MATH 5040/6810 (Fall '23)
Time & Place:
MWF 11:50AM - 12:40PM,
Mondays 1-2 PM or by appointment, at
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
C or better in MATH 5010. Fulfills Quant Reason (Math & Stat/Log) & Quant Intensive BS. Meets with MATH 6810
We will follow Introduction to Stochastic Processes
by Gregory F. Lawler
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,
homework problems in a timely fashion.
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"
Do NOT consider that you overcame a particular weakness if you looked
solution first! You will need to do other similar problems in this case
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)
, due Monday, September 11;
, due Monday, September 25;
, due Monday, October 30;
More exercises for practice
Solution of the extra exercises
, due Wednesday, November 22;
, 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.
The Americans with Disabilities Act:
The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability & Access, 162 Olpin Union Building, 801-581-5020. CDA will work with you and the instructor to make arrangements for accommodations. All written information in this course can be made available in alternative format with prior notification to the Center for Disability & Access.
Addressing Sexual Misconduct: Title IX makes it clear that violence and harassment based on sex and gender (which includes sexual orientation and gender identity/expression) is a Civil Rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran¹s status or genetic information. If you or someone you know has been harassed or assaulted on the basis of your sex, including sexual orientation or gender identity/expression, you are encouraged to report it to the University’s Title IX Coordinator; Director, Office of Equal Opportunity and Affirmative Action, 135 Park Building, 801-581-8365, or to the Office of the Dean of Students, 270 Union Building, 801-581-7066. For support and confidential consultation, contact the Center for Campus Wellness, 426 SSB, 801-581-7776. To report to police, contact the Department of Public Safety, 801-585-2677(COPS).
Campus Safety: The University of Utah values the safety of all campus community members. To report suspicious activity or to request a courtesy escort, call campus police at 801-585-COPS (801-585-2677). You will receive important emergency alerts and safety messages regarding campus safety via text message. For more information regarding safety and to view available training resources, including helpful videos, visit safeu.utah.edu
Wellness at the U: Your personal health and wellness are essential to your success as a student. Personal concerns like stress, anxiety, relationship difficulties, depression, or cross-cultural differences can interfere with a student’s ability to succeed and thrive in this course and at the University of Utah.
Please feel welcome to reach out to your instructor or TA to handle issues regarding your coursework.
For helpful resources to manage your personal wellness and counseling options, contact the Center for Campus Wellness at 801-581-7776.
Office of the Dean of Students The Office of the Dean of Students is dedicated to being a resource to students through support, advocacy, involvement, and accountability. It serves as a support for students facing challenges to their success as students, and assists with the interpretation of University policy and regulations. Please consider reaching out to the Office of Dean of Students for any questions, issues and concerns. 200 South Central Campus Dr., Suite 270. Monday-Friday 8 am-5 pm.