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Neuroscience: a mathematical primer
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This is an introductory text of mathematical neuroscience intended for anyone who wants to appreciate the role that mathematics and mathematical modeling and analysis can do to aid an understanding of how the brain works and the nature of the mind. In particular, the book will be of interest to established neuroscientists and neuroscience students who wish to know what roles mathematical formulations can play in attempting to comprehend the dynamics of a human brain. It is expected that this text will be interesting for mathematics faculty teaching in neuroscience programs. It also aims to serve as a general introduction to neuromathematics in neuroscience programs at both undergraduate and graduate levels. Physical scientists and bioengineers who plan to extend their research activities into the realms of cognitive science will find this an ideal guide, as will philosophers and social scientists who wish to understand the degree to which dynamics of a brain can be reduced to mathematical formulations. Mathematical formulations in neuroscience are of five sorts: (i) Exact descriptions of well understood dynamic processes, like the Hodgkin Huxley theory of the nerve impulse. (ii) Metaphorical descriptions of more complex phenomena, like the stationary states of a Hopfield model. (iii) Information theory for dealing with the storage and transmission of data. (iv) Logical calculus (Boolean algebra) for the analysis of information processing systems. (v) Number theory for counting large numbers of possibilities. (vi) Statistical tools for organizing and evaluating data.
Review :Neuroscience: A Mathematical Primer Alwyn Scott
"Neuroscience: A Mathematical Primer" Neuroscience  is one of contemporary science's most challenging realms. It is a complex field with dimensions of inquiry available to a variety of scientific and medical fields of study. For those readers interested in neuroscience and who have a background in physical science, engineering, or mathematics, Alwyn Scott's book provides an ideal port of entry. Dr. Scott's book is a systematic `bottomup' approach to the workings of the nervous system from the cellular to network perspectives. Each of the twelve chapters and six appendices provides a quantitativelyoriented view of the salient physical features of neurons. Dr. Scott is a highlyaccomplished scholar of nonlinearities in physical systems. His scientific career includes academic and research positions in electrical engineering, computer science, and mathematics at University of Wisconsin, Los Alamos National Labs, University of Arizona, and others. In addition to these accomplishments, the author has published fundamental studies on information propagation in nerve fibers. In his book, Dr. Scott addresses neuronal function from these unique and remarkably eclectic disciplinary perspectives. He writes in terms of physical principles, using the language of mathematics and the insights of engineering. This approach is  alas  not typical in neuroscience, which is often descriptive, avoiding the underlying physical complexities. The first nine chapters cover much of the salient biophysics of neurons. The topics include the physical properties of the neuron and its material components, the mechanisms wherecontaining entities which are modified and disseminated through the substance of the cell, over long distances and through much geometrical complexity. In his presentation, the author covers both wellknown as well as littleknown or neglected literature and concepts, an invaluable scholarly service which recaptures much significant progress ignored or forgotten elsewhere (the book's bibliographies alone are worth the price of admission). The final three chapters provide an introduction to the loftier issues of neuronal assemblies. All chapters include a recapitulation, which are invaluable for readers new to the subject.The author does not simply provide a review of the many topics in quantitative neuroscience. Rather, Dr. Scott gives the reader a totally original and carefullyconstructed stepprovoking, and highly influential in my current research. For neuroscience students and researchers coming from traditional biology backgrounds, this book provides an important opportunity to share in the unique perspective that physical science brings to neuroscience, aspects which many of us never experienced and were untrained to even imagine. For such readers, this book also will help to expand your knowledge of mathematical expression as applied to a familiar realm. Younger neuroscientists in particular who feel unsatisfied with the traditional descriptive approach can explore a new world of insight through the eyes of a brilliant analyst and a caring teacher.In summary, Dr. Scott's book is both a highlyinformative reference as well as a superb tutorial on the biophysics of neurons. Its content will be very useful for both new students of neuroscience as well for advanced students and researchers in this field. For readers from backgrounds in physics, engineering, and mathematics, this book will bring you comfortably into the neuroscience domain. For instructors seeking a textbook in theoretical neuroscience, computational neuroscience, or mathematical neurobiology courses, this book will be useful as a superb primary text or source for extra readings. In short, "Neuroscience: A Mathematical Primer" by Alwyn Scott is highly recommended. Dr. Scott has made an invaluable contribution to the neuroscience literature...it is truly an instant classic!
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