# Probability in the Real World: some rhetoric.

1. There is a 2500-year tradition and aesthetic of Pure Mathematics, and one can do Probability as part of Pure Mathematics -- I have no quarrel with that. On the other hand, most of us working in Probability -- even if we personally do it as Pure Math -- believe there is another side of the subject which does relate to the real world. So the project is:
• to articulate what mathematical probability says about the real world.

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.

In many other disciplines which are of both academic and non-academic interest:
(i) one can write a book which reasonably fits both "upper division textbook" and ``serious popular book";
(ii) one can write ``what is known" without getting drawn too deeply into ``how do we know it?" -- leaving the latter to professional researchers;
(iii) one can write so that each page says something interesting;
(iv) nothing is "just made up"; if there are speculative theories they are clearly labeled as such.

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

In Probability one more typically finds writing such as
I don't know any existing course or book on Probability in the spirit of (i) - (iv). Here are some books that come close.

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:

• asteroid impact
• influenza pandemic
• prediction/stock markets
• summary statistics for categorical data
and there are a number of extra themes I would like to develop
• separating skill and luck in sports