SPECIAL NOTE: Lectures on 1/3 and 1/5 for both sections will be in Carson L01! If you are not enrolled but are hoping to add Math 22, please attend these lectures!

General Information


Professor Sarah Frei
Office: 314 Kemeny Hall
Office Hours: Mon 2-3:30pm; Wed 4-5pm; and by appointment
Contact via email: sarah.frei(at)dartmouth.edu (Replace the (at) with an @).

Professor Misha Temkin
Office: 310 Kemeny Hall
Office Hours: TBD, and by appointment
Contact via email: misha.temkin(at)dartmouth.edu (Replace the (at) with an @).

Scheduled Lectures

Section 1: Sarah Frei
(Block 10) MWF 10:10—11:15
(x-hour) Th 12:15—1:05
Carson L01

Section 2: Misha Temkin
(Block 10) MWF 10:10—11:15
(x-hour) Th 12:15—1:05
Kemeny 004

Course Description

Linear algebra is the study of vector spaces and the linear transformations between such spaces. In this class we will work mostly with the vector space Rn. We will learn how to represent linear transformations with matrices and study different types of linear transformations, such as diagonalizable transformations. During the last weeks of classes we will concentrate on applications. For a more detailed description on the topics we will learn in this class see the day to day Syllabus.

Linear algebra is very important for both pure and applied mathematics. This is one of the reasons that it is a prerequisite for almost all of your math major courses and other STEM subjects. The techniques of linear algebra are used in engineering, physics, natural sciences, computer science and economics. For example, when we combine calculus with linear algebra we can solve linear systems of differential equations.

Goals of the course:

  • Students will learn the main concepts and techniques in linear algebra.
  • Students will learn some applications of linear algebra.
  • Students will be prepared for more advanced courses in mathematics, computer science, physics and any other subject that require linear algebra.


    David Lay, Lay and McDonald, Linear Algebra and its applications, Fifth edition (ISBN: 978-0321982384).


    There will be two midterm exams and a cumulative final exam. The exams are scheduled as follows:

    Exam 1 Thurs Jan 25, 7-9 pm Room TBD
    Exam 2 Thurs Feb 15, 7-9 pm Room TBD
    Final Exam Fri Mar 8, Time TBD Room TBD

    The midterms will be in person, 2-hours in length and the final is a 3-hour exam scheduled by the registrar. More information will be provided by your instructor in the week before the midterm.

    If you have a conflict with one of the midterm exams because of a religious observance, scheduled extracurricular activity such as a game or performance, scheduled laboratory for another course, or similar commitment, please see your instructor as soon as possible.


    Our graduate teaching assistant Lily McBeath will run tutorials Tuesdays, Thursdays, and Sundays from 7:00-9:00pm in Kemeny Hall 242, focusing on answering your questions as you work through understanding the concepts. You can get help with any questions you have regarding the course topics and homework assignments. Tutorials are open to all Math 22 students. You don't need an appointment.


    The course grade will be computed as follows:

    Percent of Final Grade
    WebWork 9
    Homework 9
    Discussion Participation 4
    Short Writing Response 3
    Midterms 45 (22.5 each)
    Final Exam 30

    Homework, participation, and short writing responses will be further explained below.

    Homework Policy

    Written Homework: Written homework assignments will be assigned once a week (usually on Wednesdays) and will be posted on Canvas. It will be collected once a week every Wednesday morning via Gradescope.

  • Check the calendar on Canvas for due dates for the written homework.
  • Homework is to be written neatly. Make sure not to write too close to the margins, otherwise when you scan it there might be missing information. Make sure that before you submit your homework you check to make sure that all information has been scanned and that it can be read.
  • Use complete sentences when writing explanations or justifications. If you can't read your solutions aloud as fluently as if you were reading a textbook, try using nouns and verbs in your write ups!
  • WeBWorK: WeBWorK assigned from each class is due at the beginning of the next class. There will be a two day built-in grace period for each WeBWork assignment to allow you to complete the assignment. These daily web-based problems can be accessed via the WeBWorK homepage. See also the WeBWorK login containing a FAQ and quick start guide. Your login name is your netID, and your initial password is also your netID.

