familiar with applied mathematics at the advanced undergraduate level or preferably higher
In working through the text, I have found that my undergraduate engineering degree and mathematics minor would not have been sufficient to understand the details of Jaynes' arguments, following the derivations and solving the problems. I took some graduate courses in math and statistics, and more importantly I've picked up a smattering of many fields of math after my formal education, and these plus Google have sufficed.
Be advised that there are errors (typographical, mathematical, rhetorical) in the text that can be confusing if you try to follow Jaynes' arguments exactly. Furthermore, it is most definitely written in a blustering manner (to bully his colleagues and others who learned frequentist statistics) rather than in an educational manner (to teach someone statistics for the first time). So if you want to use the text to learn the subject matter, I strongly recommend you take the denser parts slowly and invent problems based on them for yourself to solve.
I find it impossible not to constantly sense in Jaynes' tone, and especially in his many digressions propounding his philosophies of various things, the same cantankerous old-man attitude that I encounter most often in cranks. The difference is that Jaynes is not a crackpot; whether by wisdom or luck, the subject matter that became his cranky obsession is exquisitely useful for remaining sane.
Not too long ago, I asked LessWrong which math topics to learn. Eventually, I want to ask for what the prerequisites for each of those topics are and how I should go about learning them. This is a special case of that.
I'm rereading the sequences and Eliezer seems to love E.T. Jaynes. As part of my rationality self-study, I want to work my way through his Probability Theory: the Logic of Science. What math topics do I already need to understand to prepare myself for this? I learned calculus once upon a time, but not fantastically well, and I plan to start by reviewing that.
Also,
Despite Eliezer's praise of the "thousand-year-old vampire", it there a better book to learn probability theory?
Does anyone want to learn this (or the other math from my post above) with me? I'd love to have a partner or maybe even a work group. Location is no obstacle. [Two caveats: 1. I'm busy with stuff and may not be able to get into this for a few months 2. I hard, but I am incredibly slow at computation (such that on every math test I have ever taken, it took me at least 3 times as long as the second slowest person in the class to finish). You might find that I go to slow for you.]