| Name | Role | Office | Office hours | |
| Yuriy Nemish | Instructor | AP&M 6442 | ynemish@ucsd.edu |
|
| Kejin Wu | Teaching Assistant | AP&M 1132 | kwu@ucsd.edu |
|
| Date | Time | Location | |
| Lectures (YN) | Monday, Wednesday, Friday | 3:00 - 3:50 PM | WLH 2205 |
| Discussion A01 (Wu) | Thursday | 6:00 - 6:50 PM | CENTR 217B |
| Discussion A02 (Wu) | Thursday | 7:00 - 7:50 PM | CENTR 217B |
| Week | Date | Time | Location | |
| Midterm Exam 1 | 4 | Friday, April 22 | 3-3:50 PM | WLH 2205 |
| Midterm Exam 2 | 8 | Wednesday, May 18 | 3-3:50 PM | WLH 2205 |
| Final Exam | Finals | Wednesday, June 8 | 3-6 PM | WLH 2205 |
Welcome to Math 180C: a one quarter course introduction to stochastic processes (II). According to the UC San Diego Course Catalog, the topics covered are Markov chains in discrete and continuous time, random walk, recurrent events and other topics.
Here is a more detailed listing of course topics, in the sequence they will be covered, together with the relevant section(s) of the textbook. While each topic corresponds to approximately one lecture, there will be some give and take here. This is a rough schedule that will be updated during the term.
| Date | Week | Topic | PK | Durrett | Pre-lecture slides | Post-lecture slides | Additional videos |
|---|---|---|---|---|---|---|---|
| 3/28 | 1 | Administrivia. Birth processes | 6.1 | - | Lecture 1 | Lecture 1 | - |
| 3/30 | 1 | Birth processes | 6.1 | - | Lecture 2 | Lecture 2 | - |
| 4/1 | 1 | Birth and death processes | 6.2 - 6.3 | - | Lecture 3 | Lecture 3 | Lectures 1-3 |
| 4/4 | 2 | Birth and death processes | 6.2 - 6.3 | - | Lecture 4 | Lecture 4 | Lecture 4 |
| 4/6 | 2 | Strong Markov property. Hitting probabilities | 6.5 | - | Lecture 5 | Lecture 5 | Lecture 5 |
| 4/8 | 2 | General continuous-time Markov chains. Q-matrices. Matrix exponentials | 6.6 | 4.1 | Lecture 6 | Lecture 6 | Lecture 6 |
| 4/11 | 3 | General continuous-time Markov chains. Q-matrices. Matrix exponentials | 6.6 | 4.1 | Lecture 7 | Lecture 7 | Lecture 7 |
| 4/13 | 3 | First step analysis for general Markov chains | 6.5, 6.6 | 4.4 | Lecture 8 | Lecture 8 | Lecture 8 |
| 4/15 | 3 | Kolmogorov forward and backward equations | 6.3, 6.6 | 4.2 | Lecture 9 | Lecture 9 | Lecture 9 |
| 4/18 | 4 | Stationary distributions and long-run behavior | 6.4, 6.6 | 4.3 | Lecture 10 | Lecture 10 | Lecture 10 |
| 4/20 | 4 | MC review. Conditioning on a continuous random variable | 2.4 | - | Lecture 11 | Lecture 11 | Lecture 11 |
| 4/22 | 4 | Midterm 1 | |||||
| 4/25 | 5 | Conditioning on continuous random varialbes | 2.4 | - | Lecture 12 | Lecture 12 | - |
| 4/27 | 5 | Introduction to renewal processes | 7.1 | 3.1 | Lecture 13 | Lecture 13 | Lecture 13 |
| 4/29 | 5 | Poisson process as a renewal processes | 7.3 | 3.1 | Lecture 14 | Lecture 14 | Lecture 14 |
| 5/2 | 6 | Examples of renewal processes | 7.2 - 7.3 | 3.1 | Lecture 15 | Lecture 15 | Lecture 15 |
| 5/4 | 6 | Asymptotic results for renewal processes | 7.4 | 3.1, 3.3 | Lecture 16 | Lecture 16 | Lecture 16 |
| 5/6 | 6 | Asymptotic results for renewal processes | 7.4 | 3.1, 3.3 | Lecture 17 | Lecture 17 | Lecture 17 |
| 5/9 | 7 | Asymptotic results for renewal processes | 7.5 | 3.1, 3.3 | Lecture 18 | Lecture 18 | Lecture 18 |
| 5/11 | 7 | Generalizations of renewal processes | 7.5 | 3.1, 3.3 | Lecture 19 | Lecture 19 | Lecture 19 |
| 5/13 | 7 | Generalizations of renewal processes | 7.5 | 3.1, 3.3 | Lecture 20 | Lecture 20 | Lecture 20 |
