School of Informatics | Mathematical Foundations of Informatics
I201 | 6955 | Eberle

I201 Mathematical Foundations of Informatics (4 cr.)  Recommended
prerequisite or concurrent:  INFO I101.  An introduction to the suite
of mathematical and logical tools used in information sciences,
including finite mathematics, automata and computability theory,
elementary probability and statistics, and basics of classical
information theory. Cross listed with COGS Q250 Mathematics and Logic
for the Cognitive & Information Sciences.  Credit given for only one
of INFO I201 and either COGS Q250, or CSCI C241.

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 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
first-order logic, machines, and linear algebra for a 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.