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… [Read more…]
February 14, 2007
What does “Wayne’s World” have to do with Real Analysis? Good question. I inadvertently structured my lecture in such a way that it reminded me of the old saturday-night-live-turned-box-office-money-maker. Both in the sketch and the movies, Wayne and Garth would broadcast their rock-n-roll show from Wayne’s basement. Anyways, whenever they would do a dream segment… [Read more…]
February 12, 2007
We had no homework assignments due on Thursday, so I dove right into lecture. We proved a few more results following from our ordering of the reals. Upon completing these theorems, we were then able to do the basic sorts of solving of inequalities we teach in our lowest level of algebra. It is interesting… [Read more…]
February 6, 2007
During this morning’s class I surprised the students by letting them know that today was my turn to answer homework questions at the board. As I have mentioned in previous posts, the students are being randomly selected to present some of the homework problems at the board. For many of them this is a considerably… [Read more…]
February 2, 2007
On Thursday, we began the chapter on Real Numbers. We are taking the axiomatic approach to defining the set of real numbers. I demonstrated the difficulty of defining Real Numbers in the techniques that have been typically used in their earlier classes, such as by decimal expansion or as points on the real number line.… [Read more…]
January 31, 2007
During I.A. on Tuesday (Holy Cow 7:25 am is early to start a class) two students presented problems at the board. I really enjoy having this part of the class. All of these students have taken courses from a colleague of mine. She has made oral presentation of homework a regular part of her upper… [Read more…]
January 25, 2007
In Intermediate Analysis this morning, three students each went to the board to present homework problems on basics of sets and mappings. This is first time that I have incorporated the oral presentation of homework as a part of an upper level mathematics course. It was one of my least favorite aspects of the graduate… [Read more…]
February 18, 2007
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