Cognitive Science | Mathematics & Logic for Cognitive and Information Science
Q250 | 1065 | Ruth Eberle
One source of scientific theory comes from the analysis of empirical
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 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 first-order logic, machines, and linear algebra for
parallel distributed processing (neural nets). 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.