Tutorials in Mathematical Biosciences I

1. Front Matter

   Pages I-IX

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2. Introduction to Neurons

   • Avner Friedman

   Pages 1-20

3. An Introduction to Dynamical Systems and Neuronal Dynamics

   • David Terman

   Pages 21-68

4. Neural Oscillators

   • Bard Ermentrout

   Pages 69-106

5. Physiology and Mathematical Modeling of the Auditory System

   • Alla Borisyuk

   Pages 107-168

6. Back Matter

   Pages 169-170

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This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.

• Computational Neuroscience
• Cortex
• anatomy
• auditory system
• dynamical systems
• neural oscillations
• neuronal dynamics
• neurons
• physiology
• ordinary differential equations
• partial differential equations

From the reviews:

"Each paper ends with a valuable bibliography. The volume introduces some basic theories on computational neuroscience. I recommend this volume as a very good book in mathematical neurosciences." (Ioan A. Rus, Zentralblatt MATH, Vol. 1062 (13), 2005)

"The present volume, a collection of four articles, introduces some basic theories of mathematical and computational neuroscience. … I found the book to be a very good tutorial in mathematical neuroscience, well written and organized. … The core is a compilation of mathematical results from a rich bibliography … . In conclusion, I strongly recommend this volume to any graduate student, postdoctoral fellow or researcher moving to the field of theoretical neuroscience." (Rodica Curtu, Mathematical Reviews, Issue 2007 d)

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