A screening of a Nova episode about the proving of Fermat's Last Theorem.
Dr. James Hamblin
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.
Angelo Polo '05
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.
Steven Fealtman '94
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.
Dr. David Collins
Dr. Tim Wahls
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.
Dr. Randy Ford
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.
Dr. Thang N. Bui
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.
Dr. Marc Renault
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.
Chats from previous semesters:
4/28: Designing Origami Octagons
Assistant Professor of Mathematics
Shippensburg University
4/21: p-Groups and Nilpotency
Department of Mathematics and Computer Science
Dickinson College
4/7: Bar Codes: An Evolving Technology
for Uses Beyond the Grocery Industry
President of SDF Consulting Alliance, Inc.
3/28: Quantum Computing with Ensembles
Bucknell University
3/24: Constraint Programming Tutorial
Department of Mathematics and Computer Science
Dickinson College
3/10: Talking to Your Computer
Associate Professor of Computer Science
Hood College
3/3: Evolutionary Algorithms in Combinatorial Optimization
Associate Professor of Computer Science
The Pennsylvania State University at Harrisburg
2/10: Catalan Numbers and Lattice Paths
Assistant Professor of Mathematics
Shippensburg University
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