Probability, Math 20

Instructor: Nadia Lafrenière (Kemeny 318; nadia.lafreniere@dartmouth.edu). Pronouns: She/Her. I go by my first name.
Class schedule: 9L MWF 8:50-9:55 AM, in Kemeny 007
x-hour: 9Lx Th 9:05-9:55, will be used for study groups (mandatory)
Office hours: Monday 10-11 AM and Tuesday, 1:30-2:30 PM, or by appointment. My office is Kemeny 318.

Tutorial: Monday and Wednesday 7-9 pm (Kemeny 105)
TA: Anna Vasenina (anna.vasenina.gr@dartmouth.edu)

Course description (adapted from the ORC)

Our capacity to fathom the world around us hinges on our ability to understand quantities which are inherently unpredictable. Therefore, in order to gain more accurate mathematical models of the natural world we must incorporate probability into the mix. This course will serve as an introductions to the foundations of probability theory. Topics covered will include some of the following: (discrete and continuous) random variable, multivariate distributions, expectations; independence, conditioning, conditional distributions and expectations; law of large numbers and the central limit theorem; random walks and Markov chains.

Assessment

Here is how much I will consider every assignment towards the final grade:

Evaluation	Date	Value
Homework (written)	Every Friday (starting the second week), except April 28 and June 2	20%
Study groups (participation)	Every Thursday (x-hour)	8%
Study groups (evaluation of peers)	twice	2%
Midterm	April 28	30%
Final project (oral presentation)	May 24, 26 & 31	10%
Final exam	June 2	30%

Finding the right answer is not equivalent to solving a problem, and therefore your solution will be evaluated as a whole. Please, keep in mind while writing the assignments that I will not be with you when I will read it, so it must be complete.

The student presentations can be about any probability topic not covered in class. Around the middle of the term, I will provide you with a list of topics I encourage you to explore. Students having further ideas should talk to me about the project idea they have. The project will be done as a team, with the members of your study group. More info on the project here.

The following conversion gives guaranteed minimum letter grades based on your numerical grade. We reserve the right to grade more generously, depending on the difficulty of our exams and homework. This means a grade of 89% will definitely be at least a B+ but may be an A-. A grade of 90 will always be at least an A-.
Grade guarantees: 95% A; 90% A-; 85% B+; 80% B ; 75% B-; 70% C+; 65% C; 60% C-; 55% D.

Extension policy

Every student is granted an automatic extension for one problem set; you however have to tell me before the submission deadline. This policy does not apply to the exams, nor to students talks, given that this would involve scheduling issues. I might grant extensions after the automatic one based on special circumstances, but students will need to ask for it.

Study groups

We will use the x-hour for study groups. During the first week of the term, you will be assigned a study group of 4-5 people. These are mandatory and serve as a way to improve the quality of the understanding of everyone: more experienced students might gain a lot of insight from explaining ideas to students who have not as much experience with proofs. As part of the evaluation, your contribution to study groups will be assessed. I expect the study groups to meet in the classroom, and I will make the groups myself to ensure a good balance.

Textbook

Charles M. Grinstead and J. Laurie Snell. Introduction to probability, 2nd edition, American Mathematical Society, 1997.
The home page of the textbook can be found here. On this page, you can download the PDF of the book for free. You can also buy a desk copy or borrow it from the library.

Day-by-day Syllabus

	Sections of the book	Brief Description - Course content
Week 1	1.1, 1.2, 2.1	Discrete probability distributions, simulation of continuous probabilities. Notes for 3/27 Notes for 3/29 Notes for 3/31
Week 2	2.2, 3.1, 3.2	Continuous probability distributions, Combinatorics: permutations, subsets and combinations Notes for 4/3 Notes for 4/5 + code Notes for 4/7
Week 3	3.3, 4.1, 4.2	Applications: Card shuffling, Secret Santa and Birthday paradox. Independence and conditional probability. Notes for 4/10 Notes for 4/12 Notes for 4/14 + video (starting at 4:18)
Week 4	4.3, 5.1, 5.2	Distributions and Densities. Notes for for 4/17 Notes for 4/19 Notes for 4/21 End of the content for Midterm.
Week 5	6.1, 6.2	Expected value and variance. Notes for 4/24 Notes for 4/26 No x-hour (Anna and Nadia will be available for questions). Friday's class replaced with exam, at 8 am.
Week 6	6.3, 7.1, 7.2	Expected value and variance for continuous random variables. Sums of random variables. Notes for 5/1 Notes for 5/3 Notes for 5/5
Week 7	8.1, 8.2, 9.1, 9.2, 9.3	Law of large numbers and Central Limit Theorem. Notes for 5/8 Notes for 5/10 Notes for 5/12
Week 8	11.1, 11.2, 11.3 12.1	Intro to Markov chains, Absorbent and ergodic Markov chains, Random walks. Notes for 5/15 Notes for 5/17 Notes for 5/19
Week 9	12.2	The Gambler's ruin. Notes for 5/22 Final project presentations
Week 10		Monday: No class, Memorial day. Final project presentations Final exam on June 2 (3 pm).

