Probability (SP20)

My Contact Info


Name: Erik Slivken
Office: Kemeny 334
Lectures/Discussion (via Zoom): MWF 11:30am-12:35pm 
Zoom Meeting Room:

Office Hours (via Zoom): MF 2:30-4:00pm
Twitch Office Hours: M,W,Sat 10:00-11:00 pm @


Remote Learning

As with many things these days COVID-19 will disrupt the normal flow of class.  Instead of a classroom we will use Zoom to facilitate lecture and discussion.  Mini-lectures will be made available through TechSmithRelay that expand on topics introduced during the normal Zoom meetings.  The Zoom meetings will be used to go introduce and expand on the main concepts.  Homework will be submitted by PDF on Canvas.  And regular quizzes will be posted through Canvas as well.  It might take some time to familiarize yourself with all the new technology in use, but we should be able to cover all the important content of this course with the alternate style of course.    

The Zoom meetings will be recorded (see below for a more detailed policy) for asynchronous participation.  

There is also a Slack workspace for the class to discuss the homework and other things related to the class.  


Course Description

The world is filled with unpredictable events. Probability helps us build models that reflect this randomness. This course will serve as an introduction to the foundations of probability theory. Topics covered will include some of the following: discrete and continuous random variables, random vectors, multivariate distributions, expectations; independence, conditioning, conditional distributions and expectations; strong law of large numbers and the central limit theorem; random walks and Markov chains.

There is an honors version of this course: see MATH 60.


We will use the following material.  Both are filled with nice exercises with a free PDF version available.  

1. Introduction to Probability, by Grinstead and Snell.

2. Lecture Notes to Introductory Probability, by Janko Gravner.    


Both are useful.  The first book has a number of simulation exercises if you like programming.  The lecture notes follows more closely to how material will be presented for this course.    

Office Hours

Office hours on MF from 2:30-4:00 will be via Zoom.  For people unable to attend at that time, please utilize the Slack workspace to ask questions in the HW discussion channel.  

Computational tools:

For computations SageMath and Wolfram Alpha are useful resources.   

Full Schedule

Day and Date Suggested Readings and Practice Problems  Notes and Announcements
M 3/30 (Recording) G&S 1.2 

What is Probability?

W 4/1 (Recording)

G&S 3.1

Gravner 2


HW 1 assigned

F 4/3 (Recording)

G&S 3.2

Gravner 2

More Combinatorics
M 4/6 (Recording)

G&S Chapter 3

Gravner 3

Axioms of Probability


W 4/8 (Recording)

G&S 4 

Gravner 4


Conditional Probability

HW 1 due

HW 2 assigned

F 4/10 (Recording) More Conditional Probability
M 4/13 (Recording)

G&S 4 and 5 and a little from 1.2

Gravner 5

Independent and Dependent events

Choose Project Topic

W 4/15 (Recording)


Random Variables

HW 2 Due

HW 3 assigned

F 4/17 (Recording)


More RVs

M 4/20 (Recording)

Gravner  5

Expectation and Variance


W 4/22 (Recording)

Gravner 5.3 

Binomial Distribution and other common distributions

HW 3 due

HW 4 assigned

F 4/24 (Recording)

Gravner 5.4

Poisson Random Variables
M 4/27 (Recording) Gravner 5.5

Geometric Distribution

W 4/29 (Recording)

Practice with random variables

HW 4 due

HW 5 assigned

F 5/1 (Recording)

Gravner 6

Continuous Random Variables

M 5/4 (Recording)

Gravner 6 and 7

Continuous RVs Continued

Joint Distributions

Independence and Dependence with Random Variables

W 5/6 (Recording)


Exponential Random Variables

HW 5 due 

HW 6 Assigned

F 5/8 (Recording)


Normal Random Variables


M 5/11 (Recording)

G&S 7

Gravner 8

Sums of Random Variables

W 5/13 (Recording)



First Draft of final project Due


F 5/15 (Recording)

Weak Law of Large Numbers


HW 6 Due

HW 7 Assigned

M 5/18 (Recording)

Central Limit Theorem

W 5/20 (Recording)

Union Bound

F 5/22 (Recording)

Probability Generating Functions

HW 7 due

HW 8 assigned

W 5/27 (Recording)

Erdos-Renyi random graphs.

