Mathematics for Neuroscientists

1st Edition

Print ISBN: 9780323163866
eBook ISBN: 9780080890494
Imprint: Academic Press
Published Date: 26th July 2010
Page Count: 498
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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.

Key Features

  • A very didactic and systematic introduction to mathematical concepts of importance for the analysis of data and the formulation of concepts based on experimental data in neuroscience
  • Provides introductions to linear algebra, ordinary and partial differential equations, Fourier transforms, probabilities and stochastic processes
  • Introduces numerical methods used to implement algorithms related to each mathematical concept
  • Illustrates numerical methods by applying them to specific topics in
    neuroscience, including Hodgkin-Huxley equations, probabilities to describe stochastic release, stochastic processes to describe noise in neurons, Fourier transforms to describe the receptive fields of visual neurons
  • Provides implementation examples in MATLAB code, also included for download on the accompanying support website (which will be updated with additional code and in line with major MATLAB releases)
  • Allows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework


  • 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

Table of 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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"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)