Course Syllabus
Math 5050/6815 Stochastic processes II
Basic information
| Class when & where: | MWF 11:50-12:40 pm in LCB 215 |
| Instructor: | Li-Cheng Tsai |
| Email: | licheng.tsai@utah.edu |
| Office hours: | [TBA] |
Accommodation policy. If any conflict may prevent you from completing an assignment, you should notify me by email as soon as you become aware of the conflict, even if it's just a possibility. If it is an emergency, you should notify me by email as soon as it is safe for you to do so. I may not be able to accommodate requests that do not follow the above guidelines.
Course information, prerequisites, goals
Math 5050 / Math 6815 introduction to probability is a 3 credit course. The prerequisite is "C" or better in Math 5040.
This course provides a rigorous theoretical foundation in stochastic processes. Students will learn the mathematical frameworks of martingales, Markov chain Monte Carlo, and stochastic calculus to analyze systems where randomness evolves over time.
Components, evaluation
Course components
- Lecture-based classes
- Worksheet classes
Your performance will be evaluated as follows.
- Attendance 10%
- Weekly worksheet 90%
Out of 100,
- a final score of 92.00 or above will receive the letter grade A,
- a final score from 88.00 to 91.99 will receive the letter grade A−,
- a final score from 84.00 to 87.99 will receive the letter grade B+,
- a final score from 80.00 to 83.99 will receive the letter grade B,
- a final score from 76.00 to 79.99 will receive the letter grade B−,
- a final score from 71.00 to 75.99 will receive the letter grade C+,
- a final score from 66.00 to 71.99 will receive the letter grade C,
- a final score from 61.00 to 65.99 will receive the letter grade C−,
- a final score from 56.00 to 60.99 will receive the letter grade D+,
- a final score from 51.00 to 55.99 will receive the letter grade D,
- a final score from 46.00 to 50.99 will receive the letter grade D−.
Meetings, office hours
Classes will meet in LCB 215 (LeRoy Cowles Building) 11:50-12:40 pm on Monday, Wednesday, and Friday.
If you feel ill, please stay home and take some rest. If you miss a an assignment due to illness, please let me know (licheng.tsai@utah.edu) and we'll find ways around it.
I'll hold an office hour [TBA] in JWB 322 (John Widtsoe Building). Come to my office hours for help or questions. If the time doesn't work for you, we can try to schedule an appointment; you can also email me (licheng.tsai@utah.edu) your questions.
Lecture notes and textbook
Lecture notes. I will be posting lecture notes that cover the content of the lectures. To access them, go to "Files" and then the folder "lecture notes".
Textbook. I will also refer you to the book "Introduction to stochastic processes" by Lawler, which you can access by going "Bookshelf". I will include in the lecture notes which sections of the book is relevant for reading.
Accommodations
If any conflict may prevent you from completing an assignment, you should notify me by email as soon as you become aware of the conflict, even if it's just a possibility. If it is an emergency, you should notify me by email as soon as it is safe for you to do so. I may not be able to accommodate requests that do not follow the above guidelines.
I'd also like to let you be aware of the University's resources for students' well being. To find out about them, scroll down to "University Policies".
Schedule
| Week 01 (1/5, 7, 9) | Conditional expectation |
|
|
| Week 02 (1/12, 14, 16) | Martingales, stopping times |
|
|
| Week 03 (1/21, 23) | Optional stopping |
|
|
| Week 04 (1/26, 28, 30) | Gambler's fortunate, martingale convergence |
|
|
| Week 05 (2/2, 4, 6) | Polya's urn, random sums and products |
|
|
| Week 06 (2/9, 11, 13) | |
|
|
| Week 07 (2/18, 20) | Markov chain Monte Carlo, detailed balance |
|
|
| Week 08 (2/23, 25, 27) | Metropolis-Hastings, examples |
|
|
| Week 09 (3/2, 4, 6) | mixing time, rate of convergence |
|
|
| Week no class | spring break |
| Week 10 (3/16, 18, 20) | Brownian motion |
|
|
| Week 11 (3/23, 25, 27) | reflection principle |
|
|
| Week 12 (3/30, 4/1, 3) | stochastic integral, Ito isometry |
|
|
| Week 13 (4/6, 8, 10) | Ito's formula, applications |
|
|
| Week 14 (4/13, 15, 17) | Langevin dynamics, applications |
|
|
| Week last (4/20) |
Lecture-based classes
When. Every Monday and Wednesday, except that it'll be on Monday and Friday on Week 09
What. We will run lectures on most Monday and Wednesday, covering the topics listed on the schedule. Within the lectures, I will give you some problems I'll ask you to work on in-class.