F 5/29 (Recording)

Galton-Watson trees

HW 8 Due

M 6/1 (Recording)

Special Topics

W 6/3

Last day of class

Final Project Due


A major component of your grade for this course will be participation.  First watch the videos before discussion.  For students that are able to attend the Zoom meetings, this can be established by asking questions, or answering questions in Zoom chat.  For students unable to attend the Zoom meetings, participation can be met by watching Zoom recordings and other relevant videos and posting questions on the weekly class discussion open thread.  


Homework will be assigned each Wednesday and due the following Wednesday. There will be a total of seven homework assignments. 

Homework Collaboration Policy

It can be very helpful to study and work with a group. This type of cooperative learning is encouraged; however, be sure that you have a thorough understanding of the concepts as well as the mathematical steps used to solve a problem. You must be able to work through the problems on your own. Each student must complete her or his assignment individually and independently and must turn in their own work.

On each homework assignment, you must list any resources you used to help you complete the assignment.

This includes other class members with whom you discussed the problems.


Weekly quizzes will be done through canvas.  They will be timed, though can be started at anytime during the appropriate window.  Make sure that you give yourself enough time to complete the quiz before you start.  Typically 30 minutes will be more than enough time.


Transitioning to remote learning means there will be no exams for this course.


Students will pick a topic for further exploration related to the material in the course.  I will provide a list of possible topics, though students may propose a topic of their choosing if they so desire.   The project may be done in groups of up to size 5.   Here is the rubric for the written project.

Grading Scheme

Course scores are weighted as follows:

Homework: 30%
Quizzes: 10%
Participation: 30%
Final Project 30%


Students requesting disability-related accommodations and services for this course are encouraged to schedule a phone/video meeting with me as early in the term as possible. This conversation will help to establish what supports are built into my online course. In order for accommodations to be authorized, students are required to consult with Student Accessibility Services (SAS;; SAS website; 603-646-9900) and to email me their SAS accommodation form. We will then work together with SAS if accommodations need to be modified based on the online learning environment. If students have questions about whether they are eligible for accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential."

Religious Observances

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.


Zoom Recordings

(1) Consent to recording of course and group office hours 

  1. a) I affirm my understanding that this course and any associated group meetings involving students and the instructor, including but not limited to scheduled and ad hoc office hours and other consultations, may be recorded within any digital platform used to offer remote instruction for this course; 
  2. b) I further affirm that the instructor owns the copyright to their instructional materials, of which these recordings constitute a part, and distribution of any of these recordings in whole or in part without prior written consent of the instructor may be subject to discipline by Dartmouth up to and including expulsion;
  3. b) I authorize Dartmouth and anyone acting on behalf of Dartmouth to record my participation and appearance in any medium, and to use my name, likeness, and voice in connection with such recording; and 
  4. c) I authorize Dartmouth and anyone acting on behalf of Dartmouth to use, reproduce, or distribute such recording without restrictions or limitation for any educational purpose deemed appropriate by Dartmouth and anyone acting on behalf of Dartmouth.

 (2) Requirement of consent to recordings 

By enrolling in this course, I hereby affirm that I will not under any circumstance make a recording in any medium of any one-on-one or group meeting with the instructor and/or students without obtaining the prior written consent of all those participating, and I understand that if I violate this prohibition, I will be subject to discipline by Dartmouth up to and including expulsion, as well as any other civil or criminal penalties under applicable law.

Proposed notification to faculty [from Dean’s Office and/or Department Chair] 

Please be aware that any recording you make within any digital platform used to offer remote course instruction may be regarded as an education record within the meaning of the Family Educational Rights and Privacy Act, which prohibits the disclosure to a third party of any student’s personally identifiable information from such records, in the absence of that student’s prior written consent, unless a specified exception to prior written consent applies. 

Please also be aware that you are prohibited from making a recording in any medium of any one-on-one meeting with a student without obtaining that student’s prior written consent.  If you violate that prohibition, please understand that you will be subject to discipline by Dartmouth up to and including dismissal, as well as any other civil or criminal penalties under applicable law.  This prohibition does not apply to recordings of the course and any associated group meetings, to which students are being asked to consent via their enrollment in this course.

Finally, please be reminded that the instructor owns the copyright to their instructional materials, of which these recordings constitute a part.  Distribution of another instructor’s recordings in whole or in part without prior written consent of that instructor may be subject to discipline by Dartmouth up to and including dismissal.

If you have any questions about any of these prohibitions or instructions, please consult your Dean’s Office. 


Course Summary:

Date Details Due
Public Domain This course content is offered under a Public Domain license. Content in this course can be considered under this license unless otherwise noted.