|Some functions to use with Maple.(pdf)|
|My tutorials page for Maple and Magma.|
We will study algebraic geometry, one of the richest and oldest areas of mathematics. During the 20th century, the theoretical and very abstract side of the subject was prominent, but with the availability of computers, the computational roots have been reinvigorated. This course will develop the theory behind the computational tools.
What is algebraic geometry? Think back to high-school algebra where you graphed polynomial equations and perhaps found the interestection of plane curves defined by polynomials. Now think about higher dimensional space and look at intersections of hyper-surfaces defined by polynomial equations. What is the dimension? How many components are there? What is the simplest way to describe the intersection? These are some fundamental questions of algebraic geometry.
The textbook we are using is excellent. I hope to cover the core
material, chapters 1-4, and then let student interest guide the rest
of the semester. There will be homework assignments with proofs and
compational exercises. I expect to incorporate computer assignments
as well. There will also be a final project, with a great deal of
latitude in choice of topic. You may focus on theoretical questions,
implementation of an algorithm, an applied problem, or some
combination. You may also develop an educational module for advanced