# Computational Neuroscience

## MATH/BIOL/EECS/EBME/NEUR 478

MATH/BIOL/COGS 378

### 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

### Textbooks

### The NEURON simulation environment

### XPP/AUTO

Download XPP here.

Download the first set of course exercises separately or all in one
tar file.
For the second set of XPP exercises (for Friday 2/12/2010) here are
For the third set of XPP exercises (for Monday 2/22/2010) here is a
.tar file containing
the following:
For the fourth set of XPP exercises (for Wednesday 4/21/2010) here are the files with
### MATLAB

- Matlab is available through CWRU's site license, including the Matlab Neural Network
Toolbox. To see whether the version of matlab you have installed includes this
toolbox, start matlab and type "ver" in the command line window.
- For matlab neural network exercises you will need to download the
nnet documentation and the
instructions.
- For the first exercise work through chapters 2 (Neuron Model and
Network Architectures) and 3 (Perceptrons) and (time permitting) 5 (Backpropagation). Here is a
Matlab script,
or "m-file" to get you started in chapter 2 by taking you through a series of small exercises.
- The second matlab neural network exercise explores Kohonen's self-organizing map. Here is
an m-file with instructions and a copy
of Trappenberg's code
som.m.

### Miscellany

#### Izhikevich's code for "simple models"

Download the tar file.
#### Statistical Neural Field Models

Download Wilson and Cowan's 1972 Biophysical Journal article.
#### Bursting and Dendritic Morphology

Download
Mainen & Sejnowski's 1996 Nature paper
and the
hoc code for the associated exercise.

Contact Prof. Thomas.
Updated: January 6, 2010