The PDP books are good, but only after you understand what is currently relevant. I recommend more modern treatments first.

I reject that. Russell and Norvig really turned me off to AI, because they mainly come from a perspective "good old-fashioned AI" (GOFAI). This mindset is more about discrete symbols and logics, and reject uncertainty, probability, and fuzziness.

I was turned off by the entire field until I began learning about statistical, empirical, and data-driven approaches.

I heartily endorse Bishop (2006). It's a much more modern treatment.

Make sure you know basic calculus, and understand derivatives. More math is always better, of course.

"I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense." --- Charles Darwin

Here are some classics in the field. I'll let you google them yourselves.

LeCun et al, 1998: Gradient-based learning applied to handwriting recognition. A deep convolutional net that can read handwriting, and was deployed nationally . Yann LeCun tells me that a patent lawyer in California reimplemented in his free time as a hobby, so it can't be that hard.

LeCun et al, 1998: Efficient BackProp. Tricks and implementation details that are not discussed often.

Btw, as I understand it LeCun was offered a position to be head of Google research. He declined, and Corinna Cortes took the job instead. Regardless, if you googled Yann for a while, Google ads would try to entice you to work at Google.

There is a recent trend in neural networks towards something called Deep Learning. This deep neural networks more closely mimic how the brain works, and are supported by arguments from neuroscience, circuit complexity, and machine learning. You can read more about them here:

Bengio, 2007: Learning deep architectures for AI