Yesterday I took the second of three exams in my statistics course. While I felt reasonably well prepared for the exam when I sat down to take it, I realized—about three minutes after handing in my work—that I had incorrectly answered the first part of the first question on the exam. Unfortunately, this probably means I also answered the second, third and fourth parts of the question incorrectly.

Of course I have no one to blame but myself. Perhaps I should have triple checked my work. Perhaps I should have done more studying. Perhaps I shouldn't have eaten that cookie before the exam. Still, I feel a certain indignation.

For whatever reasons, I find my professor's lectures do virtually nothing to improve my understanding of the subject matter. (Anecdotal evidence suggests I'm not alone.) Worse still, I find the assigned text for the course (which I blogged about last week) difficult to understand and lacking in depth.

Not one to just give up, I did some research. Professors Charles M. Grinstead (Dartmouth) and J. Laurie Snell (Swarthmore) provide a fantastic introductory probability text online as a free download. I also bought myself a copy of Professor Morris H. DeGroot's (CMU) excellent introductory statistics textbook, Probability and Statistics from Amazon.com. I also owe a big thank you to the folks at MIT's Economics Department, who have published a set of lecture notes for their economics statistics course, 14.30, on OpenCourseWare. Armed with those tools, I have essentially been teaching myself basic statistics and probability, including a raft of material that my professor and the assigned textbook don't so much as allude to.

On the one hand, this approach has provided me with a great deal more material to digest and enjoy than I would have seen otherwise. At the same time, these two—arguably superior—texts do not put the same weight on certain subjects as my professor or the assigned text, which, as I have now discovered, leads me to over study some subjects and under study others.

Which leads me back to my indignation.

It drives me crazy that I will receive a lower grade than other students because I have difficulty following the style of teaching my professor uses, and have taken steps to go beyond the course's purview to master the subject as a consequence. In some sense, I'm being punished for learning too much.

More than that, though, this problem underscores a more fundamental problem with the Bates Economics Department's quantitative course requirements. To their credit, unlike many other schools, our economics department requires students take two quantitative courses—probability and statistics, and econometrics—rather than one course that mixes together probability, statistics and econometrics in a single semester.

But while many people speak highly of the econometrics half of the sequence, I have yet to find a student with the same amount of praise for the statistics half. At least from my perspective, the statistics course would be much, much better if the course had a math prerequisite—single variable calculus is a must for the study of continuous probability distributions—and were a more in-depth study of the material.

To his credit, I suspect my professor chose the awful textbook he did because, unlike many other, more modern texts, it include a fair number of "proofs" of various mathematical properties. Unfortunately, most of these "proofs" aren't really proofs, in a mathematical sense. That, and the text omits some standard mathematical conventions for dealing with probability and statistics. The first few chapters, for instance, don't even mention sets (in the mathematical sense) when treating probability theory.

That and both the exams tested my ability to memorize formulas, not my ability to use the formulas as tools to reach meaningful conclusions, which should be the goal of an economics and statistics course. (By comparison, the exams I studied with on MIT's OpenCourseWare, taken from a 2006 section of 14.30, provided a formula sheet that could easily have represented the answer key for the exam I just sat.)

Writing the course evaluation for this class will be a real treat come April.