## Spring 2012

**Tuesday, January 24** —"Technology on Wall Street"

Abstract: Bob Garrett '90 will be coming to Dickinson to share experiences from his 22 year technology career. He began his career as a programmer at AT&T and slowly progressed into senior management roles on and off Wall Street. He is currently the CTO of Merlin Securities in New York City. Just prior to Merlin, Bob was the Global head of Equity Electronic Trading Technology at Deutsche Bank. He will be talking about the relevance of CS/Math major, technology and Wall Street, and the different job opporunities available to CS/Math majors. The agenda will be fluid with the goal of providing as much value to the attendees as possible. There will be plenty of time for Q&A.

Bob Garrett '90, Senior Partner/CTO, Merlin Securities

Stafford Lecture Room/Rector Science Complex

12:00-1:00 p.m.

Lunch provided

**Tuesday, February 7** - "Water, water everywhere, but is it safe to drink?"

Abstract: In Pennsylvania and throughout North America, clean potable water is in abundance, or is it? Interestingly, answers to this question are formulated using remarkably accessible mathematics. In this talk, we will introduce basic hydrogeologic principles and use algebraic manipulation - as well as a little calculus - to develop a working subsurface fluid flow model. The talk will conclude with a brief discussion on the direction of current research in the discipline.

Benjamin J. Galluzzo, Shippensburg University

Tome 115

12:00-1:00 p.m.

Lunch provided

**Tuesday, February 21** - “On the Stretch Factor of the Delaunay Triangulation"

Abstract: Let S be a finite set of points in the Euclidean plane. Let D be a Delaunay triangulation of S. The stretch factor (also known as dilation or spanning ratio) of D is the maximum ratio, among all points p and q in S, of the shortest path distance from p to q in D over the Euclidean distance ||pq||. Proving a tight bound on the stretch factor of the Delaunay triangulation has been a long standing open problem in computational geometry.

In this talk we present an improved upper bound of the stretch factor of the Delaunay triangulation which is less than 1.998 (SoCG'11). This improves the previous best upper bound of 2.42 by Keil and Gutwin (1989). This upper bound breaks the barrier 2, which is significant because previously no family of plane graphs was known to have a stretch factor guaranteed to be less than 2 on any set of points. We also present an improved lower bound of the stretch factor of the Delaunay triangulation (1.5932, CCCG'11) and conjecture on the possible configuration and value of the tight bound.

Ge Xia, Lafayette College

Tome 115

12:00-1:00 p.m.

Lunch provided

**Tuesday, February 28** - "Computation and Chaos"

Abstract: A dynamical system is one that evolves over time according to fixed rules -- for example, the motion of the planets, the populations of competing species of animals, or the formation of traffic jams. Simple rules can often lead to chaotic behavior. It's natural to try to use computers to understand these systems, but unfortunately even the tiniest numerical error renders the results useless for pure mathematics, which demands exact answers, not approximations. The problems are especially bad when we try to study the long-term behavior of chaotic dynamical systems, since small errors can quickly accumulate into big ones. We'll look at these problems, and at ways in which we can overcome them to use numerical approximation to prove mathematically rigorous results.

Jim Wiseman, Agnes Scott College

Tome 115

12:00-1:00 p.m.

Lunch provided

**Thursday, March 8** - "Testing in Resource Constrained Environments"

Abstract: Testing is a critical and expensive part of the software development life cycle. Often, test suites grow in size to the extent that they may take days, weeks, or months to excute. Because the time to test is limited, test cases are selected and prioritized. More effective prioritizations can be created when the constrained resources, such as time or power, are considered. By prioritizing with constraints in mind, the final test case prioritization will yield a higher average percent of faults detected than more naive prioritization approaches.

One challenge of prioritizing and selecting test cases is in estimating the fault finding ability of the tests. This is traditionally performed through test coverage analysis.

The overhead of test coverage analysis is dominated by monitoring the application, which is traditionally performed using instrumentation. However, instrumentation can prohibitively increase the time overhead and code growth of an application. As an alternative to instrumentation, we explore how recent hardware advances can be leveraged to improve the overheads of test coverage analysis. These hardware advances include hardware performance monitors and multicore technology.

