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Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory.

Fully revised material and corrected text
Additional chapters on extracellular potentials, motion detection and neurovascular coupling
Revised selection of exercises with solutions
More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts

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1. Introduction 2. The Passive Isopotential Cell 3. Differential Equations 4. The Active Isopotential Cell 5. The Quasi-Active Isopotential Cell 6. The Passive Cable 7. Fourier Series and Transforms 8. The Passive Dendritic Tree 9. The Active Dendritic Tree 10. Extracellular Potential 11. Reduced Single Neuron Models 12. Probability and Random Variables 13. Synaptic Transmission and Quantal Release 14. Neuronal Calcium SignalingNeuronal Calcium Signaling 15. Neurovascular Coupling, the BOLD Signal and MRI 16. The Singular Value Decomposition and ApplicationsThe Singular Value Decomposition and Applications 17. Quantification of Spike Train Variability 18. Stochastic Processes 19. Membrane NoiseMembrane Noise 20. Power and Cross-Spectra 21. Natural Light Signals and Phototransduction 22. Firing Rate Codes and Early Vision 23. Models of Simple and Complex Cells 24. Models of Motion Detection 25. Stochastic Estimation Theory 26. Reverse-Correlation and Spike Train Decoding 27. Signal Detection Theory 28. Relating Neuronal Responses and Psychophysics 29. Population CodesPopulation Codes 30. Neuronal Networks 31. Solutions to Exercises

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"This is a big book in more than one sense. It has a large page format measuring about 20cm x 27cm making it easy to open up and take in large swathes of text, equations, and figures. More importantly, it covers a very wide range of mathematical methodologies relevant to neuroscience. ...I would highly recommend this book to those with an interest in computational neuroscience who wish to delve more deeply into the biophysics underlying cell-based dynamics and computations, especially if they are interested in flexing their mathematical muscles." --MathSciNet

Amazon Editorial Reviews for First Edition: "I really think this book is very, very important. This is precisely what has been missing from the field and is badly needed. " -- Dr. Kevin Franks, research fellow, Richard Axel´s laboratory Columbia University, NYC

"The idea of presenting sufficient maths to understand the theoretical neuroscience, alongside the neuroscience itself, is appealing. The inclusion of Matlab code for all examples and computational figures is an excellent idea. " -- David Corney, research fellow, Institute of Ophthalmology, University College London

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