Current Problems in Applied
Mathematics:
Mathematical Methods and Models in Visual Neuroscience
Instructor: D.
Graham
Fall Term 2009
Meeting Time: Tuesday and Thursday, 2pm Ð 3:50pm (02A
block)
Room: Kemeny 244
DEVELOPMENT OF THIS COURSE IS SUPPORTED BY:
NATIONAL SCIENCE FOUNDATION GRANT DMS-0746667 &
THE WILLIAM H. NEUKOM 1964 INSTITUTE FOR
COMPUTATIONAL SCIENCE
SYLLABUS
(2009) (old
syllabus: 2008)
Description
This course is designed to introduce
graduate students and advanced undergraduates from a variety of disciplines to
mathematical methods used to measure and model neural mechanisms underlying the
function of the human visual system. The course will focus primarily on neural
coding strategies in the early visual system (retina, thalamus, primary visual
cortex). General topics will include receptive fields, information-theoretic
approaches, efficient coding theory, and nonlinearities. Higher-level cortical
representations and object recognition strategies will also be discussed.
Prerequisites: No background in neurobiology is expected, though
experience with differential equations, linear algebra, computer programming
and basic biology will be very useful.
Evaluation: Students will be evaluated based on problem sets
(mostly Matlab-based) and a final project/presentation.
Useful links
http://www.handprint.com/HP/WCL/color.html
-- An excellent site describing the retina in fantastic detail.
http://faculty.washington.edu/chudler/neuroroot.html
-- A site that gives the Greek or Latin root of many common brain terms.
http://white.stanford.edu/Useful_Numbers.php
-- Useful numbers in vision science.
http://www.jove.com/index/details.stp?ID=771
-- See how retinal recordings are actually made.
http://www.cis.hut.fi/projects/ica/imageica/
-- A good, transparent ICA package
http://www.med.harvard.edu/AANLIB/cases/caseM/case.html
http://www.brainconnection.com/topics/?main=anat/vision-anat
http://brainmaps.org/index.php
http://www.brainexplorer.org/brain_atlas/Brainatlas_index.shtml