• The Hodgkin–Huxley Equations.- Dendrites.- Dynamics.- The Variety of Channels.- Bursting Oscillations.- Propagating Action Potentials.- Synaptic Channels.- Neural Oscillators: Weak Coupling.- Neuronal Networks: Fast/Slow Analysis.- Noise.- Firing Rate Models.- Spatially Distributed Networks.

From the reviews: "This excellent 422 page hardcover publication is an accessible and concise monograph. ... Mathematical Foundations is a timely contribution that will prove useful to mathematics graduate students and faculty interested in the application of dynamical systems theory to cellular and systems neuroscience. ... welcome addition to the pedagogical literature. ... For mathematics graduate students who are investigating the field of computational neuroscience, I would highly recommend Mathematical Foundations of Neuroscience as their first computational neuroscience text." (Gregory D. Smith, The Mathematical Association of America, December, 2010) "...it is a good substitute for a lengthy regime of abstract maths classes, but it is also well integrated into the field of neuroscience. Ermentrout and Terman's book conveys much of the advanced mathematics used in theoretical neuroscience today." (Vincent A. Billock, Nature) "Gives an engaging, detailed, and truly authoritative treatment of neural dynamics ... . suited for mathematicians at the advanced undergraduate and beginning graduate level, and beyond, who wish to enter the field. ... a valuable and often-consulted text for researchers. It is also an excellent resource for instructors of intermediate to advanced courses ... . the text is very readable, even with its impressively wide scope. In addition, many subsections give short, independent reviews of mathematical topics that will be very useful in the classroom." (Kresimir Josic and Eric Shea-Brown, SIAM Review, Vol. 53 (3), 2011) "This book emphasises the use of dynamical systems techniques in building and understanding models of neural cells and tissues. It has an extensive set of exercises at the end of each chapter and is ideally suited as a course text in a final-year undergraduate or first-year Ph.D. applied mathematics programme in mathematical neuroscience. ... Overall this is a unique text on the topic of mathematical neuroscience ... that fills a much-needed gap in the mathematical literature for both students and researchers." (Stephen Coombes, Mathematical Reviews, Issue 2012 a)