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Mathematics for Neuroscientists

ISBN-10: 0123748828
ISBN-13: 9780123748829
Edition: 2010
List price: $99.95
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Description: The central aim of Mathematical Neuroscience is to establish a language with which to build and test a platform for the quantitative investigation of the central problems of neuroscience. Success is measured in our ability to not only reaffirm or  More...

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Book details

List price: $99.95
Copyright year: 2010
Publisher: Elsevier Science & Technology Books
Publication date: 7/26/2010
Binding: Hardcover
Pages: 498
Size: 8.00" wide x 11.00" long x 1.25" tall
Weight: 3.586
Language: English

The central aim of Mathematical Neuroscience is to establish a language with which to build and test a platform for the quantitative investigation of the central problems of neuroscience. Success is measured in our ability to not only reaffirm or synthesize existing theories but in our ability to guide existing, or suggest novel, experiments. Although Mathematical Neuroscience has developed along side and in conjunction with Experimental Neuroscience, both sub-disciplines have matured to a level where experts in one may be novices in the other and where passage to the research frontier carries a fairly high entry cost. The best way to train aspiring neuroscientists is to integrate early instruction in mathematics and biology. Currently there does not exist an introductory text that simultaneously develops concrete biological and mathematical skills as means to a deeper understanding of neuroscience. ?Introduction to Mathematical Neuroscience?, is just such a text. The book will introduce mathematical and computational tools in precisely the contexts that first established their importance for neuroscience. It will develop partial differential equations via the seminal work of Hodgkin and Huxley (1952) on nerve conduction, probability theory following the beautiful work of Fatt and Katz (1951) on synaptic transmission, dynamical systems theory in the context of FitzHugh?s (1955) critical investigation of action potential threshold, and linear algebra in the context of Hines? (1984) important work on dendritic processing. In addition, the book will apply Fourier transforms to describe neuronal receptive fields following Enroth-Cugell and Robson?s (1966) work on retinal ganglion cells and its subsequent extension to Hubel and Wiesel?s (1962) characterization of cat cortical neurons. Lastly it will introduce and motivate statistical decision methods starting with the historical photon detection experiments of Hecht, Shlaer and Pirenne (1942). All mathematical concepts will be introduced from the simple to complex using a the by far most widely used computing environment, Matlab. From this foundation INtroduction to Mathematical Neuroscience will embark on a number of important modern themes, such as the role of noise in shaping the responses of neurons both at the subthreshold and suprathreshold level, the role of active conductances in determining the transfer properties of dendritic cables and the backpropagation of action potentials, the role of neuronal calcium signaling, the coding and decoding of information in neuronal spike trains, as well as the role of correlations in population coding. This book will provide a grounded introduction in the fundamental concepts of mathematics, neuroscience and their combined use, thus providing the reader with a spring-board to cutting-edge research topics and fostering a tighter integration of mathematics and neuroscience for future generations of students. ?A Concrete Introduction to Mathematical Neuroscience? will cover approximately 400 pages of text with accompanying illustrations. A companion website accessible to students will contain solutions to approximately half of the exercises, comprising both theoretical derivations and Matlab code to solve numerical problems and reproduce the book?s figures. The remaining solutions will be included in an instructor?s websites that will be accessible to faculty adopting the book for an academic course. Developed from a course given simultaneously to Computational and Mathematics, Science, and Engineering undergraduate and graduate students from Rice University and Neuroscience graduate students from Baylor College of Medicine over the last six years. The book will alternate between mathematical chapters, introducing important concepts and numerical methods, and neurobiological chapters, applying these concepts and methods to specific topics. We aim to cover topics ranging from classical cellular biophysics and p

Introduction
The Passive Isopotential Cell
Differential Equations
The Active Isopotential Cell
The Quasi-Active Isopotential Cell
The Passive Cable
Fourier Series and Transforms
The Passive Dendritic Tree
The Active Dendritic Tree
Reduced Single Neuron Models
Probability and Random Variables
Synaptic Transmission and Quantal Release
Neuronal Calcium Signaling
The Singular Value Decomposition and Applications
Quantification of Spike Train Variability
Stochastic Processes
Membrane Noise
Power and Cross Spectra
Natural Light Signals and Phototransduction
Firing Rate Codes and Early Vision
Models of Simple and Complex Cells
Stochastic Estimation Theory
Reverse-Correlation and Spike Train Decoding
Signal Detection Theory
Relating Neuronal Responses and Psychophysics
Population Codes
Neuronal Networks
Solutions to Selected Exercises

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