A Mathematical Primer
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. The Book Is Readable By Those Who Have Little Knowledge Of Mathematics For Neuroscience But Are Committed To Begin Acquiring Such Knowledge.
|Uitgever:||Springer-verlag New York Inc.|
|Plaats van publicatie:||01|
|NUR:||Anatomie en fysiologie|
|Afmetingen:||235 x 155|
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. For this purpose, the book is designed as a text with problems at the end of each chapter. 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 theoryfor 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.
From the contents:§- A Short History of Neuroscience§- Structure of a Neuron§- Nerve Membranes§- The Hodgkin-Huxley (H-H) Axon§- Leading Edge Models§- Recovery Models§- Myelinated Nerves§- Ephatic Interactions Among Neurons§- Neural Modeling§- Constructive Brain Theories§- Neuronal Assemblies§- The Hierarchical Nature of Brain Dynamics
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