## Spring 2005

[ 2/10 | 3/3 | 3/10 | 3/24 | 3/28 | 4/7 | 4/21 | 4/28 | 5/5 ]

**5/5: The Proof
**A screening of a Nova episode about the proving of Fermat's Last Theorem.

**4/28: Designing Origami Octagons
**Dr. James Hamblin

Assistant Professor of Mathematics

Shippensburg University

In this talk, I will teach the audience how to construct origami octagons. In addition, we will consider the problem of how many "different" octagons can be constructed. This will involve various counting techniques including Burnside's Theorem.

**4/21: p-Groups and Nilpotency
**Angelo Polo '05

Department of Mathematics and Computer Science

Dickinson College

We will be doing an investigation in Group Theory into the isomorphism types of certain groups. Specifically all possible isomorphism types of groups of order p, p2, p3, and pq, where p, q are distinct primes will be shown. We will also prove a classification of nilpotent groups and show all isomorphism types of extra-special 2-groups.

**4/7: Bar Codes: An Evolving Technology for Uses Beyond the Grocery Industry
**Steven Fealtman '94

President of SDF Consulting Alliance, Inc.

Bar coding began as an idea at Drexel University by two gentlemen who overheard a conversation between a grocery executive and university professor. Despite obtaining a patent for their "invention", neither became wealthy as a result of this eventual billion-dollar industry. Bar Codes continue to evolve from the initial 2-digit idea beyond the typical UPC style grocery labels. New labels are 2-dimensional, image matrix or are wireless, radio frequency emitting tags. Examples of bar code integration into software applications are discussed.

**3/28: Quantum Computing with Ensembles
**Dr. David Collins

Bucknell University

**3/24: Constraint Programming Tutorial
**Dr. Tim Wahls

Department of Mathematics and Computer Science

Dickinson College

Constraint programming is a technique for solving problems for which no efficient algorithms are known (i.e., NP-complete problems). In this tutorial, we will use the Oz programming language to develop a program for solving the money problem: uniquely assigning the digits 0 - 9 to the letters S, E, N, D, M, O, R, Y so that the equation SEND + MORE = MONEY is satisfied. We will then discuss how constraint programming techniques can be applied to the course scheduling problem.

**3/10: Talking to Your Computer
**Dr. Randy Ford

Associate Professor of Computer Science

Hood College

Decades ago, artificial intelligence scientists announced to the world that we would soon be able to chat with computers as effortlessly as we do when we communicate with each other. As it turned out, they severely underestimated the complexity of the task. This presentation will focus on how this misstep occurred and how it influenced the current state of the art in Natural Language Processing. In addition, some new breakthrough technology in this field will be demonstrated.

**3/3: Evolutionary Algorithms in Combinatorial Optimization
**Dr. Thang N. Bui

Associate Professor of Computer Science

The Pennsylvania State University at Harrisburg

In this talk we describe the main ideas of evolutionary algorithms. In particular, we discuss genetic algorithms, evolution strategies, evolutionary programming, genetic programming, and ant colony optimization. We also describe the NP-hard graph bisection problem. This is the problem of partitioning a graph into two disjoint subgraphs of equal size while minimizing the number of edges connecting the two subgraphs. We then show how a genetic algorithm and an ant based optimization algorithm were used to solve the graph bisection problem.

**2/10: Catalan Numbers and Lattice Paths
**Dr. Marc Renault

Assistant Professor of Mathematics

Shippensburg University

The Catalan numbers, 1, 2, 5, 14, 42, 132, ... are not quite as well known as the Fibonacci numbers, but like the Fibonacci numbers, they often appear in unexpected places. The n-th Catalan number turns out to be the number of lattice paths from (0,0) to (n,n) that stay below or on the line y = x. (A lattice path is a path in the plane where each step moves one unit in the positive x or y direction - no backtracking is allowed.) We will look at where the Catalan numbers occur, a few combinatorial derivations of their n-th term formula, and consider some ways to generalize Catalan numbers using lattice paths.