East coast computer algebra day 2005: poster abstracts

We present a system that allows wireless smartphones to be used for mathematics communication, that is, for the creation and exchange of mathematical formulas, diagrams, and text between two or more participants. The system enables two or more persons with smartphones or traditional computers to participate in a session. Each of the participants may convey textual, graphical and mathematical information to the other participants. Users can draw, edit, and label geometric shapes, send chat messages, and compose formulas. A turn taking mechanism moderates the communication. The system also supports the addition of services that can be used to provide individual users with additional functionality. Currently, a L ATEX rendering service is available to allow users to create and share mathematical formulas in typeset quality. As the use of smartphones becomes more widespread we expect that our system will be used by online communities such as the Math Forum at Drexel University. Students and teachers of all levels use the Math Forum in order to ask questions, solve problems, and pursue interests in mathematics. The service Ask Dr. Mathreceives as many as 9,000 questions a month and over 200 trained volunteers—teachers, professionals in the workplace, college students, and hobbyists—answer close to 4,000 of these directly within a few hours of their submission. Over 7,800 questions and answers have been published in public archives, with another 400,000 questions and 120,000 answers stored for research and future use. Currently the Math Forum receives about 1.7 million visits a month, and approximately 450,000 of those include the Dr. Math area. Some of the challenges of developing a system for mobile communication of high school mathematics are posed by the input and output limitations of the devices and the enormous heterogeneity of the available hardware platforms. We are using the Treo 600 as our hardware platform. Our software is written in pure Java and can potentially be run on any platform that supports the Java Virtual Machine. Our software architecture makes it easy to add new local or remote services to enhance the communication. Using Riemannian SVD for Problems in Approximate Algebra Brad Botting, Mark Giesbrecht, John May University of Waterloo Abstract. Many problems in abstract algebra can be reformulated as structured linear approximation problems. Problems such as finding polynomials with a GCD which are nearest to given relatively prime polynomials, finding the nearest multivariate polynomial which factors, and finding the nearest polynomial which functionally decomposes, can all be cast as so-called Structured Total Least Squares (STLS) problems. More generally, given a basis of “structure” matrices X1, ...,Xm for a vector spaceV of structured matrices, and a matrix A in V, the STLS problem seeks to find the nearest B to A in V such thatB is singular. Many problems in abstract algebra can be reformulated as structured linear approximation problems. Problems such as finding polynomials with a GCD which are nearest to given relatively prime polynomials, finding the nearest multivariate polynomial which factors, and finding the nearest polynomial which functionally decomposes, can all be cast as so-called Structured Total Least Squares (STLS) problems. More generally, given a basis of “structure” matrices X1, ...,Xm for a vector spaceV of structured matrices, and a matrix A in V, the STLS problem seeks to find the nearest B to A in V such thatB is singular.