**Instructor:**Richard Sowers**Office:**227B Illini Hall**Phone:**(217) 333-6246**email:**r-sowers@math.uiuc.edu**Home page:**`https://faculty.math.illinois.edu/~r-sowers`

(this syllabus can be found there)**Office Hours:**MWF 12-1 and by appointment**Class meets:**MWF 1-1:50 P.M. in 241 Altgeld Hall

**Outline:** This is an undergraduate course on
stochastic processes, or more exactly, Markov processes. We will
more or less follow the textbook. We start out by understanding
what the Markov property is (loss of memory, a reasonable assumption
if one's viewpoint is sufficiently complex). Our understanding will
come about from studying a two-state Markov chain, which is the
simplest nontrivial Markov process. After spending some time on this,
we will study more complicated Markov chains. We hope to also
consider some diffusion processes, as time permits. As examples
which will guide our studies, we will consider branching processes and
queuing chains. We will also, as time permits, study some
applications
of Markov processes to financial mathematics.
We will try to go at a reasonable pace. Understanding, not formulae,
will be our goal. The general theory of Markov processes is
incredibly rich, so we can only try to understand some basic
phenomena. To make an analogy, if the other courses you have been
taking have been proteins and carbohydrates, this course should be a
dietary supplement, to allow you to gain a useful edge in
understanding various phenomena.

**Grading policy:** There will be three exams, final,
and either some homeworks or some class presentations.
The relative weights will be:

Final: | 150 pts (30% of grade) |

Hourly Exam 1: | 100 pts (20% of grade) |

Hourly Exam 2: | 100 pts (20% of grade) |

Hourly Exam 3: | 100 pts (20% of grade) |

Homework/Presentation: | 50 pts (10% of grade) |

Total: | 500 pts (100% of grade) |

Department of Mathematics

University of Illinois at Urbana-Champaign

1409 W Green St.

Urbana, IL 61801

r-sowers@math.uiuc.edu

(217) 333-6246