Instructor: Robert Dougherty-Bliss
Email: rdbliss@dartmouth.edu
Time: 10:10–12:00, TTh
X-hour: 3:30–4:20, F
Office hours: TBA
Textbook: Introduction to
Probability, by Joseph Blitzstein and Jessica Hwang
Probability is the study of random events and the likelihood that they occur. A fair coin comes up heads half the time, but how likely are you to see exactly 50 heads in 100 tosses? Why is a full house worth more than a flush in poker? What exactly is a ‘bell curve’, and why do we care so much about it? We will discuss these questions and more.
Selected topics: Probability axioms, counting, random variables, discrete and continuous distributions, expectation, moments, joint distributions, independence, generating functions, limit theorems.
Below is a tentative schedule for the course. It may change as we go along.
Sections are from Blitzstein and Hwang.
| Week (first class day) | Tuesday | Thursday | Readings |
|---|---|---|---|
| 1 (March 31) | introductions, naive probability problems |
counting | 1.1-1.5 |
| 2 (April 7) | probability axioms | No class! (I have to go to Canada) |
1.6 |
| 3 (April 14) | Bayes’ theorem, independence | conditioning, paradoxes | 2.1–2.7 |
| 4 (April 21) | Midterm 1 random variables |
discrete random variables | Chs. 3–4 |
| 5 (April 28) | discrete random variables | continuous random variables | Chs. 4–5 |
| 6 (May 5) | continuous random variables | continuous random variables | Ch. 5 |
| 7 (May 12) | Midterm 2 moments |
moment generating functions | Ch. 6 |
| 8 (May 19) | joint distributions | No class! (I have to go get married) |
Ch. 7 |
| 9 (May 26) | joint distributions | inequalities | Chs. 7, 9 |
| 10 (June 2) | limit theorems | Ch. 10 |
Class meets in person twice a week for approximately two hours each. These meetings will be a mix of lecture and problem solving. If necessary, we may use our X-hour to makeup any missed lectures.
Problems will be posted each week for homework. The goal is to have three to five problems per hour of class, which means around 15 problems a week. This is a substantial amount. You should consider not waiting until the last minute!
Problems are submitted on Gradescope. Unlike the in-class assessments, they will be mostly graded for completion, meaning that you get full credit if the grader thinks you put in serious effort on at least half the problems.
It is vital that you do the homework. That means that you, personally, work through the problems and computations. Mathematics demands that you manipulate ideas in your head; that you turn them over, flip them upside down, connect them with other ideas, and so on. This is immensely difficult on the best of days, and almost impossible without practice. You have the capability to do it, but you must work hard!
After the first week, every Tuesday will start with a 10 minute quiz (unless there is something else planned). These quizzes will consist of questions almost-randomly chosen from the previous week’s homework. These are intended to keep everyone on track with the homework.
There are no quiz makeups, but we will drop the lowest two quiz grades. There are seven quizzes in total, so only five are graded.
There will be two midterm exams on the dates indicated in the calendar. These test that you can recall the material we have learned up to those points.
There will be a final exam. The date and time will be announced later. It, like the midterms, tests that you can recall most of the material that we learned.
Office hours are a time outside of class for you to ask me questions. We can talk about the course, other math, or whatever might be helpful for you to succeed. We will schedule them at the start of the term. You are always welcome to ask to meet outside of office hours as well!
Our graduate teaching assistant, Rohan Kapoor, will run tutorials. These are like office hours, but with Rohan instead of Robert. We will announce the days and times near the beginning of the term.
If you need any accommodations for the course, please get in touch with me and Student Accessibility Services as soon as you can! In particular, we will need to figure out accommodations for our quiz structure.
You should be advised of Dartmouth’s Academic Honor Principle. For this course, the important rules are:
No outside help on exams or quizzes. You should only have something to write with, the paper, and your brain.
Only turn in homework which reflects your own understanding of the material. Feel free to work with other people, consult the internet, books, and so on, but whatever you turn in must be your own independent work.
Outside of quizzes and exams, you can use AI tools or the internet or whatever else you want during the course. The rule that homework should reflect your own understanding and not be copied always applies.
A word of advice: Probably every popular AI system could instantly solve every problem you will see in the course. This is dangerous! Almost all of your grade is determined by in-class assessments; even if you intend well, you might fool yourself into thinking you know up from down, only to confuse left and right on exams and quizzes.