Math 180A

Fall 2019, Lecture B00 (Kemp) MWF 1:00-1:50pm

Introduction to Probability for Data Science


Course Information

Instructional Staff

Todd Kemp Instructor APM 5202
Denise Rava Teaching Assistant APM 2220
Jiangchuanhai Wang Teaching Assistant APM 1220
Lin Zheng Teaching Assistant APM 2000A

Our office hours can be found in the following calendar.


Class Meetings

Lecture B00 (Kemp) Monday, Wednesday, Friday1:00pm - 1:50pmCENTR 115
Discussion B01 (Rava) Tuesday5:00pm - 5:50pmERC 117
Discussion B02 (Rava) Tuesday6:00pm - 6:50pmERC 117
Discussion B03 (Wang) Tuesday7:00pm - 7:50pmERC 117
Discussion B04 (Wang) Tuesday8:00pm - 8:50pmERC 117
Discussion B05 (Zheng) Tuesday8:00pm - 8:50pmCSB 115
Discussion B06 (Zheng) Tuesday9:00pm - 9:50pmCSB 115
First Midterm Exam Wednesday, Oct 238:00pm - 9:50pmPCYNH 109
Second Midterm Exam Wednesday, Nov 208:00pm - 9:50pmCENTR 101
Final Exam Monday, Dec 911:30am - 2:29pmREC GYM


Lectures Slides

All lectures of this course are podcast, both as a screencast and classroom video; they podcasts are available beginning right after the lecture at

The lectures are typically given via tablet, on notes/slides with some information prepared before lecture, and some filled-in during the lecture. Below, you will find the before and after slides for each lecture (as they are produced).

1 180A-Lec1-Before.pdf 180A-Lec1-After.pdf
2 180A-Lec2-Before.pdf 180A-Lec2-After.pdf
3 180A-Lec3-Before.pdf 180A-Lec3-After.pdf
4 180A-Lec4-Before.pdf 180A-Lec4-After.pdf
5 180A-Lec5-Before.pdf 180A-Lec5-After.pdf
6 not available 180A-Lec6-After.pdf
7 180A-Lec7-Before.pdf 180A-Lec7-After.pdf
8 180A-Lec8-Before.pdf 180A-Lec8-After.pdf
9 180A-Lec9-Before.pdf 180A-Lec9-After.pdf
10 180A-Lec10-Before.pdf 180A-Lec10-After.pdf
11 180A-Lec11-Before.pdf 180A-Lec11-After.pdf
12 180A-Lec12-Before.pdf 180A-Lec12-After.pdf
13 180A-Lec13-Before.pdf 180A-Lec13-After.pdf
14 180A-Lec14-Before.pdf 180A-Lec14-After.pdf
15 180A-Lec15-Before.pdf 180A-Lec15-After.pdf
16 180A-Lec16-Before.pdf 180A-Lec16-After.pdf
17 180A-Lec17-Before.pdf 180A-Lec17-After.pdf
18 180A-Lec18-Before.pdf 180A-Lec18-After.pdf
19 180A-Lec19-Before.pdf 180A-Lec19-After.pdf
20 180A-Lec20-Before.pdf 180A-Lec20-After.pdf
21 180A-Lec21-Before.pdf 180A-Lec21-After.pdf
22 180A-Lec22-Before.pdf 180A-Lec22-After.pdf
23 not available 180A-Lec23-After.pdf
24 180A-Lec24-Before.pdf 180A-Lec24-After.pdf
25 180A-Lec25-Before.pdf 180A-Lec25-After.pdf
26 180A-Lec26-Before.pdf 180A-Lec26-After.pdf
27 180A-Lec27-Before.pdf 180A-Lec27-After.pdf
28 180A-Lec28-Before.pdf 180A-Lec28-After.pdf
29 180A-Lec29-Before.pdf 180A-Lec29-After.pdf


Math 180A is 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) and Math 189 (Exploratory Data Analysis and Inference). It is also prerequisite for the new Data Science topics course DSC 155 (Hidden Data in Random Matrices) in Winter 2020. 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.

This lecture (B00) is a new version of Math 180A, which is targeted towards data science theory and applications. The course material is the same as the other lecture of Math 180A; the primary addition is the Python-based lab component of this course, which can be accessed through Jupyter Hub. We will also refer to the online textbook Probability for Data Science by Adhikari and Pitman as a secondary resource for the lecture.

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.

09/270 Administrivia and Motivation
09/301 Definition of Probability, Sampling, Combinatorics 1.1-1.2 1.1-1.2, 2.0
10/021 Uniform Probability, Basic Properties of Probability 1.3-1.4 2.0-2.2, 5.2
10/041 Conditional Probability, Bayes' Rule 2.1-2.2 2.3-2.5
10/072 Independence 2.3 4.5
10/092 Random Variables 1.5, 3.1 3.0-3.1
10/112 Probability Distributions 3.1-3.2 3.2, 15.1
10/143 Independent Trials and Sampling 2.4-2.5
10/163 Binomial, Geometric, and Poisson Distributions 3.1-3.2, 4.4 6.0-6.2, 6.5
10/183 Expected Value 3.3 8.1, 8.3, 15.3
10/214 Variance 3.4 12.1
10/234 Review (+ Evening Midterm)
10/254 Normal (Gaussian) Distribution 3.5 18.1
10/285 Normal Approximation 4.1-4.2
10/305 Confidence Intervals 4.3
11/15 Poisson Approximation 4.4 6.5, 7.0
11/46 Exponential Distribution 4.5 15.4
11/66 Poisson Process 4.6
11/86 Moment Generating Function 5.1 16.1-16.3
11/117 Veterans Day
11/137 Functions of Random Variables 5.2 19.2
11/157 Joint Distributions 6.1-6.2 4.1, 4.3, 17.1, 17.3
11/188 Independence of Random Variables 6.3 4.5, 17.2
11/208 Review (+ Evening Midterm)
11/228 Expectations of sums 8.1-8.3 8.2, 19.2
11/259 Covariance, correlation, and variance of sums 8.4 13.0-13.3
11/279 Law of Large Numbers 9.1-9.2 12.3, 14.4
11/299 Thanksgiving
12/210 Central Limit Theorem 9.3 14.3, 19.3
12/410 Review
12/610 Review

Prerequisite:  The only prerequisites are calculus up to and including Math 20C (Multivariate Calculus). Math 109 (Mathematical Reasoning) is also strongly recommended as a prerequisite or corequisite. For the lab component of the course, some familiarity with any coding language (ideally Python) is helpful, but not required.

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. 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.

Labs:  The data science labs are accessible through DataHub. The turn-in components should be exported as pdf files and turned in through Gradescope; they are due at 11:59pm on the dates indicated on the labs.

Lowest two scores:   There will be 15 assignments throughout the term: 8 homework sets and 7 labs. Among these, only the 13 highest scores will be counted towards your grade; the two lowest scoring assignments be dropped.

Midterm Exams:  The two midterm exams will take place in the evenings of the dates listed above. The scheduled time for each midterm exam is 2 hours; however, the exam itself is designed for you to complete in 50 minutes. The 2 hours time-limit will also be lax. We do not want time pressure to be a factor in your exam performance.

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 two 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 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.


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. 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 11:59pm on the posted date, through Gradescope. Late homework will not be accepted.