Neural networks have been around for decades. But it hasn't been until recently, with the rise of big data and the availability of ever increasing computation power, that we have really started to see a lot of exciting progress in this branch of machine learning.
The most ground breaking advances in the field of machine learning over the past decade, from computer vision to NLP, can be attributed to the rise of neural networks, and in particular deep learning.
The following post is a theoretical introduction to neural nets. We start by learning how we represent neural networks in terms of math and code. We cover the structure of a basic neural net, how a hypothesis function looks like in neural net, and also start to represent some of the theory and bring that into some Matlab code.