# Undergraduate Colloquium

**Spring 2010**

**Wednesdays 12:55 - 1:45**

**LCB 222**

Pizza and discussion after each talk

Receive credit for attending

Past Colloquia

- January 13 No Talk

- January 20 Dan Ciubotaru
**Straightedge and Compass Constructions**

*Abstract:*One of the most famous problems coming from the ancient Greeks is what geometric constructions are possible using only a straightedge and a compass. Is it possible to:

1) construct a cube with precisely twice the volume of a given cube?

2) trisect any given angle?

3) construct a square whose area equals the area of a given circle?

The answers to these questions are all negative, and this has been known for almost 200 years. In this talk, I will try to explain why this is the case, and also why certain regular polygons (like the 5-gon or the 17-gon) can be constructed with only a straightedge and compass, but not most of them.- January 27 Peter Trapa
**Topological Plays and Winning Ways**

*Abstract:*This week's talk will be about the possibility of devising a winning strategy for the following game (as described in Chapter 5 of Sam Vandervelde's book "Circle in a Box"):

The game of Criss-Cross is played on a blank sheet of paper by two players. The game board is created by drawing three points at the vertices of a large equilateral triangle, along with two to nine points anywhere in its interior. Players alternate turns drawing a single straight line segment joining any two points, as long as the segment does not pass through any other points or segments already appearing on the game board. The winner is the last player able to make a legal move.

Perhaps surprisingly, the game is related to a famous topological invariant, the Euler Characteristic.- February 3 Yael Algom Kfir
**Hanging a Picture Using the Free Group**

*Abstract:*Suppose you want to hang a picture on two nails in such a way that if you pull either nail out the string will come loose and the picture will fall. Is there a way to do it? We will discuss an algebraic solution to this problem. We will then introduce an algebraic invariant of geometric objects called "the fundamental group," and give some history of why it was invented and how it can be useful.- February 10 Peter Alfeld
**Hotel Infinity**

*Abstract:*You are the owner of Hotel Infinity. It has infinitely many rooms, and it's full. A new guest arrives and insists you give her a room. How do you accommodate her? The next day, a family with infinitely many members arrives, each of whom wants a private room. The next day infinitely many families, each with infinitely many members, arrive. Each family member insists on a private room. You can do it! Infinity is different.- February 17 Jimmy Dillies
**Who said divergent?**

*Abstract:*We are taught in calculus that series such as 1-1+1-1+1-1+1-1+... are divergent. Could we, however, make sense of these series? What about 1+infinity+infinity^2+... ? In this lecture, we will see how mathematicians have tried to give a formal framework in order to understand these 'not so badly' diverging series.- February 24 Muhammad Adeel
**Geometry of Mobius Transformations**

*Abstract:*Symmetry is created by repeating or iterating the same motion a number of times. The group concept describes the rules which govern the repetitive aspect of symmetry. This should not be surprising as the idea of a group was developed in the context of geometry--number theory came in much later. In this presentation, we will explore the theory of groups generated by Mobius transformations of the Riemannian sphere. We can generate interesting symmetrical patterns by applying mobius transformations to geometrical objects such as a square. This is then extended to generate the limit set (fractal) of a discrete Schottky group using the Depth-First Search Algorithm.- March 3 Brendan Kelly
**Zero Divisor Graphs**

*Abstract:*This seminar will introduce a beautiful, graphical way to investigate an algebraic problem. The focus will be on developing a graph that encodes information about the zero divisors of a ring and investigating properties of this graph. The interplay between graph theory and algebra will allow us to see algebraic structure in commutative rings. A lot of examples and pictures will be provided.- March 10 Domingo Toledo
**Euclid's Parallel Postulate and Hyperbolic Geometry**

*Abstract:*For many centuries geometers tried to prove that Euclid's parallel postulate was a consequence of his other axioms. In the 19th century Gauss, Bolyai and Lobachevsky independently came to the conclusion that the parallel postulate was independent of the other axioms. They founded a new geometry, called hyperbolic geometry. This talk will review some of this history and describe some properties of hyperbolic geometry.- March 17 Alan Cannaday
**A Study of Numerical Methods for the Inverse Laplace Transform**

