Fall 1999

[ 9/13/99 | 10/4/99 | 10/11/99 | 10/25/99 | 11/8/99 | 11/22/99 | 12/6/99 ]

9/13/99 - Welcome Back Picnic
This is a chance for everyone in the Mathematics and Computer Science program to get together for an informal lunch. Join current and interested Math and CS majors, along with faculty for this week's Math/CS Chat. Be there or be squared...

10/4/99 - Student Internship Report
Joe Rodgers
Dickinson College

Joe Rodgers, a senior computer science major will discuss his summer internship. Joe worked this past summer creating database applications for a company close to his home. He will discuss how he found the internship and the types of work he did.

10/11/99 - Student Internship Report
Ryan Doherty
Dickinson College

Ryan Doherty, a senior mathematics and computer science major will discuss his summer internship. Ryan worked developing web based interfaces that access databases. He will talk about the technologies involved in these projects and the advantages and disadvantages of using a proprietary solution such as the Microsoft Visual tools.

10/25/99 - Scitamehtam = Reverse Mathematics
Thomas Drucker

There is nothing more frustrating than trying to prove something but missing the result you need to get the proof to work. Reverse mathematics takes care of this problem by asking, not what you can prove from a given set of statements, but rather what set of statements you need to start with in order to prove something. This sounds as if it is a cure for all problems with proofs that have ever been proposed. What may be a little more surprising is that reverse mathematics offers a way of breaking down all of mathematics into building blocks. This talk will look at some of the building blocks at the basis of mathematics and describe how they fit together to produce some of the standard results which make up forward mathematics as well.

11/8/99 - Talking about Reuse - Recycling in a Digital World
David Stahl
Department of Mathematics and Computer Science
Dickinson College

Reuse of software is one important goal of object oriented methodology. I will talk about what constitutes reuse of software and why reuse is important to the discipline of computer science. I'll show some classic examples of reuse, and demonstrate why reuse is difficult to do in practice. I'll talk about how the Java language encourages reuse, and how the paradigm presented in Java can help us write reusable code in other computer languages. I will speculate on why application frameworks are a popular software development topic. Finally, I'll conclude with some techniques that have helped me practice creative recycling in my own software development.

11/22/99 - Bayesian Projections for Baseball, Football, and Real Life
Phil Everson
Department of Mathematics and Statistics
Swarthmore College

When making statistical inference about a parameter, such as an underlying population mean or rate, the classical (or frequentist) approach is to treat the parameter value as being fixed and unknowable. Conclusions are based on how likely (or unlikely) the observed data would have been for various parameter values. In contrast, the Bayesian approach is to treat the parameter as a random variable following some probability distribution. This enables one to make actual probability statements about the parameter value, having conditioned on the observed data. The Bayesian paradigm is particularly satisfying when making projections based on partial data. Examples from sports include predicting season batting averages for baseball players, or rushing yardage for football players, based on data from only a few games.

12/8/99 - A Back-and-Forth Approach to Automated Reasoning
David Reed
Department of Mathematics and Computer Science
Dickinson College

Suppose you are in charge of a murder investigation. You have basic knowledge at the beginning of the investigation, including rules (e.g., the killer must have means and motive) and facts (e.g., the butler hates the victim). There are two approaches that you could take toward finding the killer. You could work forwards from the known facts, deducing new information that might eventually lead to the unveiling of the killer. Conversely, you could work in a backwards direction, starting from a specific suspect and building the case back to known facts. Each of these approaches has its advantages and might be useful in different scenarios.

Automated Reasoning is a branch of Artificial Intelligence research concerned with the mechanization of human reasoning. In this talk, I will discuss the role of directionality (forward vs. backward) in automated reasoning, and the tradeoffs between the two. I will then present a bidirectional reasoning system which is able to integrate both types of reasoning and so maintain many of the advantages of both. This system, known as SATCHMORE, is elegant and straightforward to implement, yet surprisingly powerful. In fact, a variation of this system was used to solve open problems in certain finite algebras.