Computational Neuroscience

MATH/BIOL/EECS/EBME/NEUR 478
MATH/BIOL/COGS 378

Full Syllabus

Course Description

Computer simulations and mathematical analysis of neurons and neural circuits, and the computational properties of nervous systems. Students are taught a range of models for neurons and neural circuits, and are asked to implement and explore the computational and dynamic properties of these models. The course introduces students to dynamical systems theory for the analysis of neurons and neural circuits, as well as to cable theory, passive and active compartmental modeling, numerical integration methods, models of plasticity and learning, models of brain systems, and their relationship to artificial neural networks. Term project required. Recommended prerequisites: multivariate calculus (MATH 223) and a first course in differential equations (either MATH 224 or the sequence BIOL 300 and BIOL 306). Cross-listed as BIOL 378/478, MATH 378/478, COGS 378, EECS 478, EBME 478, NEUR 478. Students enrolled in MATH 478 will make arrangements with the instructor to attend additional lectures and complete additional assignments addressing mathematical topics related to the course. Consent of department required.

Instructor

Peter Thomas Asst. Prof. of Mathematics, Biology & Cognitive Science
pjthomas--at--case.edu / 216-368-3623
Office hours: MW 12:30-2:00 or by appointment.
Course meeting: MWF 10:30-11:20 a.m.
Location: White 324

Course Grader & Teaching Assistant: Catherine Kehl.

COURSE RESOURCES

Course Folder on Google Docs

Assignment Schedule
Project Instructions
Homework assignments (also available under the google docs folder):
1. First Homework Assignment
2. Second Homework Assignment
3. Third Homework Assignment and companion file resistor-tmp.ode.

Textbooks

Spikes, Decisions and Actions by Hugh R. Wilson.
Here is a link to the (online) chapters of Dynamical Systems in Neuroscience by Eugene Izhikevich.
Fundamentals of Computational Neuroscience by Thomas Trappenberg.
Here is Thomas Trappenberg's course page at Dalhousie University.

The NEURON simulation environment

The NEURON simulation environment.
Hands-on exercises for learning NEURON.

XPP/AUTO

Download XPP here.
Download some simple course exercises separately or all in one tar file.

Miscellaneous Stuff

Izhikevich's code for "simple models"

Download the tar file.

Exploring the Morris Lecar Burster with XPP