue has a section that poses problems sent in by readers and asks others to submit solutions to these problems. The talk will investigate some of the problems posed in the magazine last year. The speaker will try to choose problems for which the solutions are most accessible for an undergraduate audience.

Rob Calcaterra is currently the only member of the Mathematics Department to have spent more than half of his life at UWP. He enjoys teaching a wide range of mathematics courses and interacting with students. He has spent a lot of time in the past decade traveling around the USA with his family.

**Speaker**- Dr. Angela Kohlhaas
**Title**- Origami Mathematics
**Abstract**Origami is an ancient, tightly constrained art: a traditional model is made from a single uncut square creased by straight lines and folded to resemble a 3-dimensional object. Though one might expect the possible constructions to be over-used and thoroughly investigated, the last two decades have seen incredible advancements in the detail, technical understanding, and practical applications of origami. Why? Mathematical tools have increasingly been applied to the artform, generating a host of solved and unsolved mathematical and computational problems. In this talk, I will highlight some surprising mathematics involved in two types of problems: origami design and flat-foldability.

Angela Kohlhaas is an Assistant Professor of Mathematics at Loras College. She has dangerously been known to fold cranes out of candy wrappers while driving a car.

**Speaker**- Dr. Clem Jeske
**Title**- Fun with Conics
**Abstract**"Did you know that if you construct the tangents to an ellipse at the endpoints of a chord that passes through a focus then...?"

When I was asked this question, the answer was "No." When they told me what happened, I wondered why it was true. This talk will complete the statement above and provide a proof (sort of). But the talk is more about what can happen when one starts to make connections and ask "Gee I wonder...."

Clem Jeske is in his 28th year on the faculty at UWP. He serves the department as the chair of the Math Contest Committee and the Department Bibliographer. He has written the course packet for the Math of Finance course, as well as his own course notes for College Geometry. He lives in Platteville with his wife Susan.

**Speaker**- Dr. Susan Hollingsworth
**Title**- Packing Trees into Complete Graphs
**Abstract**A long-standing conjecture states that a sequence

*T*is a tree with_{1}, T_{2},..., T_{n-1}, where T_{i}*i*edges, can be packed into the complete graph*K*. We will explore some variations on this conjecture, and see some of the progress that has been made towards its solution. Students are welcome. No prior coursework in graph theory will be assumed._{n}Susan Hollingsworth received her Ph.D. in Mathematics from the University of Wisconsin - Madison, studying graphs, matrices, and the interconnections between them. Susan is a professor at Edgewood College in Madison, Wisconsin, where she has been teaching since 1996.

**Speaker**- Lisa Hefel
**Title**- Price Leaders and Their Effect on Profit
**Abstract**Game theory will be used to mathematically capture the competition between two competing stores for greater profits. Concepts in economics and marketing will be utilized to appropriately capture consumer behavior relating to changes in prices due to marketing activities. The specific marketing approach I will be analyzing and discussing is the use of a price leader, where low or no profit is generated; but the approach is used to increase customer traffic in hopes of increasing profits.

Lisa Hefel is a senior at Loras College. This presentation is in partial fulfillment of the Loras College mathematics major.

**Speaker**- Om Gurung
**Title**- Finite Element Analysis
**Abstract**Finite Element Analysis is a numerical technique for finding approximate solutions of partial differential equations. The technique has very wide application, and has been used on problems involving stress analysis, fluid mechanics, heat transfer, diffusion, vibrations, electrical and magnetic fields, etc. I will be analyzing and presenting the one dimensional boundary value problem using springs and two dimensional boundary value problems using trusses, frames, and heat transfer.

Om Gurung is a senior at Loras College. This presentation is in partial fulfillment of the Loras College mathematics major.

**Speaker**- Dr. James Swenson
**Title**- The Geometry of Cubic Polynomials
**Abstract**A degree-three polynomial has two critical points (in the complex plane). Where are these critical points, relative to the roots of the polynomial? Can we reconstruct the polynomial from its critical points? What if we only know the average of the two critical points -- or only one of the critical points? I'll share the geometric properties that Chris Frayer, Miyeon Kwon, Chris Schafhauser and I discovered while trying to answer such questions.

