MATRICES,
VECTOR SPACES,
AND INFORMATION RETRIEVAL
Professor Liz Jessup - University of Colorado
Friday, March 15, 2002, 1:35, Room E104
of
Moench Hall.
Abstract:
The growth of the Internet and of digital libraries in recent years have overwhelmed traditional methods for the processing, storage, and retrieval of information. In particular, procedures for indexing or extracting the knowledge or conceptual information contained in the vast collections of textual material can be lacking. Recently developed information retrieval technologies are based on the concept of a vector space. Data are modeled as a matrix, and a user's query of the database is represented as a vector. Relevant documents in the database are then identified via simple vector operations. Orthogonal factorizations of the matrix (such as the QR factorization) provide mechanisms for handling uncertainty in the database itself. We will discuss how fundamental mathematical concepts from linear algebra can be used to manage and index large text collections.
REFLECTIONS ON THE ARBELOS
Professor Harold Boas - Texas A&M
Friday, March 15, 2002, 7:00 - 8:00, Room E104
of
Moench Hall.
Abstract:
The geometric shape bounded by three mutually tangent semi-circles having collinear diameters (see the figure) was named the arbelos by Archimedes. The arbelos has many surprising geometric properties, some known to the ancient Greeks and some discovered in modern times. The geometry of reflections offers insight on the arbelos, but a full appreciation of its properties, like the work of Archimedes, reflects other subjects too, such as number theory and mechanics.
WHAT
CAN ONE SAY ABSOLUTELY ABOUT
POWER
SERIES?
Professor Harold Boas - Texas A&M
Saturday, March 16, 2002, 9:30 - 10:30, Room E104
of
Moench Hall.
Abstract:
A fundamental property of power series is that in the interior of the region of convergence, they actually converge absolutely. What other properties of power series depend only on the absolute values of the terms of the series? Answers to this question come from complex analysis in one and several variables, from functional analysis, and from probability theory.