Honor Principle

Assignments serve both the purpose of fixing your ideas on a given subject and, for the evaluator, to assess the comprehension you have of the class and how the class material has been understood. None of these goals can be achieved if you hand out a solution that is taken from someone else or from a publicly available source.
Nevertheless, students are allowed to work together on problems to explore their solutions. The homework you submit must reflect your own understanding, and you thus need to write your own copy of the solution, in your own words. You also need to cite the source of any idea that is not yours.
More information on the Academic Honor Principle can be found on Dartmouth’s website: https://students.dartmouth.edu/judicial-affairs/policy/
academic-honor-principle

You may not give nor receive any help on the exams, except from the instructor.

Attendance and Health policy

You are expected to attend class in person unless you have made alternative arrangements due to illness, medical reasons, or the need to isolate due to COVID-19 or other diseases. For the health and safety of our class community, please: do not attend class when you are sick, nor when you have been instructed by Student Health Services to stay home. My lectures notes are available on the course website, and I will provide the support you need to catch up on class material and submit your work. If needed, one-on-one office hours over Zoom will be offered.

Dartmouth Policies

Student Accessibility and Accommodations

Students requesting disability-related accommodations and services for this course are encouraged to schedule a meeting with me as early in the term as possible. This conversation will help to establish how your accommodations will be implemented in my course and what role Student Accessibility Services (SAS) or its Testing Center may play in assisting. In order for accommodations to be authorized, students are required to register with SAS (Getting Started with SAS webpage; student.accessibility.services@dartmouth.edu; 603-646-9900) and to request an accommodation email be sent to me in advance of the need for an accommodation. If students have questions about whether they are eligible for accommodations, they should contact
the SAS office. All inquiries and discussions will remain confidential.

Mental Health

The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean (http://www.dartmouth.edu/~upperde/), Counseling and Human Development (http://www.dartmouth.edu/~chd/), and the Student Wellness Center (http://www.dartmouth.edu/~healthed/). Remember, mental and physical health should be your number one priority!

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 as soon as possible, preferably before the end of the second week of the term to discuss appropriate accommodations.

Financial Needs

All material for this class is aimed to be freely available, either at the library or online. If you encounter financial challenges related to this class (because of the workload for example), please let me know.

Title IX

At Dartmouth, we value integrity, responsibility, and respect for the rights and interests of others, all central to our Principles of Community. We are dedicated to establishing and maintaining a safe and inclusive campus where all have equal access to the educational and employment opportunities Dartmouth offers. We strive to promote an environment of sexual respect, safety, and well-being. In its policies and standards, Dartmouth demonstrates unequivocally that sexual assault, gender-based harassment, domestic violence, dating violence, and stalking are not tolerated in our community.

The Sexual Respect Website (https://sexual-respect.dartmouth.edu) at Dartmouth provides a wealth of information on your rights with regard to sexual respect and resources that are available to all in our community.

Please note that, as a faculty member, I am obligated to share disclosures regarding conduct under Title IX with Dartmouth’s Title IX Coordinator. Confidential resources are also available, and include licensed medical or counseling professionals (e.g., a licensed psychologist), staff members of organizations recognized as rape crisis centers under state law (such as WISE), and ordained clergy (see https://dartgo.org/titleix_resources).

Should you have any questions, please feel free to contact Dartmouth’s Title IX Coordinator or the Deputy Title IX Coordinator for the Guarini School. Their contact information can be found on the sexual respect website at: https://sexual-respect.dartmouth.edu.