2. The explicit proposition the main purpose of an undergraduate Math program is as the first step toward a research career strikes me as ridiculous; we don't believe this for History or Literature or most academic subjects, and empirically most Math graduates surely don't follow a research career (quantitative data is surprisingly hard to find). But in my experience most undergraduate instructors (at major universities) and textbook authors act as if this ridiculous proposition were true, because (I guess) either they follow without conscious consideration a mathematical culture in which this proposition is implicitly assumed, or because they cannot imagine an alternative. So one goal of this project is to suggest an alternative. This is intended to complement, not replace, standard math courses. If you really want it, here's my short rant against U.S. undergraduate Math programs and my commentary on the mathematician's blind spot.
3. Let's compare math books with books in other academic subjects by looking at page 59 of several books. The titles are unimportant -- I give the discipline and the topic under discussion.
Part of my goal is to teach and write about Probability in the spirit of (i) - (iv). Good textbooks on Statistics come close, for instance
4. Practical details about teaching the course.
(a) I maintain a list and short reviews of about 80 non-technical books relating to probability. At the start of the course, I tell students to choose and read one of these books (or some other material of their choice), find some topic interesting to them, and give a 5-minute talk on that topic. (Incredibly, about 10% of the class are unable to comprehend those instructions ..... )
(b) Since the only other requirement is doing a course project, I require and take attendance at class.
(c) Teaching the course is fun but a lot of work. It's intended for students who want to take a course like this; the only annoying aspect is that in practice, bureaucratic constraints force some students to take it involuntarily, yielding 36 students, and then I can't supervise projects very well.
(d) I teach 25 - 30 classes, each 50 minutes, and my goal is to do a different topic every class, without any particular ongoing logical development. Though by chance some topics recur: