Navigating mathematical basics: A primer for deep learning in science

We present a gentle introduction to elementary mathematical notation with the focus of communicating deep learning principles. This is a “math crash course” aimed at quickly enabling scientists with understanding of the building blocks used in many equations, formulas, and algorithms that describe deep learning. While this short presentation cannot replace solid mathematical knowledge that needs multiple courses and years to solidify, our aim is to allow nonmathematical readers to overcome hurdles of reading texts that also use such mathematical notation. We describe a few basic deep learning models using mathematical notation before we unpack the meaning of the notation. In particular, this text includes an informal introduction to summations, sets, functions, vectors, matrices, gradients, and a few more objects that are often used to describe deep learning. While this is a mathematical crash course, our presentation is kept in the context of deep learning and machine learning models including the sigmoid model, the softmax model, and fully connected feedforward deep neural networks. We also hint at basic mathematical objects appearing in neural networks for images and text data.