Mathematics for Neuroscientists

Mathematics for Neuroscientists

1st Edition - July 26, 2010

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  • Authors: Fabrizio Gabbiani, Fabrizio Gabbiani, Steven Cox, Steven Cox
  • eBook ISBN: 9780080890494

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Description

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. 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
  • Allows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework

Readership

* 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

Product details

  • No. of pages: 498
  • Language: English
  • Copyright: © Academic Press 2010
  • Published: July 26, 2010
  • Imprint: Academic Press
  • eBook ISBN: 9780080890494

About the Authors

Fabrizio Gabbiani

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.

Affiliations and Expertise

Baylor College of Medicine, Houston, TX, USA

Fabrizio Gabbiani

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.

Affiliations and Expertise

Baylor College of Medicine, Houston, TX, USA

Steven Cox

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.

Affiliations and Expertise

Computational and Applied Mathematics, Rice University, Houston, TX, USA

Steven Cox

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.

Affiliations and Expertise

Computational and Applied Mathematics, Rice University, Houston, TX, USA

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