Mathematics for Neuroscientists

Neuroscience relies on a broad array of mathematical methods in order to express and synthesize existing theories, to analyze data and to inform new experiments. This book introduces and develops the most salient of these methods through a sequence of concrete computational models that guide the reader from the elementary to the advanced stage. It is intended as a textbook for undergraduate and graduate students in Neuroscience, as well as students in Mathematics, Physics or Engineering with an interest in Neuroscience. In addition, it should serve as a useful reference for the practicing neuroscientist. The book introduces computational methods based on an extensive collection of simulations using the MATLAB programming language. These programs offer a springboard for new classroom or research projects. The book starts by introducing differential equations and linear algebra via their application to models of cellular, and sub-cellular, processes. Probabilistic methods are then introduced and brought to bear on the study of synaptic transmission and noise in single neurons. Finally, signal-processing theory is covered and applied to systems level Neuroscience topics.