## Spring 2006

[ 2/21 | 3/21 | 3/23 | 4/06 | 4/18 | 5/02 | 5/04 | 5/10 ]

**5/10: Knowledge Discovery in Medical Image Data Sets
**Adam Reagan

Department of Computer Science

Appalachian State University

Medical images contain a vast amount of information. These images are often stored in digital format on computer disks for further study and analysis.Some of this information is hidden and not easily discernible. In the past decade, significant progress has been made in knowledge discovery from a wide variety of large data sets. Previous research in this area show that both wavelet lifting schemes and neural network based data mining techniques can be used to detect cancer in seemingly clear images. This talk discusses how wavelet lifting schemes and 3-dimensional shape histogram sectoring techniques can be used to classify images based on their content and identify potentially cancerous regions in 2-dimensional mammogram images.

**5/04: The Role of Mathematics in Undergraduate CS & SE Education
**Peter B. Henderson, Head

Department of Computer Science and Software Engineering

Butler University

Computer science and software engineering are young, maturing disciplines. As with other mathematically based disciplines, such as the natural sciences, economics and engineering, it takes time for the mathematical roots to grow and flourish. The current mathematics requirements for computer science and software engineering majors may not be appropriate, and the mathematics material that is appropriate is not integrated into the courses. Computing Curricula 2001 (CC 2001) and Software Engineering 2004 include discrete mathematics in the core and recommends that this material be covered early. This partly addresses the requirements issue, but not the integration problem.

This presentation will identify and motivate the topics to be included in freshman discrete mathematics, discuss curricula issues, present evidence that teaching discrete mathematics and problem-solving early is beneficial, and discuss ways in which mathematical concepts can be integrated and reinforced throughout undergraduate computer science and software engineering curricula.

**5/02: Evolving Small-World Neural Networks
**Stevan Kominac

Department of Mathematics and Computer Science

Dickinson College

The goal of this research is to evolve neural networks with a genetic algorithm in order to investigate the circumstances, if any, under which neural networks evolve as small-world networks. The fact that small-world networks appear so frequently in nature, where they have emerged through the process of evolution, is the motivation behind this research. Hence, the question is, if we evolve neural networks through a genetic algorithm that mimics natural evolution, could neural networks also evolve as small-world networks?

**4/18: Student Reports
**Trevor Davis

Anne Maiale

Department of Mathematics and Computer Science

Dickinson College

Crossing the Language Barrier - Translating Mathematical Documents (Anne Maiale): A large amount of the research and writing on Euler's Polyhedral Formula is by German-speaking (and writing) mathematicians from the 18th and 19th centuries. I will give a brief synopsis of the content of the papers that I have been translating and also speak about the challenges of translating technical, somewhat archaic texts.

Applying Something I Love to School (Trevor Davis): During my internship with the Harrisburg Horizon semi-pro basketball team, I was able to combine my love for basketball with my web development skills. I designed and updated both the team website as well as the league website, all while earning credit for class.

**4/06: Probability and Expectations in Games
**James Hamblin

Assistant Professor of Mathematics

Shippensburg University

One of the most common applications of the ideas of probability is to games. However, in many games, the same action is repeated many times: a die is rolled, a card is drawn, a coin is flipped, and so on. People have certain expectations, knowing the probability, for how many times we would need to repeat these actions to get a certain number of desired outcomes. We will explore these ideas and how they apply to some common (and some uncommon) games.

**3/23: Metric Spaces
**Beth M. Campbell Hetrick

PhD Candidate

Department of Mathematics

Bryn Mawr College

This talk provides a basic introduction to metric spaces. We will define a metric space and consider examples of several different metrics. We also consider unit balls. Finally, we mention some applications of metric spaces.

**3/21: Cluster Analysis and its Application to Systems Biology
**Dr. Jeffery Forrester

Research Instructor

Vanderbilt University Medical Center

Innovations in genomics and proteomics have revolutionized the collection of biological data, allowing researchers to generate huge data sets with a reasonable expenditure of resources. Cluster Analysis provides an elementary statistical tool for exploring these data sets, assisting in the identification of internal data structures that would be difficult to find without computational assistance. In this talk, we explore the concepts of metrics, similarity/dissimilarity matrices, clustering routines, and dendrogram construction. Examples are taken from biological signaling networks and the mass spectral analysis of cancer biopsies.

**2/21: What in the world is mathematical biology?
**Holly D. Gaff

Assistant Professor

University of Maryland School of Medicine

Department of Epidemiology and Preventive Medicine

Are you are a math major, but you want to do something with real world applications, or are you a biology major, but you secretly really enjoy math? What are you going to be when you grow up? How about a mathematical biologist? So what is math biology? Mathematical biology is a relative new field of study that can bring together mathematicians who enjoy applying math to the real world and biologist who have strong quantitative fields. Are there jobs in math biology? What if I haven't had biology since junior high? The best way to understand this newly emerging field is by example. We will play some math biology games. I will also show some examples of my research that will hopefully help you to understand what math biology is and maybe even give you some new ideas of what you want to be when you grow up.