I am not sure about the prerequisites you need for "rationality" but take a look at the following courses:
(1) Schaum's Outline of Probability, Random Variables, and Random Processes:
The background required to study the book is one year calculus, elementary differential equations, matrix analysis...
(2) udacity's Intro to Artificial Intelligence:
Some of the topics in Introduction to Artificial Intelligence will build on probability theory and linear algebra.
(3) udacity's Machine Learning: Supervised Learning :
A strong familiarity with Probability Theory, Linear Algebra and Statistics is required.
My suggestion is to use khanacademy.org in the following order: Precalculus->Differential calculus->Integral calculus->Linear Algebra->Multivariable calculus->Differential equations->Probability->Statistics.
If you prefer books:
Statistics comes last, here is why. Take for example the proof of minimizing squared error to regression line. You will at least need to understand how to solve partial derivatives and systems of equations.
(Note: Books 4-7 are based on my personal research on what to read. I haven't personally read those particular books yet. But they are praised a lot and relatively cheap and concise.)
Thank you. Having a ready made "course sequence" that I can then adapt, is really helpful.
I appreciate having Khan academy for looking up math concept that on which I need a refresher, but I've heard (or maybe just assumed?) that the higher level teaching was a bit mediocre. You disagree? I'm fully prepared to update on the estimates of people here.
What's the value of taking classes in math vs. teaching myself (or maybe teaching myself with the occasional help of a tutor)?
I have started to put together a sort of curriculum for learning the subjects that lend themselves to rationality. It includes things like experimental methodology and cognitive psychology (obviously), along with "support disciplines" like computer science and economics. I think (though maybe I'm wrong) that mathematics is one of the most important things to understand.
Eliezer said in the simple math of everything:
I want to have access to outlook-changing insights. So, what math do I need to know? What are the generally applicable mathematical principles that are most worth learning? The above quote seems to indicate at least calculus, and everyone is a fan of Bayesian statistics (which I know little about).
Secondarily, what are some of the most important of that "drop-dead basic fundamental embarrassingly simple mathematics" from different fields? What fields are mathematically based, other than physics and evolutionary biology, and economics?
What is the most important math for an educated person to be familiar with?
As someone who took an honors calculus class in high school, liked it, and did alright in the class, but who has probably forgotten most of it by now and needs to relearn it, how should I go about learning that math?