Theoretical and Computational Neuroscience

Course Description

This course provides an introduction to the realm of theoretical and computational neuroscience, specifically concentrating on models of individual neurons. Neurons use sequences of short electrical pulses called spikes to encode information. The course explores how mathematical tools like differential equations, phase plane analysis, time scale separation, and stochastic processes can aid in understanding neuron dynamics and neural encoding.

What Students Will Learn

  • Utilization of mathematical tools such as differential equations and phase plane analysis to model neuron dynamics.
  • Understanding the impact of stochastic processes and how they relate to the variability in spike trains and neural encoding.

Prerequisites or Skills Necessary

Students enrolling should have a foundation in calculus, differential equations, and probability theory. A recommended textbook for supplementary reading is "NEURONAL DYNAMICS - from single neurons to networks and cognition" from Cambridge University Press, 2014.

Syllabus

  • Week 1: Introduction to simple neuron models
  • Week 2: Hodgkin-Huxley models and detailed biophysical modeling
  • Week 3: Two-dimensional neuron models and phase plane analysis
  • Week 4: Continued exploration of two-dimensional models and dendrites
  • Week 5: Examining the variability of spike trains and implications for the neural code
  • Week 6: Noise models, the role of noisy neurons in encoding
    • Week 7: Techniques for estimating neuron models for effective coding and decoding

Who This Course Is For

This course is tailored for students and professionals interested in brain functions, particularly at the neuronal level. It's best suited for those who already have a basic understanding of calculus and differential equations and are intrigued by the computational aspects of neuroscience.

Real-World Application

Skills developed in this course can be applied in academic research, particularly in fields relating to neuroscience and computational biology. Understanding neural dynamics facilitates more effective models of brain function, which can contribute to medical advancements and the development of new neurological therapies.