Math 499 Project Guidelines

Spring 2005

Each student is required to give a twenty-five minute presentation to the class. In addition, you must email me an abstract for your talk, which I will post on the web, a week in advance. This course is designed to acquaint you with plane curves, so your project should be about curves. Giving a mathematical talk in only twenty-five minutes is harder than it sounds. You must be organized in order to say all that you need to say in such a short time. Practicing your talk and timing it is a must. If you like, you can present a practice talk to me and maybe even the VIGRE post-doc James Spencer if you are feeling ambitious. The talk should be on such a level that the entire class can understand what you are saying. You may use the chalkboard, overhead transparencies, or even a computer. If you want to use a computer, tell me at least a week in advance so that we can reserve a projector.

Project Schedule:

March 25th: Everyone must have chosen a topic.

March 30th: Sean submits his abstract.

April 6th: Seanís talk. Kristian and Abraham submit abstracts.

April 13th: Kristian and Abraham give talks.Here is the link to Kristianís Presentation. Crystal and Thomas submit abstracts.

April 20th: Crystal and Thomas give talks. Lisa and Bill submit abstracts.

April 27th: Lisa and Bill give talks. Papers are due for those receiving multiple credit hours.

Project Ideas:

Bezier Curves

Classification of Cubic Curves (Two people could do this as a joint 50 minute presentation, I have a book on this)

Investigate a Family of Curves (Famous Curves Index)

Caustics of Plane curves (I have a paper)

Geometric Characterization of Parametric Cubic Curves (I have a paper)

Write a program to find and analyze plane curve singularities.

These are just suggestions. I encourage you to use part of the spring break to google ďalgebraic plane curvesĒ and/or go to the library to check out the QA565 books. Send me an email, knecht@rice.edu, when you decide on a topic. Topics will be divided up on a first write first serve basis. You must tell me a topic by March 25th.