neuralnetworksanddeeplearning.com is a free online book by Michael Nielsen. I'm reading it right now, and it's wonderful. In the first chapter, he walks you thr

neuralnetworksanddeeplearning.com is a free online book by Michael Nielsen. I'm reading it right now, and it's wonderful. In the first chapter, he walks you through implementing a basic neural network in Python that works with the MNIST data and uses no libraries (except numpy). He's really good at explaining a lot of the math for a more programmer-ish audience that might not have studied multivariate calculus.