Cognitive Science | Mathematics & Logic for Cognitive and Information Science
Q250 | 1035 | Eberle

data.  Often, however, it is not possible for the subject of study to be
investigated directly and empirically, and, even when it is possible, it
turns out that a very useful way to gain insights into scientific phenomena
is to build models of them.  Mathematics plays a key role in both these
approaches.  Mathematics provides methods for the analysis of data.  It
also provides tools for building models of objects, states and processes
studied in the different specific areas of science.
The purpose of this course is to introduce students to some of the main
mathematical and logical tools used in building models in the information
and cognitive sciences.  The emphasis will be on the intuitive ideas behind
the mathematics, i.e. the main goal will be to have the students learn the
ideas first at an intuitive level and then to go towards a deeper
acquaintance with the ideas.  The course will introduce the main concepts,
notions and results from set theory, first-order logic, automata theory,
machines, the theory of formal grammars, and linear algebra for parallel
distributed processing.  One of the problems with which  cognitive science
is deeply concerned is the relation between thought, language, and the
world.  For this reason, attention will also be given to the models used
for the study of human languages.
The lab hours will be devoted primarily to the use of computational tools.
Some of these will be used to help the students gain working experience
with the material in advance of the more formal treatment in the lectures.
The award winning programs Tarski's World and Turing's World will be used.
The material for the course is self-contained and no prerequisites beyond a
sound high school mathematics background are needed.