An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domain (Cambridge Studies in Mathematical Biology) [Paperback]

Frank C. Hoppensteadt (Author)

Book Description

ISBN-10: 0521599296 | ISBN-13: 978-0521599290 | Publication Date: June 28, 1997 | Edition: 2

This book describes signal processing aspects of neural networks, how we receive and assess information. Beginning with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, it proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, Hoppensteadt develops a theory of mnemonic surfaces and presents material on pattern formation and cellular automata. Finally, the text addresses the large networks, such as the thalamus-reticular complex circuit, that may be involved in focusing attention, and the development of connections in the visual cortex. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.

Editorial Reviews

Review

"The author undoubtedly has a strong and thorough knowledge of both mathematics and neurosciences which allows him to put the reader on what he calls 'the launching point'...an excellent door that opens the researcher to further exploration of the mysteries of the brain. I conclude this review by repeating what is at the end of this very well written book: 'Mathematics is needed to understand how the brain works.'" Catherine Garcia-Reimbert

"...a brief and nice introduction to the mathematical methods and models used in the theory of neural networks and their applications." Monatshefte fur Mathematik

Book Description

This book describes signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then moves on to applications. These applications include small networks of neurons, a theory of mnemonic surfaces, pattern formation and cellular automata, and large networks, such as the complex circuit believed to be involved in focusing attention. This is an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.

Product Details

• Paperback: 232 pages
• Publisher: Cambridge University Press; 2 edition (June 28, 1997)
• Language: English
• ISBN-10: 0521599296
• ISBN-13: 978-0521599290
• Product Dimensions: 9 x 6 x 0.4 inches
• Shipping Weight: 13.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,166,158 in Books (See Top 100 in Books)

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3 of 3 people found the following review helpful:

4.0 out of 5 stars A Condensed, Economical, and Introductory Book on Studying Neuron Firing, August 11, 2007

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Man Kam Tam (Calexico, CA USA) - See all my reviews
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This review is from: An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domain (Cambridge Studies in Mathematical Biology) (Paperback)

The goal of Hoppensteadt's book is "to study the frequency and timing of neuron firing and how these can interact in networks to carry information and to control biological systems."

Hoppensteadt's book is condensed. It has 211 pages, but seven chapters and two appendixes. The readers will need other books for better and deeper understanding on the presented material. A case in point is that I have purchased this book for a long time, but I am not able to read through it until Dr. Diana Verzi and Dr. Imre Tuba, both of San Diego State University, gave me Christof Koch's "Biophysics of Computation." Biophysics of Computation has more than five hundred (500) pages. Later on, under the suggestion of Dr. Verzi, I purchased Eugene M. Izhikevich's "Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting" for better and deeper understanding the material presented on Hoppensteadt's book. Izhikevich's book has more than four hundred (400) pages.

Hoppensteadt's book is an economical introductory book on how to apply mathematics on physiological research though. Chapter one, two, and four covers the background material for the rest of the book, such as useful electrical circuits, theory of simple clock, and signal processing in phase-locked systems. Chapter three and five covers the mathematical models of neurons and neural networks. Chapter six and seven presents memory and attention. Appendix A provides the mathematical background on low pass filter and harmonic oscillator. Appendix B presents bifurcation analysis.