Neuroscience

1. Front Matter

   Pages I-XX

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2. A Short History of Neuroscience

   Pages 1-23

3. Structure of a Neuron

   Pages 25-48

4. Nerve Membranes

   Pages 49-66

5. The Hodgkin-Huxley (H-H) Axon

   Pages 67-93

6. Leading-Edge Models

   Pages 95-113

7. Recovery Models

   Pages 115-138

8. Myelinated Nerves

   Pages 139-163

9. Ephaptic Interactions Among Axons

   Pages 165-185

10. Neural Modeling

    Pages 187-232

11. Constructive Brain Theories

    Pages 233-255

12. Neuronal Assemblies

    Pages 257-292

13. The Hierarchical Nature of Brain Dynamics

    Pages 293-313

14. Back Matter

    Pages 315-352

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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.

• cognitive science
• information processing
• information theory
• neural modeling
• neurons
• neuroscience

• Department of Mathematics, University of Arizona, Tucson, USA

  Alwyn Scott

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