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.