Upcoming Seminars for Fall Semester
Unless otherwise noted, the Fall Semester Seminars will be held on Wednesdays from 9:10am - 9:50am in PB 390.
December 4, 2013; 9:10am in PB390: Lance Burger (CSUF)
Title: An Introduction to Cramer's Paradox
Abstract: Gabriel Cramer and Leonhard Euler both wrote important books on the theory of equations in the mid 18th century. During the years leading up to their publication, they carried on a friendly and fruitful correspondence. One topic they discussed was a paradox that was first noticed by Maclaurin: that nine points should be sufficient to determine a curve of order three, and yet two different curves of order three could intersect in up to nine different places. Although this situation has come to be known as Cramer's Paradox, it was Euler who first suggested the resolution of this apparent contradiction in a letter that was lost long ago but rediscovered in the Smithsonian Institute in 2003. In this talk, we investigate the properties of algebraic curves of order two and higher and describe Cramer's Paradox and Euler's resolution, including his elegant example of an infinite family of cubic curves that all pass through the same nine points.
December 10, 2013; 2:00pm in PB390: Elda Bautista (Fresno State graduate student)
Title: Preconditioned Multigrid
Abstract: The elliptic partial differential equations (PDEs) generate large, sparse linear systems of equations. There exists the need for an efficient and robust numerical methods for solving these PDEs with very few iterations. The size problem will increase as hardware constraints allow it, so we need to develop a method whose convergence is independent of the number of unknowns. Multigrid is characterized for this and for its rapid convergence and less storage memory than other iterative methods. The power of multigrid methods resides in the combination of a simple iterative method, such as the Gauss-Seidel method, and prolongation and restriction schemes. However, multigrid methods are problem oriented and do not always converge in few iterations. We are incorporating the robustness of the preconditioners with the power of the multigrid methods. First, we examine the formulation of multigrid methods, multigrid as preconditioner of a projection method (GMRES), and preconditioned multigrid. Then, we compare the performance of the multigrid, multigrid preconditioned GMRES and the preconditioned multigrid methods using three well known preconditoners: PSSOR, ILU(0), and AINV in numerical examples.
December 11, 2013; 9:10am in PB390: Marat Markin (CSUF)
Title: A Gelfand Type Theorem for Normed Algebras
Abstract: In the course of our end-of-semester discussion, we are going to prove a Gelfand type theorem giving a characterization of one-dimensional normed algebras. A short lucid proof of this statement resting upon basic principles of linear algebra and analysis demonstrates a powerful interplay between the latter unhindered by unnecessary sophistication.
If you need a disability-related accommodation or wheelchair access information, please contact the Mathematics Department at 559.278.2992 or e-mail firstname.lastname@example.org. Requests should be made at least one week in advance of the event.