1. Overview

The book is organised in chapters that progress from the scale of a single cell up to an entire brain. The use of mathematical methodologies does not follow a natural hierarchy, and instead we introduce these as and when needed. On this note, we rely on some familiarity of the reader with techniques from applied mathematics. However, for pragmatic purposes, we have also included a number of Boxes to act as self-contained expositions or reminders of useful pieces of mathematical theory. Nonetheless, we do not expect a typical reader to come armed with the perfect mathematical repertoire to absorb the story in this book. Indeed, we hope that some of the topics covered, such as those associated with non-smooth dynamical systems, will be of interest in their own right. In a similar vein, the reader need not have any prior background in neuroscience to understand this book, and at the risk of reducing the whole of this field to a few glib paragraphs, we first mention some of the more common facts and terminology that you will come across in the pages ahead.