In this talk, she will be presenting our system, THeME (Testing by Hardware Monitoring Events), a testing framework that replaces instrumentation with hardware monitoring. THeME consists of a runtime system that takes advantage of hardware mechanisms and multiple cores and a static component to further extend the coverage derived from hardware event sampling. The results show that up to 90% of the actual coverage can be determined with less time overhead and negligible code growth compared to instrumentation, making it particularly applicable for use in resource constrained environments.

Kristen Wolcott-Justice, University of Virginia

Tome 115

12:00-1:00 p.m.

Lunch provided

**Tuesday, March 20** - "Algorithms and Artificial Intelligence for Acyclic Games of Chance"

Abstract: Economists have long been interested in games as models of behavior of competing organizations; the games of interest to them often feature simultaneous movement. Researchers in artificial intelligence have long used combinatorial games such as chess, checkers, and go as testbeds for their techniques. In the last decade or so, interest have widened to other games. In this talk he will discuss a class of games that includes Yahtzee and Can't Stop, algorithms for computing optimal strategies for them, applications of genetic algorithms to finding approximately optimal solutions, and issues in the implementation of those genetic algorithms.

James Glenn, Loyola University

Tome 115

12:00-1:00 p.m.

Lunch provided

**Thursday, March 22** - "Probability Theory and the Birthday Paradox"

Abstract: In a group of n randomly chosen people, what is the probability that at least two of these people will have the same birthday? This is known as the Birthday Problem, or Birthday Paradox, in probability theory. We will discuss this interesting result, as well as look at some basics of probability theory that will be needed to describe the solution.

Michelle Lastrina, Iowa State University

Tome 115

12:00-1:00 p.m.

Lunch provided

**Thursday, March 29** - "[1] + [1] = [0]: A Discussion on Modular Arithmetic"

Abstract: First introduced by Leonhard Euler, modular arithmetic is a system of arithmetic (for integers) where a count resets to zero once it has reached a certain value called the modular. It is prevalent in our everyday lives, from the 12-hour clock to the days of the week. We will explore how to perform modular arithmetic through various example as well discuss its numverous real-life applications, some of which may be surprising.

Jasmine Ng, Washington University in St. Louis

Tome 117

12:00 p.m. - 1:00 p.m.

Lunch provided

**Friday, March 30** -

"The Erdos-Faber-Lovasz Conjecture: A Question of Tea Parties and Seating Arrangements"

Abstract: The Erdos-Faber-Lovasz Conjection was conceived by Paul Erodos, Vance Faber, and Laszlo Lovasz in 1972. As reported by Faber (2010), it was initially stated as the n sets problem: "Given n sets, no two of which meet more than once and each with n elements, color the elements with n colors so that each set contains all the colors." Despite interesting fractional and asymptotic results, no one has yet proven - or disproven - the conjecture that this problem always has a solution. This talk will look at what makes this conjecture so interesting, as well as some of the progress that has been made on the problem since the conjecture was originally proposed.

Tracy McKay, Iowa State University

Tome 117

12:30 p.m.-1:30 p.m.

Lunch provided

Monday, April 2 - "Knots, Colors and Polynomials"

Abstract: Take a string or a rope and tie it, you get a knot. There are different types of knots. If you are into sailing or rock climbing you may know of the SQUARE KNOT or the GRANNY KNOT. A more basic knot is the one you start with as you tie your shoes, it is the TREFOIL knot. A natural question is how to distinguish knots. After all, when you tie a knot around your waist and climb a wall, you want to make sure that the knot is not going to untie itself! We will first use colors (3 to be exact) to differentiate knots. Quickly, we will realize that TRICOLORABILITY is not a very efficient way to distinguish knots. We will then associate POLYNOMIALS to knots.

David Crombecque, Gettysburg College

Tome 117

12:30 p.m. - 1:30 p.m.

