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.