A really good technical introduction to deep learning from @AndrewYNg's Coursera that touches on stocastic gradient descent for optimization, which is really cool in my book. Sample processes are provided on the original article but I think you should just take the Coursera. :)
The following problems are taken from a few assignments from the coursera courses Introduction to Deep Learning (by Higher School of Economics) and Neural Networks and Deep Learning (by Prof Andrew Ng, deeplearning.ai). The problem descriptions are taken straightaway from the assignments Read More.