481: Mathematical Neuroscience Conor Houghton Timetable: Monday 2-4 and Thursday 4 in Synge.

Thanks to everyone who took my course this year!

This course will follow material in

• Theoretical Neuroscience by Peter Dayan and LF Abbott.

It is lectured by me, Conor Houghton. It will be examined by a two hour end of year exam; 481++ will also require three computational projects.

Draft course description:

This course will come in two version; 481 is a half course (5 ECTS) with about 30 contact hours made up of lectures and tutorials. It will cover more-or-less the same material that was covered last time 481 was taught, but this time there will be problem sheets and tutorials. There will be a two hour end-of-year exam. 482 is a full course (10 ECTS), it includes 481 along with 481++ an introduction to c++ and a set of three mandatory computer projects. These will be straight-forward simulations related to neuroscience, somewhat in the spirit of the computer demonstrations included in the course last time. Help will be available in doing the project work, but passing 481++ will require that all three projects are completed.

Mathematical neuroscience, as a whole, is divided into three main areas, one of which relates to the dynamics of neurons themselves, another to networks of neurons and a third to what people in the field call neural encoding and decoding, the study of how stimulus and response are related in neurons.

This course will consider each of areas in turn. It will begin with a general introduction to neuroscience and no prior knowledge of neurobiology will be assumed. Next, the voltage dynamics of neurons will be considered with a description of the Hodkin-Huxley equation and integrate-and-fire models. Spike train statistics will then be considered, along with the neural code, correllation and reverse correllation methods and stochastic properties. These ideas will be illustrated with an introduction to the visual system. Finally, neuronal plasticity and simple network models will be discussed.

Notes

My email address is houghton@maths.tcd.ie and my office is at the top of the maths department, half way between the discussion room and Donal O'Donavan's office. If you want to contact me anonymously, for example to complain about the course, you can use the feedback facility linked from the sidebar. I also intend to give a one line description of each lecture as I go along; again, this is linked from the side bar. This is the second year 481 is being taught. The website for the previous time it was taught is here, I designed that page as a wiki, but this didn't work out, nobody else edited it and I found it much harder to maintain.

To do

• More on the note on reversal potentials.

New

• Some more correspondence. 30 May 2009.
• Some corr and added soln to problem 2a. 12 May 2009.
• Scanned the remaining lecture notes. 4 April 2009.
• Minor addition to lecture list. 1 April 2009.
• Sample paper in PS section. 27 March 2009.
• Some progress in fixing lecture list. 27 March 2009.
• Link to 2006/7 paper in PS section. 27 March 2009.
• Soln2. 8 February 2009.
• Prob2. 7 January 2009.
• Soln1. 22 November 2008.
• Prob1. 14 November 2008.
• Added a note on the after image illusion. 10 November 2008.
• Added a sketch of a pyramidal neuron. 2 November 2008.
• Added some HH plots. 30 October 2008.
• Scanned some lecture notes. 29 October 2008.
• Added a brief Boltzmann-Maxwell note. 27 October 2008.
• Added gating probabilities note 22 October 2008.
• Web page created 6 July 2008.

The picture, View of a Skull (c. 1489) is a drawing by Leonardo da Vinci, the image is in the public domain.