All materials for my classes change dependent upon the semester.  Each semester the discussion might veer from topic to topic and some topics are accented more than others.  Furthermore, by approaching a class in such a Socratic manner rather than Sophistic manner, the students are treated as adults, are challenged, and to whom are not condescended.  I opine a primary goal of any course is to establish an atmosphere that creates for students an interesting and challenging intellectual environment which ideally encourages students to further their study of mathematics.

     To put it succinctly and personally, that which I learnt the best was that which I did myself, rather than be told about, lectured to, or even read about. I must do in order to understand. That I can not explain something does not mean it does not exist, it simply means that I do not know it (at this point or perhaps it is never knowable). All our course work is designed to accentuate that learning is a never-ending process rather than a commodity or entity that can be given like the metaphor of an instructor cracking open the head of a student then pouring the knowledge into said head. In that regard it is very much reminiscent of reform methods and the philosophy of John Dewey. Dewey stated, ``the traditional scheme is, in essence, one of imposition from above and from outside.''

     I wish for all of my students to reflect on the following:  P. J. Halmos recalled a conversation with R. L. Moore where Moore quoted a Chinese proverb. That proverb provides a summation of the justification of the method I employ in teaching. It states, ``I see, I forget; I hear, I remember; I do, I understand.''  One can believe what one wants without regard to the evidence or facts. One can opine only with evidence and justification. One knows only through deduction and proof.
So in my class, you will do rather than see, hear, or read.