Neuroscience : A Mathematical Primer by Alwyn Scott
Although attempts to understand the physical bases for mental processes go back to the early Greek and Egyptian civilizations, modern electrophysiology began with the late eighteenth-century investigations by Luigi Ga.lva.ni on the sciatic nerve-muscle preparation of the frog .
In 1791, this Italian physician reported that the muscle would twitch when the nerve was stimulated by a bimetallic contact and also by atmospheric electricity. Thus, Galvani proposed three types of electricity—chemical, atmospheric, and animal—with the latter being different from the two others, but his compatriot Alessandro Volta disagreed. In the attempt to show that Galvani’s animal electricity was identical to that produced by bimetallic currents, Volta invented the battery, thereby launching the science of electricity in the historically convenient year of 1800.
All of those early experiments were carefully repeated by the German physicist Frederick von Humboldt, confirming both Volta’s view that the various forms of electricity are closely related and Galvani’s observation that animal electricity has qualitatively distinctive features. Let us consider these differences.
Arguably the most intricate dynamic object in the universe, the human brain is an unsounded source of wonder for the scientific community. The primary aim of this book is to provide both students and established investigators in the growing area of neuroscience with an appreciation of the roles that mathematics may play in helping to understand this enigmatic organ. Along with discussions of results obtained by the neuroscience 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 different levels of dynamic activity. As will be seen, these levels are hierarchically structured, beginning with the molecular dynamics of intrinsic membrane proteins and proceeding upward, through the switching properties of active membrane patches and synapses, the emergence of impulses on active fibers, overall properties of individual neurons, and the growth of functional assemblies of interacting neurons, to the global dynamics of a brain. At each level of description, reality turns different facets of her mystery to us, and diverse phenomena make their contributions to the brain’s collective behavior.
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