Mathematics for Neuroscientists

by Fabrizio Gabbiani, Steven James Cox

Overview

Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory.

• Fully revised material and corrected text
• Additional chapters on extracellular potentials, motion detection and neurovascular coupling
• Revised selection of exercises with solutions
• More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts

Product Details

ISBN-13:	9780128019061
Publisher:	Elsevier Science
Publication date:	02/04/2017
Sold by:	Barnes & Noble
Format:	eBook
Pages:	628
File size:	80 MB
Note:	This product may take a few minutes to download.

About the Author

Dr. Gabbiani is Professor in the Department of Neuroscience at the Baylor College of Medicine. Having received the prestigious Alexander von Humboldt Foundation research prize in 2012, he just completed a one-year cross appointment at the Max Planck Institute of Neurobiology in Martinsried and has international experience in the computational neuroscience field. Together with Dr. Cox, Dr. Gabbiani co-authored the first edition of this bestselling book in 2010.
Dr. Cox is Professor of Computational and Applied Mathematics at Rice University. Affiliated with the Center for Neuroscience, Cognitive Sciences Program, and the Ken Kennedy Institute for Information Technology, he is also Adjunct Professor of Neuroscience at the Baylor College of Medicine. In addition, Dr. Cox has served as Associate Editor for a number of mathematics journals, including the Mathematical Medicine and Biology and Inverse Problems. He previously authored the first edition of this title with Dr. Gabbiani.

Table of Contents

1. Introduction2. The Passive Isopotential Cell3. Differential Equations4. The Active Isopotential Cell5. The Quasi-Active Isopotential Cell6. The Passive Cable7. Fourier Series and Transforms8. The Passive Dendritic Tree9. The Active Dendritic Tree10. Extracellular Potential11. Reduced Single Neuron Models12. Probability and Random Variables13. Synaptic Transmission and Quantal Release14. Neuronal Calcium SignalingNeuronal Calcium Signaling15. Neurovascular Coupling, the BOLD Signal and MRI16. The Singular Value Decomposition and ApplicationsThe Singular Value Decomposition and Applications17. Quantification of Spike Train Variability18. Stochastic Processes19. Membrane NoiseMembrane Noise20. Power and Cross-Spectra21. Natural Light Signals and Phototransduction22. Firing Rate Codes and Early Vision23. Models of Simple and Complex Cells24. Models of Motion Detection25. Stochastic Estimation Theory26. Reverse-Correlation and Spike Train Decoding27. Signal Detection Theory28. Relating Neuronal Responses and Psychophysics29. Population CodesPopulation Codes30. Neuronal Networks31. Solutions to Exercises

What People are Saying About This

From the Publisher

Addressing a growing need of experimental neuroscientists for a good introduction and reference to the most common mathematical approaches for the analysis and computational modeling of brain signals, this is the first book to offer a thorough guide to mathematical concepts and numerical methods integrated in a neuroscience context.

Editorial Reviews

"Mathematics for Neuroscientists by Fabrizio Gabbiani and Steven Cox (GC) was developed over 8 years of teaching courses on the topic. This experience, as well as the wide-ranging research contributions of the authors, clearly shines through—the text is a landmark for the field in its scope, rigor, and accessibility. . . .This is a hallmark of the book: elegance, completeness, and economy that leave the reader with much more mathematics and science than one might expect even in a work of this size. The book further benefits from the availability of MATLAB code provided to regenerate almost every figure. . . . This integration of code and text is by far the best we’ve seen. It brings alive the science, the mathematical tools, the models, and their implementation." —Society for Industrial and Applied Mathematics SIAM Review, 2011 (Vol 53, No. 3)

From the Publisher