Within this repo there is a jupyter notebook along with two solutions using deep learning for the MNIST data set.
The first approach uses deep fully-connected networks and the second approach uses convolutional networks.
This solution should get you in the top 10% on Kaggle for MNIST.
Also, please note that to run the python notebook you will need to pull in the test csv file from Kaggle's MNIST competition: https://www.kaggle.com/c/digit-recognizer/data