Mathematics for Neuroscientists

Mathematics for Neuroscientists

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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.
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Product details

  • Hardback | 498 pages
  • 220.98 x 281.94 x 33.02mm | 1,428.81g
  • Academic Press Inc
  • San Diego, United States
  • English
  • figures
  • 0123748828
  • 9780123748829
  • 808,981

Review quote

"I really think this book is very, very important. This is precisely what has been missing from the field and is badly needed. Non-physicists or non-mathematicians coming to neuroscience try hard to get up to speed in the basic maths needed to get by but give up because there is no clear explication of this."
--Dr. Kevin Franks, research fellow, Richard Axel's laboratory Columbia University, NYC

"The idea of presenting sufficient maths to understand the theoretical neuroscience, alongside the neuroscience itself, is appealing. The inclusion of Matlab code for all examples and computational figures is an excellent idea. Many readers will want to use and explore the code, either to directly aid their understanding, or as the basis for their own ongoing research, and Matlab is a widely used tool in this area."
--David Corney, research fellow, Institute of Ophthalmology, University College London
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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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About 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. 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.
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Review Text

" 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)
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