INTRO TO PROBABILITY THEORY 2 (M464)

Spring 2021 (Jan 19-May 7)

Welcome! Probability is not only a powerful tool to understand randomness, but also one of the most fascinating areas of mathematics. It is intimately connected with statistics and to other areas of mathematics. It is widely applied to computer science, data science, engineering, law, medicine, music, philosophy, social science, etc.

Class Day and Times:  Tue/Thurs (attend your own section). First day fo class is Tues, Jan 19. Last day of classes is Sat, May 1.

• • Section 2726:  1:10pm-2:25 pm, Meeting ID:  879 5222 0641 

  • Section 9481:  3:15pm-4:30pm, Meeting ID:  842 1152 2482

Wellness days — Tuesday, February 16; Wednesday, March 24; and Thursday, April 22. We will NOT have classes on these days.

Class type:  These classes meet 100% Online through Synchronous instruction. For more information visit https://covid.iu.edu/learning-modes/index.html

Instructor:  Wai-Tong Louis Fan. Office: Rawles Hall 225. Email: waifan@iu.edu

Office Hours: Tues 2:30pm (Meeting ID:  879 5222 0641), 4:30pm (Meeting ID:  842 1152 2482) and by appointment

AI: Xinwu Yang. Office: TBD. Email: xinwyang@iu.edu 

Office Hour: Wednesday

Important dates: Make sure to reserve them in your calendar.   

• Auto-W deadline — Undergraduate students taking full semester classes will be able to drop with a grade of W until the last day of classes — Friday, April 30; Graduate students have the more traditional deadline of March 21 (Sunday)

• Midterm exam: March 16 (Tuesday) in class

• Final exam: May 4 (Tuesday)

More about academic calender can be found in https://enrollmentbulletin.indiana.edu/pages/finexpol.php?t=spring

Course description:

This is a course on the basic theory and applications of stochastic processes, with an emphasis on problem solving. This course aims to equip you with the basic tool to model and analyse random phenomena. 

Prerequisites: M 463 

The prerequisite for this course is M463. If you have not learned the material of M463 well, then it is very likely that you will struggle with M464 and not be able to earn a good grade. So you are strongly recommended to review those materials, including examples of random variables, independence, expectations, conditional probability, etc. A quick review of can be also found in Chapters 1-2 of the textbook and in the Appendix of supplementary reading.

Textbook: An Introduction to Stochastic Modeling (3rd edition) by Howard Taylor and Samuel Karlin. We will cover Chapter 3-6 in the textbook and some selected topics.

Supplementary reading (Optional): Essentials of Stochastic Processes (3rd edition) by Rick Durrett (free online copy available at IU). 

How to succeed in this course: Attend lectures (let me know if you cannot). Organize your notes. Struggle with homework and practice problems (unless the problems are too easy for you). Feel free to talk with me if you have questions. I will try my best to help you learn the subject.

---------------------------------------------------------------------------------------------------

Announcements and class information:  Official course announcements will be made through Canvas. You are required to set your Canvas notifications so that you will receive these announcements. Failure to do so will not be considered a legitimate excuse for missing assignments or any other thing that might be announced via Canvas. 

Go to Account -> Notifications and set Announcements to be received immediately. 

Expected Learning Outcomes: 

Topics of this course include discrete-time Markov chains, Poisson point processes, continuous-time Markov chains, branching processes and renewal processes. The material will be treated in a mathematically precise fashion although some proofs will be skipped due to time limitations. The core materials consists of Chapters III to VI of the textbook by Taylor and Karlin [or Chapters 1-4 of the book by Durrett]. Time permitting, we may cover some extra topics such as: queueing theory, linear and nonlinear regression and information theory. Students will

• learn how to model simple real life situations by means of discrete-space stochastic processes. Specifically they will study discrete-time Markov chains, continuous-time Markov chains, Poisson processes, branching processes, renewal processes, and models from queueing theory.  

• learn the theory associated with the previously mentioned processes. They will learn definitions and see how to formally derive certain important properties of the processes.  

• learn how to calculate the probabilities associated with different important events related to the processes. Moreover, they will learn how to check for the existence of limiting/stationary distributions, how to compute them and how to interpret them in the real life situations being modeled.

----------------------------------------------------------------------------------------------------

Evaluation

Your course grade will be computed using the following weights:

In-class Quizzes and participation (30%), Homework (20%), midterm (20%), and a final exam (30%).

Weekly Quizzes (First graded Quiz on Jan 28 Thursday)

In-class quizzes will be given every Thursday (you're expected to attend every lecture). 

Your work should be uploaded to CANVAS immediately when the quiz is finished (end of lecture). The time of upload will be shown.

Questions will be similar to homework questions.

No make-up quizzes will be given. The lowest quiz score will be dropped.

