A+ | A | A- | B+ | B | B- | C+ | C | C- |
95 | 79 | 74 | 68 | 60 | 58 | 53 | 46 | 41 |
Name | Role | Office | Office hours | |
Yuriy Nemish | Instructor | AP&M 6422 | ynemish@ucsd.edu |
|
Jiaqi Liu | Teaching Assistant | AP&M 5768 | jil1131@ucsd.edu |
|
Sheng Qiao | Teaching Assistant | AP&M 6446 | sqiao@ucsd.edu |
|
Date | Time | Location | |
Lecture A00 (Nemish) | Monday, Wednesday, Friday | 1:00pm - 1:50pm | CSB 001 |
Discussion A01 (Liu) | Thursday | 7:00pm - 7:50pm | AP&M 2402 |
Discussion A02 (Liu) | Thursday | 8:00pm - 8:50pm | AP&M 2402 |
Discussion A03 (Qiao) | Thursday | 6:00pm - 6:50pm | AP&M 6402 |
First Midterm Exam | Wednesday, Jan 29 | 1:00pm - 1:50pm | CSB 001 |
Second Midterm Exam | Wednesday, Feb 26 | 1:00pm - 1:50pm | CSB 001 |
Final Exam | Friday, Mar 20 | 11:30am - 2:29pm | ??? |
Welcome to Math 180B: a one quarter course introduction to stochastic processes (I). This course is the prerequisite for the subsequent course Math 180C (Introduction to Stochastic Processes (II)) and is recommended for MATH 112B (Introduction to Mathematical Biology (II)). According to the UC San Diego Course Catalog, the topics covered are random vectors, multivariate densities, covariance matrix, multivariate normal distribution, random walk, Poisson process 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.
Date | Week | Topic | PK | Preliminary slides | Final slides |
---|---|---|---|---|---|
01/06 | 1 | Introduction. Review of probability theory | - | - | Lecture 1 |
01/08 | 1 | Convolutions. Gamma distribution. Joint normal distribution | 1.2.5, 1.4.4, 1.4.6 | Lecture 2 | Lecture 2 |
01/10 | 1 | Gaussian random vectors | 1.4.6 | Lecture 3 | Lecture 3 |
01/13 | 2 | Gaussian random vectors. Probability review | 1.4.6, 1.5 | Lecture 4 | Lecture 4 |
01/15 | 2 | Conditional probabilities and conditional expectations (discrete case) | 2.1-2.3 | Lecture 5 | Lecture 5 |
01/17 | 2 | Conditional distributions. Random sums | 2.3 | Lecture 6 | Lecture 6 |
01/20 | 3 | Martin Luther King, Jr. Holiday | - | - | |
01/22 | 3 | Random sums. Markov chains | 2.3, 3.1 | Lecture 7 | Lecture 7 |
01/24 | 3 | n-step transition probabilities. Ehrenfest model | 3.2-3.3 | Lecture 8 | Lecture 8 |
01/27 | 4 | Review | - | - | |
01/29 | 4 | Midterm 1 | - | - | |
01/31 | 4 | First step analysis | 3.4 | Lecture 9 | Lecture 9 |
02/03 | 5 | General absorbing Markov chain. Special Markov chains | 3.4-3.5 | Lecture 10 | Lecture 10 |
02/05 | 5 | Functionals of random walks and success runs | 3.5 | Lecture 11 | Lecture 11 |
02/07 | 5 | Gambler's ruin. Branching processes | 3.6,3.8 | Lecture 12 | Lecture 12 |
02/10 | 6 | Branching processes | 3.8 | Lecture 13 | Lecture 13 |
02/12 | 6 | Regular transition probability matrices | 4.1 | Lecture 14 | Lecture 14 |
02/14 | 6 | Limiting distribution. Examples | 4.1-4.2 | Lecture 15 | Lecture 15 |
02/17 | 7 | Presidents' Day Holiday | - | - | |
02/19 | 7 | Classification of states | 4.3 | Lecture 16 | Lecture 16 |
02/21 | 7 | Basic limit theorems of Markov chains | 4.4 | Lecture 17 | Lecture 17 |
02/24 | 8 | Review | - | - | |
02/26 | 8 | Midterm 2 | - | - | |
02/28 | 8 | Poisson distribution. Poisson processes | 5.1 | Lecture 18 | Lecture 18 |
03/02 | 9 | Law of rare event and Poisson processes | 5.2 | Lecture 19 | Lecture 19 |
03/04 | 9 | Distributions associated with Poisson processes | 5.3 | Lecture 20 | Lecture 20 |
03/06 | 9 | Distributions associated with Poisson processes | 5.3 | Lecture 21 | Lecture 21 |
03/09 | 10 | Uniform distributions and Poisson processes | 5.4 | Lecture 22 | Lecture 22 |
03/11 | 10 | Uniform distributions and Poisson processes | 5.4 | Lecture 23 | Lecture 23 |
03/13 | 10 | Review | - | Lecture 24 |
Prerequisite: The important prerequisites are calculus up to and including Math 20D, linear algebra (Math 18 or Math 31AH), Math 109 (Mathematical Reasoning) or Math 31CH (Honors vector calculus), and introduction to probability (Math 180A).
Lecture: Attending the lecture is a fundamental part of the course; 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 lecture.
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 at the dates listed above.
Final Exam: The final examination will be held at the date and time stated above.
Administrative Links: Here are two links regarding UC San Diego policies on exams:
Regrade Policy:
Grading: Your cumulative average will be the best of the following three 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's 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.