This paper will focus on proving the four fundamental equations of the backpropagation. Then I will show how to use this algorithm combined with the stochastic gradient descent technique to implement the network for recognizing the handwritten digits. Parts of the proof are provided by the author Michael Nielsen in his online book Neural Networks and Deep Learning. Meanwhile, this paper will provide more details of his proofs and some basic definitions of gradient.
This paper gives a detailed proof of Euler's theorem, which is the divergence of a series of reciprocals of the primes. The key idea of the proof is to assume the series converges and then complete the proof by contradiction.
