MATH 582 E: Introduction to algebraic computation
Winter Quarter 2023, University of Washington
Meeting time and location: Mondays and Wednesdays 2:30 PM - 3:45 PM, PDL-401 Office and Office hours:
PDL-C505. Open door policy. You can come by with questions whenever I am there, or just to say hello.
I plan to hold regular hours Fri 10--12 (subject to change.)
Appointments made by email are also welcome. Contact: timduff AT uw DOT edu
Grades:
To pass, you must submit a 2--8 page paper on a topic pertaining to the course.
I suggest writing a report about a recent paper using ideas from computational algebraic geometry.
A list of possible topics is given below.
Feel free to propose your own topic.
The point of this exercise is for you to develop familiarity with the research literature.
Besides providing a summary of whatever topic you're interested in, you should feel free to try to replicate all or part of the computations used in some paper, or start thinking about your own research problem.
Feel free to discuss this with me at any time during the quarter.
Working in pairs is ok, but please ask me first.
Let me know the topic you choose by Feb 15.
First draft will be due March 1.
Final draft will be due March 18.
Syllabus:
A developing set of lecture notes will be maintained here. Announcements will appear on Canvas.
Software & exercises:Here is a list of problems that I encourage you to try solving. The techniques needed to solve them will be developed over the course of the quarter, but there is no reason not to start thinking about them now. Please feel free to talk to me and your classmates about them.
Most problems will benefit from some sort of computer experimentation. Feel free to discuss the problems that interest you with me and fellow participants.
I will demonstrate several examples, primarily using the computer algebra Macaulay2, which will be collected at this homepage.
Many examples will run easily in your browser thanks to the Macaulay2Web interface.
To run larger examples, here are installation instructions.
Contact me if you get stuck.
There are a number of other software packages for computational algebraic geometry and commutative algebra, each with a particular set of strengths.
Among the freely-available options for computing Gröbner bases, we have
