Thursday morning, three students presented homework problems at the board. I followed this with a lecture introducing the concepts of supremum and infimum of a set. Because I got a little sidetracked, I did not quite make it to the Completeness Axiom.
What was the “rabbit chase” for this class? Well, at least a couple of students had commented to me, outside of class, on the difficulty they’ve had with recent homework assignments. They pointed out that they work and work and often can’t make any headway on a few of the proofs. They seemed a little discouraged by the fact that they need help from their professor on every assignment.
I took class time to reassure them that they are not alone. Just about everyone in the class is going through the same thing. I pointed out the fact that I was in their place not that long ago. In fact, since I also did my undergrad here at Wayland, I was almost exactly in their place. I recounted tales of my discouragement as well as the fact that I also spent time in my professor’s office get help on almost every assignment. I was largely motivated by a reader of this blog, who is also a blogger I read regularly. He has recently made the point that the students can gain a new level of insight to a subject by seeing the learning process that the instructor, themselves went through to understand certain concepts.
In my mind, although some may disagree, it does not get any harder as an undergrad than a senior level mathematics course. There are many courses that require as much “work” as a course like this, but I can’t think of too many that require such an high level of abstract and critical thinking. I’ve yet to be convinced otherwise. However, I’ll admit that my undergraduate Physical Chemistry class may have been close.
Next time, we’ll finally cover the completeness axiom.