https://math.uiuc.edu/~r-sowers(this syllabus can be found there)
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)|