Thursday, January 28, 2010

Cancelled class today

I am sorry, but my substitute Allen Knutson is sick today and is not able to cover my class for me while I am away. We will just have to work extra hard for the remainder of the semester :)

See you on Tuesday,


Wednesday, January 27, 2010

First day recap, and an important announcement

On 1/26 I spent some time motivating the problems we will look at by first reminding you of the types of things one does in a linear algebra class. Some basic problems that one encounters are:

Solving systems of linear equations
Structure of the solutions to a linear system
Detecting 'redundant' systems
Parametric vs. Implicit descriptions of objects

We will handle each of these problems in this class as well, but for polynomial equations rather than linear ones, with an emphasis on the algorithms that one uses to solve these problems.

One thing that I forgot to mention is that I am going to be out of town for class on Thursday 1/28. Class is still scheduled to meet, and
Allen Knutson will be covering class for that day. I assure you that you are in excellent hands.

Allen will begin to tell you about affine space, as well as some first examples of solution sets of polynomials on Thursday, and will perhaps begin to introduce you to ideals in a polynomial ring, which is the algebraic object that replaces the 'span' of a linear system of equations in our case.

Tuesday, January 26, 2010

Course Book, other announcements

Hello everyone!

It's a pleasure to be able to introduce you to the interesting world of computational algebra. We'll learn about solving polynomial systems of equations, and their applications to some (seemingly easy, yet difficult) robotics, colorability of graphs, and automated geometric theorem proving (which you had *that* in grade 9, right?). Along the way we will learn about some deep mathematics and discover that what we are talking about is only the tip of the iceberg.

The book that I will be following for the course is Cox, Little, and O'Shea's "Ideals, Varieties, and Algorithms" published by Springer-Verlag. The bookstore has it, but if you would also like an electronic copy, then as one of the privileges of being a Cornell undergraduate, your library has phenomenal access to online mathematics texts from Springer. If you access the below link while on Cornell's campus, you will gain access to the chapters of the book (sadly, there is not a 'download book' button).

Ideals, Varieties, and Algorithms

At various points in the semester, we will also be using an open source mathematics package called Sage, and a variant of it called Sage Notebook. Sage Notebook provides access to Sage via a Java interface on the web, allowing you to tinker with mathematics with ease. It also provides a convenient interface to a more advanced computer algebra package that we will use later on in the semester, Macaulay2.

The course grade will consist of homeworks (50%), a midterm (20%) and final (30%), with both exams being take-home exams. The homework will be due roughly once a week or two weeks, depending on the assignment. As of right now, the midterm is scheduled to be handed out 3/4 and due on 3/11 and the final is scheduled to be handed out 5/6 and due the scheduled day of the final, which is 5/13. This is subject to change.

Your TA for the course is Saul Blanco Rodriguez, and he has set tentative office hours for MW 1:30-2:30. My office hours are just by discovery - I am in my office from 9-5 most days and if you find me in my office (Malott 587), then by all means ask questions. If there is a particular time that you would like to speak with me, then please email me at myname(one word) at math dot cornell dot edu and we can set up a time.

See you soon,