Homework (First graded homework due Jan 28 Thursday 5pm EST)

The point of homework is not to test you, but for you to learn the material. The reason it is graded is to give you additional incentive to do it. Midterm and final exams will contain problems similar to the homework problems in difficulty. 

Homework assignments will be posted on CANVAS. It is your responsibility to get this information. 

• Upload your Homework to CANVAS before the deadline (5pm EST on the due date).

• No late homework will be accepted.The lowest score will be dropped.

• Working in groups on homework assignments is strongly encouraged; however, every student must write their own assignments.

  • Organize your work neatly. Use proper English. Write in complete English or mathematical sentences. 

  • Answers should be simplified as much as possible. For some exercises you may need a calculator to get the final answer.

General advice on problem solving: If you find a problem difficult or can’t see how to start, 

1. Ask "which section in the book/note is related to this question ?". Then read over your notes and the book with the problem in mind.

2. As you read over your book/note, ask "is there any example that is similar to the question ? Can I solve that example without looking at the solution?"

3. Now with refreshed knowledge, try to solve the original problem again. 

Repeat step 1-3 if necessary. It is often useful to start by translating from English to math; assign suitable notation. Feel free to ask me or the AI if you have questions.

Exams:

There will be a midterm and a final, see the dates above. Make sure to reserve those dates on your calendar. 

No discussion is allowed during exams and quizzes. You are expected to have internalized important formulas while working on homework problems. 

• Make-up midterm exams will be considered only if there is a conflict with another university-related event (in which case case you need to contact me as soon as possible), or a last-minute medical/family emergency (you need to show proof of such emergency, e.g., doctor's notes). See this page for more about examination policy.  

• Default grade scale can be found in the link (https://kb.iu.edu/d/azij).

-----------------------------------------------------------------------------------------------------

Academic Misconduct: The Department of Mathematics expects its students to comply fully with Indiana University policies on academic integrity. The penalties for a student caught cheating in this course may include a final course grade of F* (the star tells the registrar that the F is due to cheating) along with probation, suspension, or expulsion from the University. Academic misconduct will be reported to the Office of Student Ethics. Students should review the Code of Student Rights, Responsibilities, and Conduct, posted at: http://studentcode.iu.edu/

Religious Holiday Policy: If you will miss class, especially a class during which there will be an exam or other required work, for a religious holiday, you must inform me during the first two weeks of the semester. Procedures and campus policy can be found at: http://vpfaa.indiana.edu/docs/religious_observances/religious-observances-statement.pdf

Other University Information

Bias-Based Incident Reporting: As your instructor, one of my responsibilities is to create a positive learning environment for all students. Bias incidents (events or comments that target an individual or group based on age, color, religion, disability, race, ethnicity, national origin, sex, gender, gender identity, sexual orientation, marital status or veteran status) are not appropriate in our classroom or on campus. What should you do if you witness or experience a bias incident? See it? Hear it? Report it by submitting a report online (biasincident.indiana.edu) or calling the Dean of Students Office (812-855-8187).

Disability Services for Students: Every attempt will be made to accommodate qualified students with disabilities (e.g. mental health, learning, chronic health, physical, hearing, vision neurological, etc.) You must have established your eligibility for support services through the appropriate office that services students with disabilities. Note that services are confidential, may take time to put into place and are not retroactive; Captions and alternate media for print materials may take three or more weeks to get produced. Please contact Disability Services for Students at http://disabilityservices.indiana.edu or 812-855-7578 as soon as possible if accommodations are needed. The office is located on the third floor, west tower, of the Wells Library, Room W302. Walk-ins are welcome 8 AM to 5 PM, Monday through Friday. You can also locate a variety of campus resources for students and visitors that need assistance at: http://www.iu.edu/~ada/index.shtml

Sexual Misconduct and Title IX: As your instructor, one of my responsibilities is to create a positive learning environment for all students. Title IX and IU’s Sexual Misconduct Policy prohibit sexual misconduct in any form, including sexual harassment, sexual assault, stalking, and dating and domestic violence. If you have experienced sexual misconduct, or know someone who has, the University can help.

If you are seeking help and would like to speak to someone confidentially, you can make an appointment with:

The Sexual Assault Crisis Services (SACS) at (812) 855-8900 (counseling services)

Confidential Victim Advocates (CVA) at (812) 856-2469 (advocacy and advice services)

IU Health Center at (812) 855-4011 (health and medical services)

It is also important that you know that Title IX and University policy require me to share any information brought to my attention about potential sexual misconduct, with the campus Deputy Title IX Coordinator or IU’s Title IX Coordinator. In that event, those individuals will work to ensure that appropriate measures are taken and resources are made available. Protecting student privacy is of utmost concern, and information will only be shared with those that need to know to ensure the University can respond and assist.

I encourage you to visit stopsexualviolence.iu.edu to learn more.