*Abstract:*The problem of determining the log-normal distribution φ(γ) from its Laplace transform of the light intensity I(t) is known to be a severely ill-posed linear inverse problem, which means that small perturbations in I(t) can lead to large errors in the estimation of φ(γ). For my project I explored alternative regularization methods for the inverse Laplace transform proposed by Epstein and Schotland [SIAM Rev., 50(3):504-520, 2008] that allows us to compute the inverse Laplace transform without requiring prior information about φ(γ). I also quantified the uncertainty in the estimation due to the presence of noise in the data. Based on an REU from Fall 2009.- March 24 No Talk - Spring Break

*Abstract:*- March 31 Jonathan Smith
**Applied Statistics and Modeling in the Business World**

*Abstract:*A review of a few interesting case studies of real world applications based on linear regression, matrix solutions and simple mathematical concepts (misapplied). The talk will be in three parts the first will cover the use of linear modeling and other even more simple approaches to modeling how business needs will change over time. The simplicity of these approaches and their relative merits will be covered using the UPS approach to package count planning. A few key limitations will be explored along with their real world impact. The second part will cover the use of linear systems (simple matrix) to solve optimization problems; a real world workforce balancing problem will be used as the example. The final part will cover a set of standard mathematical concepts and some of the more humorous and troubling mis-uses of them in business today.- April 7 Stewart Ethier
**A World Record in Atlantic City**

*Abstract:*It was widely reported in the media that, on May 23, 2009, at the Borgata Casino in Atlantic City, Patricia DeMauro, playing craps for only the second time, rolled the dice for four hours and 18 minutes, finally sevening out at the 154th roll, a world record. With L denoting the number of rolls until the shooter sevens out, we will show that the probability that L is 154 or more is about one in 5.59 billion. More generally, we will derive a closed-form expression for the distribution of L; in particular, it is a linear combination of four geometric distributions.

Even if, as is likely, this seems a rather prosaic problem, the talk may be of interest for two reasons. First, it involves some interesting mathematics (Markov chains, matrix theory, and Galois theory), and second, it can be seen as a case study in how a problem that is too complicated to solve by hand may be solved with the help of software (Mathematica, in this case).- April 14 Aaron Bertram
**Happy Pi + 1 Day!**

*Abstract:*Pi is the ratio of the circumference of a circle to its diameter. It is also one half the period of the sine and cosine functions, and makes an appearance (along with e) in Stirling's formula for the factorials of large numbers. But suppose you were stranded on a desert island (with a lot of paper and pens) and asked to calculate the first 20 digits of pi. Could you do it? How did people do it in the 19th century? How did Archimedes approximate pi? Inquiring minds want to know.- April 21 No talk
**Pi Mu Epsilon sponsored career luncheon event**

*Abstract:*Students are encouraged to attend the career event sponsored by Pi Mu Epsilon today in lieu of the colloquium:

12:45 - 1:45 in the LCB Loft

Join us for an information discussion and free lunch with professionals in various fields about how mathematics has played a role in their careers. This will be a great opportunity to ask questions about and gain insight into different career paths!

Jeffrey S. Anderson,*Assistant Professor of Radiology, Director of Functional Neuroimaging, University of Utah; Science Fiction Author*

Scott Webb,*Change Management Manager, NAND Flash Engineering, IM FLASH Technologies*

- April 28 Maritza Sirvent
**Math in the Movies**

*Abstract:*There are some movies that involve math. Sometimes a highly intelligent or intellectual character needs to be portrayed, so a mathematician will be convincing, or if someone talented with not much previous training is required, then a math wiz will do. One can find movies that do indeed contain more math, which ranges from accurate and precise to plain wrong and yes, also funny. I will show some movie clips and talk about the math behind them.