Dayan P., Abbott L.F. Theoretical neuroscience: computational and mathematical modeling of neural systems

MIT Press, 2005. — 460 p.Theoretical neuroscience provides a quantitative basis for describing what nervous systems do, determining how they function, and uncovering the general principles by which they operate. This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory.
The book is divided into three parts. Part I discusses the relationship between sensory stimuli and neural responses, focusing on the representation of information by the spiking activity of neurons. Part II discusses the modeling of neurons and neural circuits on the basis of cellular and synaptic biophysics. Part III analyzes the role of plasticity in development and learning. An appendix covers the mathematical methods used, and exercises are available on the book's Web site.Neural encoding I : firing rates and spike statistics
Neural encoding II : reverse correlation and visual receptive fields
Neural decoding
Information theory
Model neurons I : neuroelectronics
Model neurons II : conductances and morphology
Network models
Plasticity and learning
Classical conditioning and reinforcement learning
Representational learning
Linear algebra
Finding extrema and Lagrange multipliers
Differential equations
Electrical circuits
Probability theory