Mathematics for Neuroscientists

Dr. Gabbiani is Professor in the Department of Neuroscience at the Baylor College of Medicine. Having received the prestigious Alexander von Humboldt Foundation research prize in 2012, he just completed a one-year cross appointment at the Max Planck Institute of Neurobiology in Martinsried and has international experience in the computational neuroscience field. Together with Dr. Cox, Dr. Gabbiani co-authored the first edition of this bestselling book in 2010. Dr. Cox is Professor of Computational and Applied Mathematics at Rice University. Affiliated with the Center for Neuroscience, Cognitive Sciences Program, and the Ken Kennedy Institute for Information Technology, he is also Adjunct Professor of Neuroscience at the Baylor College of Medicine. In addition, Dr. Cox has served as Associate Editor for a number of mathematics journals, including the Mathematical Medicine and Biology and Inverse Problems. He previously authored the first edition of this title with Dr. Gabbiani.

1. Introduction2. The Passive Isopotential Cell3. Differential Equations4. The Active Isopotential Cell5. The Quasi-Active Isopotential Cell6. The Passive Cable7. Fourier Series and Transforms8. The Passive Dendritic Tree9. The Active Dendritic Tree10. Extracellular Potential11. Reduced Single Neuron Models12. Probability and Random Variables13. Synaptic Transmission and Quantal Release14. Neuronal Calcium SignalingNeuronal Calcium Signaling15. Neurovascular Coupling, the BOLD Signal and MRI16. The Singular Value Decomposition and ApplicationsThe Singular Value Decomposition and Applications17. Quantification of Spike Train Variability18. Stochastic Processes19. Membrane NoiseMembrane Noise20. Power and Cross-Spectra21. Natural Light Signals and Phototransduction22. Firing Rate Codes and Early Vision23. Models of Simple and Complex Cells24. Models of Motion Detection25. Stochastic Estimation Theory26. Reverse-Correlation and Spike Train Decoding27. Signal Detection Theory28. Relating Neuronal Responses and Psychophysics29. Population CodesPopulation Codes30. Neuronal Networks31. Solutions to Exercises