Probability

Welcome to Probability! If we want to use math to model the world, we must develop a framework for dealing with unpredictable events. In this course, we will introduce this framework, covering random variables, multivariate distributions, expectations, and conditioning. We will cover two theorems that underpin the connection between probability and statistics: the law of large numbers and the central limit theorem. Beyond learning the basics of these tools and how to work with them, we will incorporate a number of examples and applications, and we will conclude the class with Markov chains, which have widespread use. 

Detailed course information can be found at the Syllabus page, and any information and materials you need for class can be found at the Daily Schedule page. Additional materials can be found at the Additional Materials page. 

Course Summary

This course is an introduction to the study of probability. We will keep the occasional abstractness grounded in plenty of examples. We will require some definitions and mathematical objects, but probability (while containing paradoxes) can also be guided by our intuition, and by common examples. With the fundamentals in hand, we will turn to some applications of probability in the modern world.

I have three major goal areas for you in this course, which are:

• Content: know the definitions and properties of probability fundamentals: random variables, multivariate distributions, expectations, independence, conditioning, and conditional distributions and expectations
• Proofs: know common methods of proof (induction, construction, contradiction, contrapositive), and be able to write clear, concise proofs
• Engagement: find an area where probability intersects your life, and think about how the two fit together

Goals should be measurable, so I will do my best to measure all three of these goals. We will have weekly homework, exams, and a final project. We will also have other graded pieces of work, including surveys, exam wrappers, and feedback.

Learning is an active process, which requires your participation. With this in mind, I will do my best to present all the content to you, but a large chunk of learning will happen not when I lecture, but when you ask questions. I want you to be successful in this course, and will do everything I can to help you work through your growing understanding of probability.

The above includes structural help also. If you have conflicts or needs that I can help you work through, let me know. These include applying disability-related academic adjustments and services to the context of the course; the earlier you let me know about any such needs, the better, but whenever is most comfortable for you is good for me. Conflicts, in the form of religious observances, athletics, or life external to this class will be met with all possible accommodations.

The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. This is even more true in this time of remote learning, and uncertainty in the world. There are a number of resources available to you to support your wellness, including your undergraduate dean, Counseling and Human Development, and the Student Wellness Center.

Zoom Room

When needed, the Zoom room for this class can be found here. Links to an external site.
The meeting ID is 966 4270 0597 and the password is 863652.