دانلود کتاب ابزارهای ریاضی برای علوم اعصاب – رویکرد هندسی

This book was written as a brief but self-contained introduction to the application of geometric techniques to understanding the brain. The approach is illustrated by characterising the data structures used to describe objects geometrically and, subsequently, showing how measurements provided by sensory neurons can be used to uncover the geometric descriptions of the objects present. A similar approach is applied to characterising the actions made by an animal in order to handle an object, and what this involves at the level of muscle contractions. Finally, it is shown that the geometrical approach leads to new and distinctive experimental techniques. The approach of this book relies heavily on visual representation of the material. In this respect, I have been influenced by the book Dynamics: The Geometry of Behaviour by Abraham and Shaw 1that gives a comprehensive introduction to the ideas of nonlinear dynamics entirely in pictures. They wrote their book to show that mathematical ideas can be communicated easily, and I think the material contained in it has not been taken up as widely as it might be by neuroscientists for two reasons. Firstly, there were no examples of applications to neuroscience in the book, and secondly, they did not include the additional stage of how to turn the intuitive visual ideas into equations that could be used to make testable predictions. This book aims to fill those gaps.