The central aim of Mathematical Neuroscience is to establish a language withwhich to build and test a platform for the quantitative investigation of the central problems of neuroscience. Success is measured in our ability to not onlyreaffirm 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 mathematicaland computational tools in precisely thecontexts that first established theirimportance 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, thebook will apply Fourier transforms to describe neuronal receptive fields following Enroth-Cugell and Robson's (1966) work on retinal ganglion cells and itssubsequent 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, Shlaerand 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, therole 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 boththeoretical 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 aimto cover topics ranging from classical cellular biophysics and proceed up to systems level neuroscience.Each of the book's chapters will be relatively short, roughly corresponding to the material usually presented in one or two seventy-five-minute lectures. Starting at an introductory mathematical level, presuming no more than calculus through elementary differential equations, the level will build up as increasingly complex techniques are introduced and combinedwith earlier ones. Each chapter will include a comprehensive series of exercises with solutions, taken from the set we developed over the years. Matlab code will be included for each computational figure, to allow the reader to reproduce them. Biographical notes referring the reader to more specialized literature and additional mathematical material that may be needed either to deepen thereader's understanding or to introduce basic concepts for less mathematicallyinclined readers will complete each chapter. - Introduces the reader to mathematical concepts of importance for the analysis of data and the formulation oftheories in neuroscience, enabling all neuroscientists to apply and use thoseconcepts in their research.- Includes, for example, linear algebra, ordinary and partial differential equations, Fourier transforms, probabilities and stochastic processes, applying them to specific frequently encountered problems inneuroscience. For example, the book makes it possible for the researcher to apply linear algebra and differential equations to solve the Hodgkin-Huxley equations, probabilities to describe stochastic release, stochastic processes to describe noise in neurons, Fourier transforms to describe the receptive fieldsof visual neurons. - Introduces the numerical methods used to implement algorithms related to these mathematical concepts, including the tools necessary tosolve systems of differential equations, issues of numerical stability, discrete Fourier transforms, discrete convolutions, computation of power spectra, crosscorrelations, the generation of sample stochastic processes and random variables. Need Feature BenefitAn easy to follow introduction to the mathematicaltools most commonly used in Neuroscience Integrates mathematical analysis andmodeling tools systematically by using them to address specific well known problems in Neuroscience Saves significant time in understanding and adapting mathematical methods to common problemsA book that provides a reference of toolsto implement mathematical concepts on own problems A toolbox of Matlab code modules solving the most common mathematical problems encountered in the Neuroscience laboratory Modules can be directly adapted for use in the laboratory to save development time and costA toolset for the systems neuroscientist to support thinking about their results in a broader theoretical framework By providing a systematic introduction of the most commonly used tools needed to create cellular models of brain function, this book opens up the possibility of theoretical modeling of results to the mathematically less inclined neuroscientist Opens a new horizon for systems neuroscientists for more sophisticated analysis and modeling of their results.
- ISBN: 978-0-12-374882-9
- Editorial: Academic Press
- Encuadernacion: Cartoné
- Páginas: 498
- Fecha Publicación: 14/09/2010
- Nº Volúmenes: 1
- Idioma: Inglés