Math 180A

Fall 2020, Lecture C00 (MWF 5:00-5:50pm)

Introduction to Probability

Announcements

Course Information

Instructional Staff

NameRoleOffice hours (OH)Zoom link for OHE-mail
Benson Au Instructor Th 5:30-7 PM PT
Fri 1-2:30 PM PT
See Canvas bau@ucsd.edu
Sheng Qiao Teaching Assistant Tu 1-2 PM PT
Wed 2-3 PM PT
See Canvas altodd@ucsd.edu
Alec Todd Teaching Assistant Th 1-3 PM PT See Canvas sqiao@ucsd.edu

Note: in the event of an office hours change, the schedule below will reflect the latest information. You are welcome to attend the office hours of either of the TAs, not just your own.

Calendar



Class Meetings

DateTimeLocation
Lecture C00 (Au) Monday, Wednesday, FridayAsynchronous lecturesVideo links below
Discussion C01 (Todd) Thursday9:00am - 9:50amSee Canvas
Discussion C02 (Todd) Thursday10:00am - 10:50amSee Canvas
Discussion C03 (Qiao) Thursday11:00am - 11:50amSee Canvas
Discussion C04 (Qiao) Thursday12:00pm - 12:50pmSee Canvas

Important dates

WeekDateDetails
Quiz 1 2Wednesday, Oct 14see Quizzes
Quiz 2 3Wednesday, Oct 21see Quizzes
Midterm 1 4Wednesday, Oct 28see Midterms Exams
Quiz 3 5Wednesday, Nov 4see Quizzes
Quiz 4 7Wednesday, Nov 18see Quizzes
Midterm 2 8Monday, Nov 23see Midterm Exams
Quiz 5 10Wednesday, Dec 9see Quizzes
Final Exam Finals weekThursday, Dec 17see Final exam

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Syllabus


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 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.

DateWeekTopicASVSlidesLecturesAdditional videos
10/020 Administrivia
10/051 Definition of probability, Random sampling 1.1, 1.2 Lec 1 Lec 1
10/071 Random sampling, Basic properties of probability 1.2, 1.4 Lec 2 Lec 2
10/091 Conditional probability 2.1 Lec 3 Lec 3
10/122 Bayes' rule, independence 2.2, 2.3 Lec 4 Lec 4
10/142 Random variables and probability distributions 1.5, 3.1 Lec 5 Lec 5
10/162 Probability distributions 3.1, 3.2 Lec 6 Lec 6
10/193 Probability densities and the cumulative distribution function 3.2 Lec 7 Lec 7
10/213 Binomial, geometric, and Poisson distributions 2.4, 2.5, 4.4 Lec 8 Lec 8
10/233 Expected value 3.3 Lec 9 Lec 9
10/264 Review
10/284 Midterm 1 Solutions
10/304 Expected value 3.3 Lec 10 Lec 10
11/025 Variance, Normal (Gaussian) distribution 3.4, 3.5 Lec 11 Lec 11
11/045 Gaussian distribution, Normal approximation 3.5, 4.1 Lec 12 Lec 12
11/065 Normal approximation, Law of large numbers 4.1, 4.2 Lec 13 Lec 13
11/096 Confidence intervals, Poisson approximation 4.3, 4.4 Lec 14 Lec 14
11/116 Veterans day
11/136 Exponential distribution 4.5 Lec 15 Lec 15
11/167 Moment generating function 5.1 Lec 16 Lec 16
11/187 Distribution of a function of a random variable 5.2, 6.1 Lec 17 Lec 17
11/207 Review
11/238 Midterm 2 Solutions Q1 and Q2
Q3
Q4
11/258 Joint distributions 6.1, 6.2 Lec 18 Lec 18
11/278 Thanksgiving
11/309 Joint distributions, independence of random variables 6.2, 6.3 Lec 19 Lec 19
12/029 Independence of random variables, convolution 6.3, 7.1 Lec 20 Lec 20
12/049 Linearity of expectation, expectation and independence 8.1, 8.2 Lec 21 Lec 21
12/0710 Sums and moment generating functions, covariance, and corelation 8.3, 8.4 Lec 22 Lec 22
12/0910 Law of large numbers, central limit theorem 9.2, 9.3 Lec 23 Lec 23
12/1110 Review

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.

Quizzes: The quizzes will take place on the dates listed above.

Midterm Exams: The midterm exams will take place on Oct 28 and Nov 23 as listed above.

Final Exam:  The final examination will be held at the officially scheduled time: 7 - 10 PM PST on Dec 17.

Exam policy:

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:

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 students 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) so that accommodations may be arranged. 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.