"Machine Learning is a mathematical discipline, and students will benefit from a good background in probability, linear algebra and calculus. Programming experience is essential."
Professors teaching such courses at the graduate level primarily intend them to benefit students doing active research in the field. There's an extraordinary emphasis on mathematical derivations to show how one idea leads to another. This is intended to both (1) provide insight into why methods work—though less rigorous and more intuitive approaches frequently exist and are discovered by the less robotic students, and (2) give students practice in the mathematical gymnastics needed to publish in the field. The benefit to a practitioner, let alone an interested outsider, will likely be small.
An analogy might be to consider whether a course on type inference and Hindley-Milner offered by a computer science department would benefit someone interested in learning Haskell.
I think the Prob books by Sheldon Ross are good tho there's negative Amazon reviews, and the three LA texts by Axler, Strang and Insel/Friedberg/spence are worth buying (older editions for < $25 shd be good enough
Having looked at the problem sheets, probability (think distributions), linear algebra and calculus are a must - Khan Academy is a great resource but nothing really tests you like university level homework! There was a brilliant Prob/Stats course on iTunesU that got me through 3rd year - worth a look.
Khan academy is a great resource for remediating your math skills. I went through to cover all the last-third-of-the-textbook concepts that I never learned in school. To get good at something you just have to go do it, math included.
For example, I've never been particularly great at math.