MATH 5040/6810 (Fall '23)

Time & Place: MWF 11:50AM - 12:40PM, WEB 1250
Lecturer: Firas Rassoul-Agha
Phone: (801) 585-1647, E-Mail:
Office Hour: Mondays 1-2 PM or by appointment, at LCB 209
Forum: We will be using Piazza for class discussion and answering questions. The system is highly catered to getting you help fast and efficiently from classmates and myself.
Rather than emailing questions, I highly encourage you to post your questions on Piazza. I also highly encourage you to answer your classmate's questions, if you think you know the answer.
One advantage over CANVAS Discussion Board is that you can post anonymously, if you prefer.
You can sign up here but you will need an access code that you can find in the version of the syllabus on CANVAS.

Prerequisites: C or better in MATH 5010. Fulfills Quant Reason (Math & Stat/Log) & Quant Intensive BS. Meets with MATH 6810

Textbook: We will follow Introduction to Stochastic Processes by Gregory F. Lawler

Lecture notes: Supplementary lecture notes will be posted as we go (see below). These have been written up by a former instructor of the course and do not necessarily cover everything I cover in class. They also are not typo-free

Further supplemental material: Chapter 4 in Introduction to Probability Models by Sheldon M. Ross, Chapter 1 in Essentials of Stochastic Processes by Rick Durrett, and these lecture notes.

Homework counts 25% and is assigned every other week. It will be posted at the bottom of this page

Three midterms count 25% each and are on October 6, November 6, and December 6. Same time and place as lecture

No final exam

NO make-up tests or homework

The BEST way to keep up with the pace of this course and to prepare for exams is to solve, at the very least, the assigned homework problems in a timely fashion.
To learn the subject well you really need to solve as many problems as you can

Doing the math is the ONLY way to learn math

The student's solutions that come with the textbook have the correct ideas but may have algebra errors. Points WILL be taken off for such errors when the homework is graded.
In any case, I recommend you use the solutions as a LAST resort. Only after you have tried everything else and "suffered" enough!

Do NOT consider that you overcame a particular weakness if you looked at the solution first! You will need to do other similar problems in this case

Lecture Notes:

Lectures 1-14 (finite state space Markov chains),
Lectures 15-25 (countable state space Markov chains),
Lectures 16-33 (continuous-time countable-space Markov processes),

Homework Problems:

Homework 1, due Monday, September 11; Solutions; Google math
Homework 2, due Monday, September 25; Solutions;
Homework 3, due Monday, October 30; Solutions; More exercises for practice; Solution of the extra exercises;
Homework 4, due Wednesday, November 22; Solution;
Homework 5, due Monday, December 4;

To practice for Exam 1, solve as many exercises from the textbook's Chapter 1 as you can. You can ignore 1.7, 1.12, 1.15, 1.18, 1.20, and 1.21;

Exam 1 solution

To practice for Exam 2, solve as many exercises from the textbook's Chapter 2 as you can. You can ignore 2.14 (although it is quite interesting),
2.15, 2.16, 2.17 (although that is where the connection between transience and the alpha function is proved), and 2.18 (although this is where Stirling's formula is proved);

Exam 2 solution

To practice for Exam 3, solve as many exercises from the textbook's Chapters 3 and 6 as you can. You can ignore 3.4, 3.7, and 3.16. Solve also exercises 6.1, 6.2, 6.3 and 6.9.

Further important information:

  • It is the student's responsibility to regularly check their Umail or have it forwarded to an address they check regularly. The Umail is the only way for me to communicate privately with the student. There will be occasions during the semester that we may need to reach out to individual students (e.g. regarding a grade or assignment) and it is in their best interest to respond promptly.
  • I would like to encourage the students to email me only if it is something personal that requires individual attention. For questions about logistics of the class, course material and assignments, and anything else the classmates may wonder about as well, please post a question on the Discussions Board in CANVAS or on Piazza. This way the information is shared quickly to the entire class, and everyone can benefit from seeing other classmates’ questions.
  • Please stay updated by regularly checking: the announcements on Canvas, your Umail, the posts on the Discussions Board, the posts on Piazza, and pay attention to the announcements given in class.
  • Students are expected to log in and check canvas regularly for posted announcements and assignments. Students are also strongly advised to set up notifications for canvas so they do not miss any important notifications.
  • Respectful participation in all aspects of the course will make our time together productive and engaging. Zoom lectures, discussion threads, emails and canvas are all considered equivalent to classrooms and student behavior within those environments shall conform to the student code.
  • COVID-19 Campus Guidlines
  • Drop/Withdrawal Policies: Students may drop a course within the first two weeks of a given semester without any penalties. Students may officially withdraw (W) from a class or all classes after the drop deadline through the midpoint of a course. A “W” grade is recorded on the transcript and appropriate tuition/fees are assessed. The grade “W” is not used in calculating the student’s GPA. For deadlines to withdraw from full-term, first, and second session classes, see the U's Academic Calendar.
  • Plagiarism and Cheating: It is assumed that all work submitted to your instructor is your own work. When you have used the ideas of others, you must properly indicate that you have done so. Plagiarism and cheating are serious offenses and may be punished by failure on an individual assignment, and/or failure in the course. Academic misconduct, according to the University of Utah Student Code,
    “...Includes, but is not limited to, cheating, misrepresenting one’s work, inappropriately collaborating, plagiarism, and fabrication or falsification of information…It also includes facilitating academic misconduct by intentionally helping or attempting to help another to commit an act of academic misconduct.”
    For details on plagiarism and other important course conduct issues, see the U's Code of Student Rights and Responsibilities.
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