Meetings: Wednesday 2:30 - 5:00,
Room 308 Stanger.
Description: Computers provide us with tools to explore mathematics in deeper ways than ever before. They allow empirical testing of mathematical conjectures with elusive proofs. Computers enable us to experimentally analyze algorithms whose performance defies theoretical analysis. Mathematics provides a structure and formalism that turns the study of computers and their applications into a science and not just an engineering discipline. This learning community focuses on the delicate balance between theory and practice in computer science, revealing the dual and sometimes contradictory nature of computer science as both an engineering and a mathematical discipline.
Goals: To appreciate the symbiotic relationship between mathematics and computer science. To understand how mathematics is used to formalize computer science, and how computer science can be used as a tool to explore mathematics.
Labs and Expectations: The semester is divided up into four or five different self-contained labs as time allows. Each lab is divided up into three parts:
Everyone in class will work in groups of two, and each group is
reponsible for the first two parts of each lab. The enrichment
parts
will be distributed among the groups, each group being responsible for
one lab's enrichment.
Before each lab, each group will prepare by doing the appropriate readings and meeting in advance to discuss them. In the first meeting of each lab, the topic of the lab will be introduced and reviewed by Professors Bravaco and Simonson, after which the groups will breakout to work on their programming and problem solving. This time will be intense but interactive. It will be a collaboration as the groups use the problem sets to focus on learning the topic explored in that lab. The groups are expected to finish all programming and problems by the second meeting.
In the second meeting, the work from the first meeting will be used to explore open questions about the lab and related topics. The style will be fun and flexible. The idea is that they should reap the rewards of all the work from the first week. The explorations will be guided by Professors Bravaco and Simonson.
The third meeting will be a presentation from the group in charge of the enrichment. The enrichment will examine an aspect of the lab's topic that may relate to matters outside of computer science and mathematics. It may involve videos, group games, history, or simulations. The details are up to the group in charge that week, who are responsible for researching a topic of related interest. The groups will be guided by Professor's Bravaco and Simonson, and the enrichment presentations must be approved in advance.
A picture is worth a thousand words, so here is an example of one of our labs and its three parts.
This lab studies the abstract mathematics of Greece and the Renaissance and how it relates to modern cryptography. Before the first meeting the students read and study a brief history of cryptography from ancient times to the present.Grading: For each lab, each group will hand in a lab report consisting of:During the first meeting, the students write programs to cement their understanding and implement various cryptographic methods. They simultaneously write solutions to problem sets on number theory, to make sure their understanding of the foundations is clear.
During the second meeting, the programs are used to encrypt and decrypt various information. A contest to see who can crack whose codes will commence. Experiments as to the practicality of breaking codes and the safety of e-commerce will be performed. Discussions of the future of the internet and its dependence on results in this area will complete the day.
Enrichment for this lab might discuss the life and times of Alan Turing, a famous pioneer computer scientist and mathematician who worked in England during World War II helping to crack German codes. Turing is also famous for being an outspoken homosexual, who was tormented by his own country (for his sexual preferences) despite his heroic contributions to science and the war. He eventually committed suicide at young age. There is an excellent PBS video on Alan Turing and his life, as well as an acclaimed biography, and a broadway play based on the biography. Another possible area of discussion is the issue of government control over encrypted information, regulation versus freedom.
Each lab is graded. The group in charge of enrichment for that week, will have a separate grade given to them that incorporates the opinions and comments of their classmates. Altogether each group will have five lab report grades and one enrichment presentation grade. Final grades will consist of two parts: 75% is an even weighting of these six scores (five labs, one enrichment), and 25% is a grade on participation and interaction throughout the semester.
| Useful Links: | Mathworld | Cut-the-Knot | Math in CS |