Math 180A, Lecture A00

Introduction to Probability

Winter 2023: MWF 12:00 - 12:50 PM, MANDE B-210

Announcements

Course Information

Instructional Staff and Office Hours

Name Role Office E-mail Office hours
Yuriy Nemish  Instructor  AP&M 6321 ynemish@ucsd.edu  Wednesday 3 - 5 PM (AP&M 6321)
Sheng Qiao  Teaching Assistant  HSS 5056 sqiao@ucsd.edu
  • Thursday 3 - 5 PM (HSS 5056)
  • Thursday 5 - 6 PM (Zoom)
Toni Gui  Teaching Assistant  HSS 4086A ttgui@ucsd.edu
  • Friday, 3 - 4 PM (HSS 4086A)

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.

Calendar



Class Meetings

 Date Time Room
Lecture (YN)  Monday, Wednesday, Friday 12 - 12:50 PM MANDE B-210
Discussion A01 (TG)  Friday 4 - 4:50 PM HSS 4025
Discussion A02 (SQ)  Friday 5 - 5:50 PM HSS 4025
Discussion A03 (SQ)  Friday 6 - 6:50 PM HSS 4025

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Important dates

Week Date Time Room Policy
Midterm Exam 1 4 Wednesday, February 1 12 - 12:50 PM MANDE B-210Midterm Exams
Midterm Exam 2 8 Wednesday, March 1 12 - 12:50 PM MANDE B-210Midterm Exams
Final Exam Finals Wednesday, March 22 11:30 AM - 2:30 PM TBAFinal 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 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
1/91 Administrivia. Definition of Probability 1.1 Slides 1 Slides 1
1/111 Random sampling 1.2 Slides 2 Slides 2
1/131 Basic Properties of Probability 1.3-1.4 Slides 3 Slides 3
1/162 Martin Luther King, Jr. Holiday
1/182 Basic Properties of Probability 1.4 Slides 4 Slides 4
1/202 Conditional probability 2.1 Slides 5 Slides 5
1/233 Bayes' rule 2.2 Slides 6 Slides 6
1/253 Independence 2.3 Slides 7 Slides 7
1/273 Random variables. Probability Distributions 3.1 Slides 8
1/304 CDF and PDF 3.2, 2.4
2/14 Midterm 1
2/34 Independent Trials. Binomial, Geometric, and Poisson Distributions 2.4-2.5, 4.4
2/65 Poisson distribution. Expected Value 3.3
2/85 Expectation 3.3-3.4
2/105 Variance. Normal (Gaussian) Distribution 3.4-3.5
2/136 Normal (Gaussian) Distribution 3.5
2/156 Normal Approximation. Law of Large Numbers 4.1
2/176 Confidence intervals 4.3
2/207 Presidents' Day Holiday
2/227 Confidence intervals. Poisson approximation 4.4
2/247 Exponential Distribution 4.5
2/278 Moment generating function 5.1
3/18 Midterm 2 5.1
3/38 Joint distribution. Independence 6.1-6.3
3/69 Joint distribution. Independence 6.1-6.3
3/89 Expectations of sums and products 8.1-8.3
3/109 Covariance, correlation, and variance of sums 8.4
3/1310 Correlation. Tail probabilities 9.1
3/1510 Law of Large Numbers. Central Limit Theorem 9.2-9.3
3/1710 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.

Exams

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.

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