Introduction to Random Processes (ECE 440/DSC 240) is an entry-level graduate class that explores stochastic systems. The latter could be very loosely defined as anything random that changes in time, and the evolution of such systems is mathematically described by a random process. Stochastic systems are at the core of a number of disciplines in engineering, for example communication systems and machine learning. They also find application elsewhere, including social systems, markets, molecular biology and epidemiology, just to name a few.

**Class objectives**

The goal of the class is to learn how to model, analyze and simulate stochastic systems. With respect to analysis we distinguish between what we could call theoretical and experimental analysis. By theoretical analysis we refer to a set of tools which let us discover and understand properties of the system. Naturally, probability theory plays a key role as the mathematical language that allows us to quantify uncertainty. The theory can only take us so far and is usually complemented with numerical analysis of experimental outcomes. Although we use the word experiment more often than not we simulate the stochastic system in a computer and analyze the outcomes of these virtual experiments.

**Class information**

__When:__ Mondays and Wednesdays 4:50-6:05 pm

__Where:__ Gavett Hall 206 and online via Zoom (fully online after Thanksgiving).

__Textbook:__ We will use lecture slides
to cover the material. A good and broad text for the
class is

John A. Gubner,

*"Probability and Random Processes for Electrical and Computer Engineers,"*Cambridge University Press.

The book can be obtained online from the University of Rochester libraries here.

An additional good reference for topics including Markov chains, continuous-time Markov chains, and queuing models is

Sheldon M. Ross,

*"Introduction to Probability Models,"*11th ed. (earlier editions are fine), Academic Press.

Both books are on reserve for the class in Carlson Library, and are also available from the University of Rochester Bookstore.

__Prerequisites:__ Useful to have good background in Probability Theory (of which we will do a fast-paced
review the first five lectures), as well as Calculus and Linear Algebra (i.e., integrals,
limits, infinite series, differential equations, vector/matrix notation, systems of linear equations, eigendecomposition).
For homework assignments we will use Matlab (which can be obtained following these
instructions); see the user guide
here.

__Credit distribution:__ Homework assignments (~10, 28 points), take-home midterm (Oct. 23, 36 points), take-home final (Dec. 15-18, 36 points).

__Grading:__ At least 60 points are required for passing (C grade), a B requires at least 75 points, and an A at least 92. Undergraduate (ECE 271) students are
expected
to complete the same assignments and exams, but will be awarded extra 10 points counting towards the final grade.

__Instructor:__ Gonzalo Mateos

__Office:__ 726 Computer Studies Building.

__Office hours:__ Tuesdays 11am via Zoom (Meeting ID: 771 885 0098).

__Teaching assistants and office hours:__ TBD.