Neuroscience A Mathematical Primer
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Neuroscience
This book will be of interest to anyone who wishes to know what role mathematics can play in attempting to comprehend the dynamics of the human brain. It also aims to serve as a general introduction to neuromathematics. The book gives the reader a qualitative understanding and working knowledge of useful mathematical applications to the field of neuroscience. The book is readable by those who have little knowledge of mathematics for neuroscience but are committed to begin acquiring such knowledge.
Mathematical Neuroscience
Author: Stanislaw Brzychczy
language: en
Publisher: Academic Press
Release Date: 2013-08-16
Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. - The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience - Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain - Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling
Neuroscience
Author: Alwyn Scott
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-14
Arguably the most intricate dynamic object in the universe, the human brain is an unsounded source of wonder for the scienti?c community. The primary aim of this book is to provide both students and established - vestigators in the growing area of neuroscience with an appreciation of the roles that mathematics may play in helping to understand this en- maticorgan. Alongwithdiscussionsofresultsobtainedbytheneuroscience community, emphasis is placed on suggesting fruitful research problems for those planning to embark on mathematical studies in neuroscience. To make the overall perspectives understandable to philosophers and psychologists, essential features of the discussions are presented in ordinary English, with more detailed mathematical comments in appendices and footnotes. Although it attempts to maintain both clarity and biological relevance, this is not a text on the anatomy of nerve systems; thus readers should bring some knowledge of neurophysiology through other courses, associated studies, or laboratory research. It is a guiding theme throughout the book that the brain is organized into several quite di?erent levels of dynamic activity. As will be seen, these levels are hierarchically structured, beginning with the molecular dynamics ofintrinsicmembraneproteinsandproceedingupward,throughtheswit- ing properties of active membrane patches and synapses, the emergence of impulses on active ?bers, overall properties of individual neurons, and the growth of functional assemblies of interacting neurons, to the global - namics of a brain. At each level of description, reality turns di?erent facets of her mystery to us, and diverse phenomena make their contributions to the brain’s collective behavior.