Mathematics for Neuroscientists book cover

Mathematics for Neuroscientists

Virtually all scientific problems in neuroscience require mathematical analysis, and all neuroscientists are increasingly required to have a significant understanding of mathematical methods. There is currently no comprehensive, integrated introductory book on the use of mathematics in neuroscience; existing books either concentrate solely on theoretical modeling or discuss mathematical concepts for the treatment of very specific problems. This book fills this need by systematically introducing mathematical and computational tools in precisely the contexts that first established their importance for neuroscience. All mathematical concepts will be introduced from the simple to complex using the most widely used computing environment, Matlab. All code will be available via a companion website, which will be continuously updated with additional code and updates necessitated by software releases.
This book will provide a grounded introduction to the fundamental concepts of mathematics, neuroscience and their combined use, thus providing the reader with a springboard to cutting-edge research topics and fostering a tighter integration of mathematics and neuroscience for future generations of students.

Audience
* Graduate and post graduate students in Neuroscience and Psychology looking for an introduction to mathematical methods in Neuroscience* Researchers in Neuroscience and Psychology looking for a quick reference for mathematical methods* Students in applied mathematics, physical sciences, engineering who want an introduction to Neuroscience in a mathematical context

Hardbound, 498 Pages

Published: July 2010

Imprint: Academic Press

ISBN: 978-0-12-374882-9

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)


Contents

  • 1 Introduction
    2 The Passive Isopotential Cell
    3 Differential Equations
    4 The Active Isopotential Cell
    5 The Quasi-Active Isopotential Cell
    6 The Passive Cable
    7 Fourier Series and Transforms
    8 The Passive Dendritic Tree
    9 The Active Dendritic Tree
    10 Reduced Single Neuron Models
    11 Probability and Random Variables
    12 Synaptic Transmission and Quantal Release
    13 Neuronal Calcium Signaling
    14 The Singular Value Decomposition and Applications
    15 Quantification of Spike Train Variability
    16 Stochastic Processes
    17 Membrane Noise
    18 Power and Cross Spectra
    19 Natural Light Signals and Phototransduction
    20 Firing Rate Codes and Early Vision
    21 Models of Simple and Complex Cells
    22 Stochastic Estimation Theory
    23 Reverse-Correlation and Spike Train Decoding
    24 Signal Detection Theory
    25 Relating Neuronal Responses and Psychophysics
    26 Population Codes
    27 Neuronal Networks
    28 Solutions to Selected Exercises

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