Each class two students will give lectures. Each lecture should be about 25 minutes long. Individual lectures will not be graded, but lectures make up a good portion of the final grade. In evaluating your lectures, I will look at their clarity, organization and preparedness. I will also consider how your lectures improve over the course of the semester.
You will give a practice lecture to a small audience before your first lecture. This group will consisting of the course instructor, the mathematics writing instructor working with this class, and the other student lecturing in the same class as you.
Each lecturer will give one or two exercises relevant to the material being presented. These exercises, and their solutions, should be e-mailed to the course instructor as a Latex file. The exercises can be stated during lecture, though this is not necessary. It's ok if the exercises come from a book (although it'd be preferable if they did not, or at least if they were slightly modified), but be sure to give proper attribution.
As a member of the audience, I'd like you to write a few comments on each lecture you observe. I'm not asking for any kind of lengthy analysis; it would be enough to point out that the lecturer is writing too small. However, make sure the comments are useful—don't just say "that proof was good," say why. I will collect these comments at the end of class and e-mail them to the lecturer so that they can have some feedback. (The lecturer will not know who made which comments.)