The purpose of these problems is to help you absorb the material. Your work on these in-class problems will not contribute to your final score, and you need not worry about getting the full or correct solution on the spot. During the class, you should try these problems, see if there's any impediments, confusions, etc., and ask me about them. The more questions the better.
To review these problems after a class, click "File" in the course navigation menu and go to the lecture notes. We will not post the answer or solution key to these in-class problems, and you can ask me about them if you have any questions.
Attendance
We will take attendance for every lecture-based class. Each attendance will contribute 5 points to a total of 100. The attendance altogether will contribute to 10% of your final score.
Worksheet classes
When. Every Friday, except that it'll be on Wednesday on Week 09
What. You will be working on a printed worksheet that I make. The worksheet will consist of problems that are similar to or the same as the lectures and in-class problem in the same week.
Policies. You can work in a group of 2, can ask me for questions, can use the lecture notes and textbook, but do not any other source of information. Turn in your worksheet by the end of the class.
Grading. Attending a worksheet class and turning in the paper by the end of the class will automatically gain 40 points out of 100. The rest 60 points will be graded based on the completeness and correctness. The average of the total 14 worksheet scores will contribute to 90% of your final score.
University Policies
Americans With Disabilities Act (ADA)
The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities.
All written information in this course can be made available in an alternative format with prior notification to the Center for Disability & Access (CDA). CDA will work with you and the instructor to make arrangements for accommodations. Prior notice is appreciated. To read the full accommodations policy for the University of Utah, please see Section Q of the Instruction & Evaluation regulations.
In compliance with ADA requirements, some students may need to record course content. Any recordings of course content are for personal use only, should not be shared, and should never be made publicly available. In addition, recordings must be destroyed at the conclusion of the course.
If you will need accommodations in this class, or for more information about what support they provide, contact:
Center for Disability & Access
801-581-5020
disability.utah.edu
Third Floor, Room 350
Student Services Building
201 S 1460 E
Salt Lake City, UT 84112
Safety at the U
The University of Utah values the safety of all campus community members. You will receive important emergency alerts and safety messages regarding campus safety via text message. For more safety information and to view available training resources, including helpful videos, visit safeu.utah.edu.
To report suspicious activity or to request a courtesy escort, contact:
Campus Police & Department of Public Safety
801-585-COPS (801-585-2677)
dps.utah.edu
1735 E. S. Campus Dr.
Salt Lake City, UT 84112
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, veteran’s status, or genetic information.
If you or someone you know has been harassed or assaulted, you are encouraged to report it to university officials:
Office of Equal Opportunity and Title IX
801-581-8365
oeo.utah.edu
135 Park Building
201 Presidents' Cir.
Salt Lake City, UT 84112
Office of the Dean of Students
801-581-7066
deanofstudents.utah.edu
270 Union Building
200 S. Central Campus Dr.
Salt Lake City, UT 84112
To file a police report, contact:
Campus Police & Department of Public Safety
801-585-COPS (801-585-2677)
dps.utah.edu
1735 E. S. Campus Dr.
Salt Lake City, UT 84112
If you do not feel comfortable reporting to authorities, the U's Victim-Survivor Advocates provide free, confidential, and trauma-informed support services to students, faculty, and staff who have experienced interpersonal violence.
To privately explore options and resources available to you with an advocate, contact:
Center for Campus Wellness
801-581-7776
wellness.utah.edu
350 Student Services Building
201 S. 1460 E.
Salt Lake City, UT 84112
Academic Misconduct
It is expected that students comply with University of Utah policies regarding academic honesty, including but not limited to refraining from cheating, plagiarizing, misrepresenting one’s work, and/or inappropriately collaborating. This includes the use of generative artificial intelligence (AI) tools without citation, documentation, or authorization. Students are expected to adhere to the prescribed professional and ethical standards of the profession/discipline for which they are preparing. Any student who engages in academic dishonesty or who violates the professional and ethical standards for their profession/discipline may be subject to academic sanctions as per the University of Utah’s Student Code: Policy 6-410: Student Academic Performance, Academic Conduct, and Professional and Ethical Conduct.
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 syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.
To add some comments, click the "Edit" link at the top.