Math 180B

Winter 2020, Lecture A00 (MWF 1:00-1:50pm)

Introduction to Stochastic Processes

Announcements

Course Information

Instructional Staff and Office Hours

NameRoleOfficeE-mailOffice hours
Yuriy Nemish Instructor AP&M 6422 ynemish@ucsd.edu
  • Monday 3:30 pm-4:30 pm (AP&M 6303)
  • Wednesday 3 pm-5 pm (AP&M 6303)
Jiaqi Liu Teaching Assistant AP&M 5768 jil1131@ucsd.edu
  • Tuesday 9:30 am-11 am (AP&M 5768)
  • Thursday 9:30 am-11 am (AP&M 5768)
Sheng Qiao Teaching Assistant AP&M 6446 sqiao@ucsd.edu
  • Friday 2 pm-3 pm (AP&M 6446)

Please, check the following calendar for possible reschedulings of the office hours.

Calendar



Class Meetings

DateTimeLocation
Lecture A00 (Nemish) Monday, Wednesday, Friday1:00pm - 1:50pmCSB 001
Discussion A01 (Liu) Thursday7:00pm - 7:50pmAP&M 2402
Discussion A02 (Liu) Thursday8:00pm - 8:50pmAP&M 2402
Discussion A03 (Qiao) Thursday6:00pm - 6:50pmAP&M 6402
First Midterm Exam Wednesday, Jan 291:00pm - 1:50pmCSB 001
Second Midterm Exam Wednesday, Feb 261:00pm - 1:50pmCSB 001
Final Exam Friday, Mar 2011:30am - 2:29pm???

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Syllabus


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.

DateWeekTopicPKPreliminary slidesFinal slides
01/061Introduction. Review of probability theory--Lecture 1
01/081Convolutions. Gamma distribution. Joint normal distribution1.2.5, 1.4.4, 1.4.6Lecture 2Lecture 2
01/101Gaussian random vectors1.4.6Lecture 3Lecture 3
01/132Gaussian random vectors. Probability review1.4.6, 1.5Lecture 4Lecture 4
01/152Conditional probabilities and conditional expectations (discrete case)2.1-2.3Lecture 5Lecture 5
01/172Conditional distributions. Random sums2.3Lecture 6Lecture 6
01/203Martin Luther King, Jr. Holiday--
01/223Random sums. Markov chains2.3, 3.1Lecture 7Lecture 7
01/243n-step transition probabilities. Ehrenfest model3.2-3.3Lecture 8Lecture 8
01/274Review--
01/294Midterm 1--
01/314First step analysis3.4Lecture 9Lecture 9
02/035General absorbing Markov chain. Special Markov chains3.4-3.5Lecture 10Lecture 10
02/055Functionals of random walks and success runs3.5Lecture 11Lecture 11
02/075Gambler's ruin. Branching processes3.6,3.8Lecture 12Lecture 12
02/106Branching processes3.8Lecture 13Lecture 13
02/126Regular transition probability matrices4.1Lecture 14Lecture 14
02/146Limiting distribution. Examples4.1-4.2Lecture 15Lecture 15
02/177Presidents' Day Holiday--
02/197Classification of states4.3Lecture 16Lecture 16
02/217Basic limit theorems of Markov chains4.4Lecture 17Lecture 17
02/248Review--
02/268Midterm 2--
02/288Poisson distribution. Poisson processes5.1Lecture 18Lecture 18
03/029Law of rare event and Poisson processes5.2Lecture 19Lecture 19
03/049Distributions associated with Poisson processes5.3Lecture 20Lecture 20
03/069Distributions associated with Poisson processes5.3Lecture 21Lecture 21
03/0910Uniform distributions and Poisson processes5.4Lecture 22Lecture 22
03/1110Uniform distributions and Poisson processes5.4Lecture 23Lecture 23
03/1310Review-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:

In addition,  you must pass the final examination in order to pass the course.  Note also: there are no makeup exams, if you miss a midterm exam for any reason then your course grade will be computed with the second or third option. There are no exceptions; this grading scheme is intended to accommodate emergencies that require missing a midterm exam.

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.

Accommodations:

Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD) which is located in University Center 202 behind Center Hall. The AFA letter may be issued by the OSD electronically or in hard-copy; in either case, please make arrangements to discuss your accommodations with me in advance (by the end of Week 2, if possible). We will make every effort to arrange for whatever accommodations are stipulated by the OSD. For more information, see here.

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Homework


Weekly homework assignments are posted here. Homework is due by 11:59pm on the posted date, through Gradescope. Late homework will not be accepted.