| 5/16 | 8 | Martingales | 2.5 | 5.1 - 5.2 | Lecture 21 | Lecture 21 | Lecture 21 |
| 5/18 | 8 | Midterm 2 | |||||
| 5/20 | 8 | Martingales | 2.5 | 5.1 - 5.2 | Lecture 22 | Lecture 22 | Lecture 22 |
| 5/23 | 9 | Definition of Brownian motion | 8.1 | - | Lecture 23 | Lecture 23 | Lecture 23 |
| 5/25 | 9 | Basic properties of Brownian motion | 8.1 | - | Lecture 24 | Lecture 24 | Lecture 24 |
| 5/27 | 9 | The reflection principle | 8.2 | - | Lecture 25 | Lecture 25 | Lecture 25 |
| 5/30 | 10 | Memorial Day | - | - | - | - | - |
| 6/1 | 10 | Processes derived from Brownian motion | 8.3-8.4 | - | Lecture 26 | Lecture 26 | Lecture 26 |
| 6/3 | 10 | Processes derived from Brownian motion | 8.3-8.4 | - | Lecture 27 | Lecture 27 | Lecture 27 |
Prerequisite: MATH 180B or concent of instructor.
Lectures: You are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams that will test your understanding of concepts discussed in the lectures.
Homework: Homework assignments are posted below, and will be due at 11:59pm on the indicated due date. You must turn in your homework through Gradescope; if you have produced it on paper, you can scan it or simply take clear photos of it to upload. Your lowest homework score will be dropped. It is allowed and even encouraged to discuss homework problems with your classmates and your instructor and TA, but your final write up of your homework solutions must be your own work.
Midterm Exams: The two midterm exams will take place during the lecture time on the dates listed above.
Final Exam: The final examination will be held at the date and time stated above.
The above exam policies will be applied to in-person exams. The exam policies will be changed in case of the changes in exam modality. More detailed instructions will be posted on this website later.
Administrative Links: Here are two links regarding UC San Diego policies on exams:
Regrade Policy:
Grading: Your cumulative average will be computed as the best of the following weighted averages:
Your course grade will be determined by your cumulative average at the end of the quarter, and will be based on the following scale:
| A+ | A | A- | B+ | B | B- | C+ | C | C- |
| 97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 |
The above scale is guaranteed: for example, if your cumulative average is 80, your final grade will be at least B-. However, your instructor may adjust the above scale to be more generous.
Academic Integrity: UC San Diego code of academic integrity outlines the expected academic honesty of all studentd and faculty, and details the consequences for academic dishonesty. The main issues are cheating and plagiarism, of course, for which we have a zero-tolerance policy. (Penalties for these offenses always include assignment of a failing grade in the course, and usually involve an administrative penalty, such as suspension or expulsion, as well.) However, academic integrity also includes things like giving credit where credit is due (listing your collaborators on homework assignments, noting books or papers containing information you used in solutions, etc.), and treating your peers respectfully in class. In addition, here are a few of our expectations for etiquette in and out of class.
Weekly homework assignments are posted here. Homework is due by 11:59pm on the posted date, through Gradescope. Late homework will not be accepted.