Instructor: Allen Bell
Office: EMS E449; Phone: 229-4233; E-mail:
adbell@uwm.edu
During the academic year 1998/99, Math 841 (special topics in algebra) will be an introduction to computational algebraic geometry and commutative algebra, based on the text Ideals, Varieties, and Algorithms, Second Edition, by David Cox, John Little, and Donal O'Shea. This is a Springer-Verlag Undergraduate Text in Mathematics, which means it's written at an accessible level but not a trivial one. We will use MAPLE for computer algebra calculations. Here is a file with some MAPLE programs that will be useful (download it!). Below is information on the book and course and specific information on the first semester and second semester.
You can find out more about the book (and hence the course) in several ways:
During the first semester, we will cover the core material, which is chapters 1-4, and possibly chapter 6 on robotics and automatic geometric theorem proving. This will include the basics of algebraic geometry (except for projective space) and the study of manipulating and solving systems of polynomial equations. If the course lasts for a year, we should be able to cover most of the book, which would yield a more thorough introduction to algebraic geometry.
In fact, we only covered chapters 1-4, and the course will go on for a second semester.
The underlying problem in this course is that of manipulating sets of polynomials and solving systems of polynomial equations in multiple variables, such as the system
The above is a rather rough introduction. (Read the authors' introduction to the text for more.) I am not an expert on all of the material to be covered; maybe you can teach me something about the computational or even the mathematical aspects of the material. The prerequisites stated by the authors are an introduction to linear algebra and a familiarity with proofs: reading them and doing them. Having had an introduction to abstract algebra would be a real plus.
The course is currently scheduled for 9:30-10:20 on MWF in EMS E159 during the Fall semester, and it is scheduled for 10:30-11:45 MW in EMS E495A during the Spring semester. Some adjustment may be possible, but there is no guarantee. Let me know as soon as possible if you want to take the course but have some problems with the schedule.
During the second semester (Spring), the course is scheduled for 10:30-11:45 MW in EMS E495A. We will begin with chapters 5 and 6, and then we will decide what to do after that. I expect we will do something from chapters 8 or 9; we might even do other material. We will see! And of course, I hope to have more fun with MAPLE.