Josh gave a very good talk about the effect of row operations on the determinant of a matrix. Following his talk, there was a brief discussion, during which time the following points were brought up:

• The front board, when above the back board, projects a slight shadow onto the top of the back board. It is a bit hard to read anything written in the shadow, especially from the back of the room.
• Once something is on the board, leave it there. In particular, don't erase parts of examples to explain other (related) examples. This may save the instructor time, but it is very hard from a note-taking point of view.
• Similarly, don't add to lines of text already on the board, e.g., don't go back to an old proposition and write a note beside it.

Professor Diller

Professor Diller talked a bit about the linear algebra/ODE course. Most students in the course are engineers - it is the fourth course in the calculus sequence. The big difference between the material of this course and that of calculus is that the linear algebra is more conceptual in nature. There is really only one operation - row reduction - and all ideas and techniques boil down to this. The engineers seem to be motivated by a geometric approach to linear algebra.

The students in the course tend to be very good (as is usually the case at Notre Dame anyway). However, they do have a big range of ability - about one third of them have trouble with the material. It may be assumed that the material of this course is new to the students. Beware, though, for the ND dorms keep old copies of exams and homework for most classes!

The most unpleasant thing about this course is the syllabus. It is strange to go through two thirds of a course on linear algebra and then suddenly drop it and switch to ODEs. The class was designed for the benefit of the engineers, and that is what they wanted. The sequel to this course is a course entirely on ODEs, so it might one day happen that this course switches entirely to linear algebra (for the sake of coherence!).