[jliechti1]

My guess is that you won't find any course that explains all the prerequisite math. It's probably more useful to build a solid foundation in probability theory (and therefore calculus) before going on.

For machine learning, a good place to start is Andrew Ng's course on Coursera:

https://www.coursera.org/course/ml

It's pretty light on math, while at the same time giving you experience in implementing and understanding these techniques.

From there, I might recommend Learning from Data and the associated video lectures:

https://work.caltech.edu/telecourse.html

It is a bit of a jump, but it is a great course in presenting the field of machine learning and explaining the mathematical and statistical underpinnings in a systematic way.

[jamra]

I just finished the Coursera course by Andrew Ng. It was great. The only hand waving done with math was when calculus was necessary. You can take some extra time to do that work yourself if you like, but you will not be missing the underpinnings of why things work statistically. The introduction to neural networks what finally gave me that aha moment.

It is a very self contained course that is quite easy to follow. You can skip the programming exercises if you don't have the time.

[crazypyro]

For anyone interested in more about the specific math of neural networks, http://www.iro.umontreal.ca/~bengioy/dlbook has a couple good introductory chapters that give overviews of most of the necessary topics for NNs, but also provides additional resource suggestions if you need more in-depth info on a certain subject.