Math 180A, Lecture C00

Introduction to Probability

Fall 2022: MWF 4:00-4:50 PM, CENTR 105


Course Information

Instructional Staff and Office Hours

Name Role Office E-mail Office hours
Yuriy Nemish  Instructor  AP&M 6321  Wednesday 5-7 PM (AP&M 1260)
Sheng Qiao  Teaching Assistant  HSS 5056
  • Wednesday 10:30 - 12 PM
  • Thursday 10:30 - 12 PM
  • Friday 6 - 7 PM (remotely via zoom)
Kejin Wu  Teaching Assistant  HSS 5053  Thursday 3 - 5 PM
Toni Gui  Teaching Assistant  HSS 4086A
  • Thursday 1 - 2 PM
  • Thursday 2 - 3 PM (remotely via zoom)

Please, check the following calendar for possible reschedulings of the office hours. You are welcome to attend the office hours of either of the TAs, not just your own.


Class Meetings

 Date Time Room
Lecture (YN)  Monday, Wednesday, Friday 4 - 4:50 PM CENTR 105
Discussion C01 (SQ)  Tuesday 5 - 5:50 PM AP&M 2301
Discussion C02 (SQ)  Tuesday 6 - 6:50 PM AP&M 6402
Discussion C03 (KW)  Tuesday 7 - 7:50 PM AP&M 6402
Discussion C04 (TG)  Tuesday 8 - 8:50 PM AP&M 2301


Important dates

Week Date Time Room Policy
Midterm Exam 1 4 Wednesday, Oct 19 4 - 4:50 PM CENTR 105Midterm Exams
Midterm Exam 2 8 Wednesday, Nov 16 4 - 4:50 PM CENTR 105Midterm Exams
Final Exam Finals Tuesday, Dec 6 3 - 6 PM TBAFinal Exam



Welcome to Math 180A: a one quarter course introduction to probability theory. This course is the prerequisite for the subsequent courses Math 180B/C (Introduction to Stochastic Processes) and Math 181A/B (Introduction to Mathematical Statistics), as well as for MATH 114 (Introduction to Computational Stochastics), MATH 194 (The Mathematics of Finance) and Math 189 (Exploratory Data Analysis and Inference). According to the UC San Diego Course Catalog, the topics covered are probability spaces, random variables, independence, conditional probability, discrete and continuous probability distributions, joint distributions, variance and moments, the Laws of Large Numbers, and the Central Limit Theorem.

Here is a more detailed listing of course topics, in the sequence they will be covered, together with the relevant section(s) of the textboox. 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.

DateWeekTopicASV Preliminary slides Final slides
9/230 Administrivia. Definition of Probability 1.1 Slides 1 Slides 1
9/261 Random sampling 1.2 Slides 2 Slides 2
9/281 Basic Properties of Probability 1.3-1.4 Slides 3 Slides 3
9/301 Conditional Probability 2.1 Slides 4 Slides 4
10/32 Conditional probability 2.1 Slides 5 Slides 5
10/52 Bayes' rule 2.2 Slides 6 Slides 6
10/72 Independence 2.3 Slides 7 Slides 7
10/103 Random variables 3.1 Slides 8 Slides 8
10/123 Probability Distributions. CDF and PDF 3.1 Slides 9 Slides 9
10/143 CDF and PDF 3.2, 2.4 Slides 10 Slides 10
10/174 CDF and PDF. Review Slides 11 Slides 11
10/194 Midterm 1
10/214 Independent Trials. Binomial, Geometric, and Poisson Distributions 2.4-2.5, 4.4 Slides 12 Slides 12
10/245 Poisson distribution. Expected Value 3.3 Slides 13 Slides 13
10/265 Expectation 3.3-3.4 Slides 14 Slides 14
10/285 Variance. Normal (Gaussian) Distribution 3.4-3.5 Slides 15 Slides 15
10/316 Normal (Gaussian) Distribution 3.5 Slides 16 Slides 16
11/26 Normal Approximation. Law of Large Numbers 4.1 Slides 17 Slides 17
11/46 Confidence intervals 4.3 Slides 18 Slides 18
11/77 Confidence intervals. Poisson approximation 4.4 Slides 19 Slides 19Prerecorded video
11/97 Exponential Distribution 4.5 Slides 20 Slides 20
11/117 Veterans Day
11/148 Moment generating function 5.1 Slides 21 Slides 21
11/168 Moment generating function 5.1 Slides 22 Slides 22
11/188 Joint distribution. Independence 6.1-6.3 Slides 23 Slides 23
11/219 Joint distribution. Independence 6.1-6.3 Slides 24 Slides 24
11/239 Expectations of sums and products 8.1-8.3 Slides 25 Slides 25
11/259 Thanksgiving
11/2810 Covariance, correlation, and variance of sums 8.4 Slides 26 Slides 26
11/3010 Correlation. Tail probabilities 9.1 Slides 27 Slides 27
12/210 Law of Large Numbers. Central Limit Theorem 9.2-9.3 Slides 28 Slides 28

Prerequisite:  The only prerequisites are calculus up to and including Math 20C (Multivariate Calculus) or MATH 31BH (Honors Multivariable Calculus). Math 109 (Mathematical Reasoning) is also strongly recommended as a prerequisite or corequisite.

Lecture:  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 11:59 PM 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 change 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'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.


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.



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