Lunch provided

**Tuesday, April 3** - "Curious Catalan Numbers"

Abstract: We are all familiar with Fibonacci’s famous sequence that begins 1, 1, 2, 3, 5, 8, … as well as other popular sequences such as the perfect squares 1, 4, 9, 16, 25, … or the triangular numbers 1, 3, 6, 10, 15, … But what about the sequence 1, 1, 2, 5, 14, …? These are the Catalan numbers, named after the Belgian mathematician Eugène Catalan (1814 – 1894), despite having been described by Leonhard Euler 100 years earlier. It turns out these numbers take a variety of different guises as they provide the solution to numerous combinatorial problems! After introducing this sequence, we will explore some of the many ways in which the Catalan numbers are hidden throughout mathematics.

Alissa Crans, Loyola Marymount University

Tome 115

12:00-1:00 p.m.

Lunch provided

**Tuesday, April 10** - "A Variation on the Money-Changing Problem"

Abstract: Suppose you move to a country that has 5-cent, 12-cent, and 26-cent coins. Which denominations can you make change for? Which denominations can you *not* make change for? For those denominations that you can make change for, how many ways are there to do it? This number is called the denumerant, and has been studied extensively. In this talk we investigate the maximal denumerant, which counts the number of ways to make change for an amount using the largest possible number of coins.

Here's a challenge to get you started thinking about this problem. Using 5, 12, and 26, find a number whose maximal denumerant is greater than 1. In other words, find an amount that you can make change for using the same number of coins in at least two different ways, and for which there is no other way to make change for it using more coins.

James Hamblin, Shippensburg University

Tome 115

12:00-1:00 p.m.

Lunch provided

**Tuesday, April 17** - Mathematics & Computer Science Majors Dinner

Talk Title: "Mutations and Cancer - Using Mathematics to Peer Inside the Cell"

Professor Jeffrey Forrester, Dickinson College

Social Hall West

6:00-8:00 p.m.

Catered Dinner by Dining Services

*MUST sign up in Tome 201 or email millert@dickinson to attend this dinner closer to event date*

**Tuesday, May 1** -"Dynamics of the Complex Hyperbolic Consine-Root Family"

Abstract: In this paper, we investigate the dynamics of the complex family of hyperbolic cosine-root functions fα(z) = α·cosh(√) where αis a complex parameter. These functions have infinitely many critical points but only two critical values. The Julia set of a complex function is the set on which chaotic behavior occurs. We discuss properties of the Julia set of this family. We locate parameters αfor which super-attracting fixed points and super-attracting three cycles exist. Finally, we study the parameter space of the hyperbolic cosine-root family and investigate the symmetries of that space.

Honors Thesis Defense - Haosong (Tony) Wang

Tome 115

12:00-1:00 p.m.

Lunch provided

**Thursday, May 3** - "Improving the jmle Tool's Constraint Solving on Sets"

Abstract: The jmle tool executes JML specifications (formal specifications for Java) by translating them to constraint programs. This tool has useful applications such as prototyping and specification testing; however, it uses backtracking, which runs in exponential time. We aim to reduce jmle's running time by adding new constraint handling rules that remove elements from the domains of variables, reducing the search space for backtracking. These constraint handling rules use properties of and relationships between sets to prune variable domains. The addition of our rules has decreased the running time of some specifications in jmle, so we conclude that the careful addition of constraint handling rules can have a positive impact on jmle's performance.

Honors Thesis Defense - Katherine Veil

Tome 117

12:00-1:00 p.m.

Lunch provided

**Wednesday, May 9** - Mathematics & Computer Science BBQ @ Noon on KW Lawn (Rain Location is Tome Hall 2nd Floor Library)

Join us as the Math/CS professors will BBQ hamburgers, hot dogs & veggie burgers to perfection. They will also provide side dishes & desserts. Come & join the fun!

Noon on KW Lawn (Rain Location is Tome Hall 2nd Floor Library)

Wednesday, May 9 - Computer Science Senior Talks @ 2:00 pm in Tome 115

2:20 - Diego Struk

2:40 - Ilya Kamens

3:00 - Ouwen Xi

3:20 - Matt Linnehan

3:40 - Ted Dunmire & Stephen Pierce

4:00 - Snack Break

4:20 - Adam Fothergill

4:40 - Phil Hubert

5:00 - Michael Ryan

5:20 - Seth Tracy

2:00-5:30 pm in Tome 115

**Sunday, May 20** - Mathematics & Computer Science Graduation Reception

Immediately following graduation

Tome Hall 2nd Floor Library