This web site is part of a project to articulate what mathematical probability says about the real world. The project has two faces.
1. It is intended as a complement to undergraduate mathematically-focussed courses. I teach a junior-senior "topics" course on this material. Following the link to the Fall 2011 class-by-class topics gives a bottom-up view of what I actually can do, and draft write-ups of many lectures. This page starts a top-down discussion of what I would like to be able to do.
2. The material is also intended for a general audience -- people who read "serious popular science" books. Though given my track record for actually finishing books, it may just stay forever as a web site. As such it provides a more idiosyncratic complement to two existing web sites: Understanding Uncertainty and Chance News.
This is a beta version cover page, currently used in talks to academics, urging them to consider teaching a course in this style.
1. Saying "Hamlet is fiction" is not dissing Shakespeare. Similarly, saying
2. Turning to the second part, let me start with a narrow interpretation of "fact":
As their main requirement, my students actually do course projects -- in practice, not as sharply focussed as I would prefer -- and here are some interesting student project write-ups.
3. Though only 1/3 of the course, perception of probability is the main focus of this web site, so follow the link to get started.
Adding one word to the opening statement, my goal is to articulate critically what mathematical probability says about the real world. Here are several critiques of existing course and book material, and indications of what I seek to do instead.
Critique of introductory mathematical probability courses. A typical introductory textbook, in its introduction or back cover, makes extravagant claims about the usefulness of mathematical probability, but very little in the actual book demonstrates this usefulness -- such demonstation being implicitly postponed to future courses. What one sees in more advanced courses and research literature is "complex fiction"-- models that use technically sophisticated mathematics (compared to the 10 simple models I mention) -- but the vast majority of models are never actually checked against data. So
Critique A: most of the content of introductory mathematical probability courses serves as ``technical prerequisites for complex fiction" rather than saying something interesting about the real world.
The focus of my parts 1-3 is different; I want a course which is satisfactory as a terminal course (analogous to the Freedman et al. Statistics course), while hopefully whetting the curiousity of occasional students and motivating them to study the subject further. Closely related is
Critique B: even in the best textbooks, the majority of examples and exercises are ``just made up" -- see e.g. this list of exercises.
To phrase this more humorously, I urge instructors to
If you really care, here is some more rhetoric about how this course differs from a standard College course.
At some opposite extreme from mathematical probability, one can ask about the Big Picture -- what is the role of probability in Life, the Universe, and Everything? This is the domain of philosophers or writers of popular science style books. My overall opinion of such work is:
Critique C: Writers who claim, explicitly or implicitly, to be dealing with "probability in general" tend in fact to be working within some very narrow vision of the contexts in which Probability arises.
To demonstrate this, I need to exhibit a broader vision, and this is (under construction in) a representative list of perceived instances of chance in the real world.