You may have read in the news that computers have just now 
become able to beat top human players at the ancient Chinese 
strategy game of Go.

https://gogameguru.com/alphago-defeats-lee-sedol-4-1/

Besides faster hardware, the key advance over old
Go engines involves "neural networks" that must be
"trained" in order perform well.

That training involves lots of statistics, but one of the key
steps, "backpropogation," is a simple application of 
the chain rule for partial derivatives:

http://colah.github.io/posts/2015-08-Backprop/

As I mentioned in class this week, gradient descent is
also a key tool:

http://peterroelants.github.io/posts/neural_network_implementation_part01/#Gradient-descent

See also this nice overview if you're interested:

http://highscalability.com/blog/2016/3/16/jeff-dean-on-large-scale-deep-learning-at-google.html