Math 425 Fall 2020 Section 010
Introduction to Probability

Instructor: Thomas Lam tfylam@umich.edu

Course structure: This class will be held completely online. Be aware that much of the class plan is experimental, and may change.

• Recordings of lectures, to be viewed outside of class time, will be made available on the Canvas site.
• Class meeting time: Tuesday and Thursday 8:30am-10:00am EST
• Class meetings are held online via Zoom, or possibly other platforms. They may serve as recitations, problem sessions, group discussions, and online office hours.
• All students are expected to attend all class meetings. Repeated absences without explanation may affect the final grade.

Text (required): Sheldon Ross, A First Course in Probability, 10th edition, Pearson, 2019.

Prerequisites: Math 215 or 285 (multi-variable calculus).

Course synopsis: This course is an introduction to the theory of probability and to a number of applications. We will discuss both discrete and continuous probability. Some concepts that will be introduced include: conditional probability, independent events, random variables, expectation, variance, correlation.

Acadmic Integrity: Students are expected to have read and understood the LSA Community Standards of Academic Integrity. By taking this course, students are agreeing to abide by the wording and spirit of these standards.

Grading:

• Grades will be based on web homework (15%), written homework (25%), and three exams (60%).
• This course will not be graded on a curve. There will not be a set number of each letter grade to be given out. A student with a total score of 90% (or 80%, or 70%) is guaranteed a minimum final letter grade of A of some kind (or B of some kind, or C of some kind).

Exams: There will be three 80 minute exams held on Zoom during class times. More information on exam procedures will be made available closer to the exam date. The dates of the exams are
Exam 1: Tuesday September 29
Exam 2: Thursday October 29
Exam 3: Thursday December 3
If you are unable to attend the exams via Zoom for any reason, please contact me immediately.

Webwork: Web homework will be located here.

Written homework:

• There will be approximately 8 written problem sets.
• Problem sets will consist mainly of problems chosen from the textbook.
• Problem sets are to be uploaded to Gradescope.
• The lowest homework score will be dropped.
• Late homework will not be accepted.
• Collaboration on written homework is allowed and encouraged. All collaborators must be acknowledged by name. Each student is responsible for writing up his/her own solutions.
• You are not allowed to post homework problems seeking solutions on websites such as mathoverflow or mathstackexchange.
• If you find the solution to a homework problem in a book, or online, etc., you must acknowledge the source.

Disabilities: If you think you need an accomodation for a disability, please let me know as soon as possible. In particular, a Verified Individualized Services and Accomodations (VISA) form must be provided to me at least two weeks prior to the need for a test/quiz accomodation. The Services for Students with Disabilities (SSD) Office (G664 Haven Hall, webpage here) issues VISA forms.

Weekly Syllabus (subject to change):

• Week 1 (09/01, 09/03): Counting and probability (Chapter 1)
• Week 2 (09/08, 09/10): Axioms of probability (Chapter 2)
• Week 3 (09/15, 09/17): Conditional probability, etc. (Chapter 3)
• Week 4 (09/22, 09/24): Independent events, etc. (Chapter 3)
• Week 5 (09/29, 10/01): Exam 1, (start Chapter 4)
• Week 6 (10/06, 10/08): Random variables (Chapter 4)
• Week 7 (10/13, 10/15): Expectation and variance (Chapter 4)
• Week 8 (10/20, 10/22): Continuous distributions (Chapter 5)
• Week 9 (10/27, 10/29): Gaussian distribution, Exam 2
• Week 10 (11/03, 11/05): No meeting on 11/3, (start Chapter 6)
• Week 11 (11/10, 11/12): Joint distributions (Chapter 6)
• Week 12 (11/17, 11/19): Expectation, correlation (Chapter 7)
• Week 13 (11/24, 11/26): Thanksgiving break
• Week 14 (12/01, 12/03): Central limit theorem (Chapter 8), Exam 3
• Week 15 (12/08): Last class meeting