An Infinite Descent into Pure Mathematics

The goal of this book is to help the reader make the transition from being a consumer of mathematics to a producer of it. This is what is meant by ‘pure’ mathematics. While a consumer of mathematics might learn the chain rule and use it to compute a derivative, a producer of mathematics might derive the chain rule from the rigorous definition of a derivative, and then prove more abstract versions of the chain rule in more general contexts (such as multivariate analysis).