James Swenson is in his seventh year on the faculty of UW-Platteville. He earned the Ph.D. at the University of Minnesota under the direction of Mark Feshbach. He is currently Chair-Elect of the Wisconsin Section of the Mathematical Association of America. For fun he plays hand chimes, and directs the choir at his church. His brackets are terrible this year; he only got eight of the right teams in the Sweet Sixteen!

**Speaker**- Nicole Jess
**Title**- Exploring Patterns in Fibonacci Numbers
**Abstract**A wide variety of interesting patterns may be observed within the well-known sequence of Fibonacci numbers, which is generated by the relationship F

_{n}= F_{n-1}+ F_{n-2}beginning with F_{1}= F_{2}= 1. The goal of this research project was to make conjectures regarding the patterns observed and prove or disprove these conjectures. We draw upon a variety of methods for analysis, including the recursive definition as well as techniques from linear algebra applied to the Fibonacci Q-matrix. We will use an assortment of techniques to prove the conjectures including proof by induction.Nicole Jess is a senior at Loras College. This presentation is in partial fulfillment of the Loras College mathematics major.

**Speaker**- Kyle Riegel
**Title**- Mathematical and Experimental Investigations in Electromagnetic Field Theory
**Abstract**James Clerk Maxwell is known as the father of electromagnetic theory, which is the relation between electric fields, magnetic fields and optics. A vector analysis approach will be used to relate the electromagnetic fundamentals Ampere's law, Gauss' law, and Faraday's law into Maxwell's equations. Concepts will be explained with a vector field mindset along with experiments for Faraday's law, Coulomb's law, and Biot-Savart law, which is used to calculate the strength of earth's magnetic field during the presentation.

Kyle Riegel is a senior at Loras College. This presentation is in partial fulfillment of the Loras College mathematics major.

**Speaker**- Dr. Jacob Heidenreich
**Title**- Gaming the System: How to Engage Students in the Classroom
**Abstract**There are many similarities between playing a game and taking a math class. They both involve problem solving, resource management, learning curves, successes and failures. But often one is fun while the other isn't. In this talk we'll look at psychological research into the enjoyment of game-playing, and how it can be applied to the classroom to engage the students we're teaching. We'll look at the experiences of flow and fiero, what the requirements are for an activity to be intrinsically motivating, what makes something a 'game', as well as what challenges this line of pedagogy faces. And, yes, we'll play some games as part of the seminar!

Jacob Heidenreich is an Associate Professor of Mathematics at Loras College.

**Speaker**- Dr. Daniel Willis
**Title**- Autonomous Differential Equations
**Abstract**In an autonomous differential equation, the right hand side function does not depend explicitly on time. A simple but important example of an autonomous differential equation is

*dx/dt = ax*, where*a*is a constant. The speaker will survey analytical, numerical, and qualitative solution methods for autonomous differential equations, and discuss applications to physics and biology.Dan Willis is an Associate Professor of Mathematics at Loras College.

**Speaker**- Dr. Jonas Meyer
**Title**- Divergent Series
**Abstract**Series involve, roughly, adding infinitely many numbers. While infinitely many additions are not literally carried out, we can agree about infinite "sum" formulas such as

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + ... = 1, or

1 + x + x

^{2}/2! + x^{3}/3! + x^{4}/4! + x^{5}/5! + ... = e^{x}.These are examples of convergent series. On the other hand, there is good reason for skepticism about the “sum”

1 - 1 + 1 - 1 + 1 - 1 + ... = 1/2,

and it would seem that there is even more reason to question the sanity of someone who asserts that

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + ... = -1.

These are examples of divergent series. In this talk, various methods of making sense of sums of divergent series will be discussed, along with examples and applications where it is useful to do so. There will be some historical reflection on the stature of divergent series in mathematics.

Jonas Meyer is an assistant professor of math at Loras College. Last year he was a lecturer in the math department at UW-Platteville. Jonas enjoys long walks and summing divergent Fourier series.