Math & CS Chats - Spring 2004
[ 3/25 | 4/1 | 4/5 | 4/12 | 4/13 | 4/22 | 4/29 ]
4/29: Square Roots of Matricies
If A is a square matrix, how do we define its square root? We know that every non-zero number has exactly two square roots, but the situation is more complicated for matrices. In this talk we will derive explicit formulae for all the square roots of 2x2 matrices; they indicate when a 2x2 matrix has square roots and the number of such roots. The results will be surprising!
4/22: Analyzing Ball Movement in Triangular Billiard Tables
Department of Mathematics & Comptuer Science
(Honors Thesis Defense)
When people think of pool and billiards, they visualize a rectangular table, a cue, and playing 8-ball. What happens to the path of a billiard ball if we change the shape of the table to a triangle? This talk explores different types of billiard tables and investigates how to construct periodic paths within acute, right, and obtuse triangular billiard tables.
4/13: Convex Hulls
Department of Computer Science
University of Virginia
For applications such as collision detection in video games and simulations, pattern recognition in images, and analyzing search data, we often need to find the shape and extent of a set of points. Convex Hulls are a way of capturing this information quickly. Finding a convex hull is also an essential step in many other algorithms in computational geometry. How can we apply approaches such as incremental construction, divide-and-conquer, rotational sweep, and recursion to the problem of finding convex hulls?
4/12: Strategies for the Statistical Analysis of Mass Spectral Data and the Construction of Lipid Arrays
Dr. Jeff Forrester
Phospholipids are the primary building blocks of cell membranes and are important participants in transmembrane signaling processes. Until recently, analysis of these molecules at the species level has required labor-intensive techniques. The development of electrospray ionization mass spectrometry (ESI-MS) has made possible the measurement of thermally labile biological molecules, such as phospholipids. Evaluating the vast amounts of data resulting from these measurements is now the rate-limiting step in the assessment of phospholipid composition. This talk presents a methodological strategy for using time-dependent changes in cellular phospholipids after the addition of a stimulant or drug. As a result, lipid arrays are generated to indicate qualitative changes that occur in lipid composition between experimental or disease states, similar to proteomic and genomic analyses. These arrays are contributing to a more complete understanding of the participants of cellular signaling pathways after activation of cell surface receptors.
4/5: A Short Discussion on Sorting
Department of Computer Science
We will cover the Bubble Sort algorithm in detail as well as its implementation in Java, and comment on improvements. In addition we will also discuss the Insertion Sort algorithm and interactively develop an implementation.
4/1: When Close Enough is Close Enough
Dr. Edward Scheinerman
Department of Applied Mathematics and Statistics, Professor & Chair
Whiting School of Engineering, Interim Associate Dean for Academic Affairs
The Johns Hopkins University
Suppose two real numbers x and y agree to 50 decimal digits. Does this mean that x=y? Of course not! It is possible that they differ in, say, the 52nd digit. Still, if two simple expressions are calculated and the results agree to 50 digits of accuracy, it's a safe bet that the two expressions are equal. In this talk we'll transform "safe bet" to "proof".
3/25: RAD = White Elephant, Solution RAD - R = Stable Application
Dickinson Alumnus, Class of 2001
Over the past few years there has been an increasing need by businesses to develop applications quickly. To address these needs Microsoft, Borland and others have developed integrated development environments (IDE) so that Rapid Application Development (RAD) is possible. While RAD has cut application development time considerably, it often has huge drawbacks most importantly being scalability. RAD has indirectly contributed to the idea of "design on the fly".
The solution to the problem is a design focused approach. Through thorough design the following is achieved: the problem (purpose of the program) becomes clear, the rules and logic are clearly stated ahead of time, the necessary resources required to complete the problem are known, ideas on how the problem may change over time develop. Each of these components is critical to delivering a finished product that is stable, reliable and scalable.