Kaggle notebook with all the code: https://www.kaggle.com/wwsalmon/simple-mnist-nn-from-scratch-numpy-no-tf-keras

Blog article with more/clearer math explanation: https://www.samsonzhang.com/2020/11/24/understanding-the-math-behind-neural-networks-by-building-one-from-scratch-no-tf-keras-just-numpy.html