    It is highly recommended that you keep a notebook in which you write up your WeBWorK homework (including your work as well as the answers). Then when you are studying for exams, you will have a record of your work to which to refer.


    We will be using the Discussions in Canvas as an avenue for discussing linear algebra and how it relates to our technological and digital world. We will start each discussion with a prompt. Your posts can be in response to earlier posts or start new subjects, and they should demonstrate thoughtfulness (e.g., "I agree" is not acceptable) and civility. They are graded as 0 (didn't do it) or 1 (did it) and the total comprises your participation grade. The prompts will be posted on Fridays.

    Please keep the Discussion boards focused on the given topic(s). If you have a specific question related to a homework problem, that should be discussed in Tutorials or office hours. Do not post solutions to homework problems in the Discussions.

    Short Written Responses

    We will maintain a list of Outside Readings on Canvas about linear algebra and its effects on our day to day lives. We ask that you write a short (300 word) response to one of the articles, reflecting on the perspectives and ideas presented. It will be due at 5pm on Friday, March 1, but you can complete and submit it anytime throughout the quarter.

    Student Office Hours

    These are times your instructor has set aside specifically for you. Please come to office hours for any of the following reasons:

  • To ask a question you have about homework or any other upcoming assessment.
  • To ask a question about something that was said or done in class that you didn't understand.
  • To listen and learn from other people's questions.
  • To ask a question about why you received the grade you did on an assessment.
  • To discuss how you're doing overall in the class.
  • To tell your instructor more about yourself, why you're taking this class, and what you hope to get out of your time at Dartmouth.
  • To tell your instructor about some other math that you recently learned, thought was cool, and want to share.
  • To ask your instructor about what it's like to do math research, take more advanced math classes, etc.
  • To discuss...(it isn't an exhaustive list!)
  • You are also welcome to schedule an appointment if you would like to meet outside of the above scheduled times (send an email to your instructor).

    The Honor Principle

    Students are encouraged to work together to do homework problems. What is important is a student's eventual understanding of homework problems, and not how that is achieved.

    The honor principle on homework: What a student turns in as a homework solution is to be his or her or their own understanding of how to do the problem. Students must state what sources they have consulted, with whom they have collaborated, and from whom they have received help. If you did not talk with anyone or consulted any source, please write "No Collaborators". If you have taken the solution whole cloth from some other source or a Generative AI solver has given you the solution please say so, but even in that case you must still write them out in your own hand. The solutions you submit must be written by you alone.

    ChatGPT/Generative AI policy: Machines can now do many of the homework assignments that you are asked to do. In doing the actual mathematics homework, if you have the machine do it, then you will not learn how to do it and you will probably do poorly on the exams. That said, I won't be checking to see if you had a machine do your mathematics assignments. As for the writing part of the course, it is expected that you do it yourself. The goal of these assignments is to get you to see how linear algebra is used in the world. If you let the machine tell you how, then you are not thinking about the world, you are letting a machine think about it for you. If it is determined that you used ChatGPT or some other form of generative AI to do these writing assignments you will be brought to COS. Honestly, it's not worth it - in every sense. Use your brain.

    The honor principle on exams: Students may not give or receive assistance of any kind on an exam from any person except for the professor or someone explicitly designated by the professor to answer questions about the exam.

    If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to your instructor and we will be glad to help clarify things. It is always easier to ask beforehand than to have trouble later!

    Student Accessibility and Accommodations

    Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services (SAS; Getting Started with SAS webpage; student.accessibility.services@dartmouth.edu ; 1-603-646-9900) and to request that an accommodation email be sent to their instructor in advance of the need for an accommodation. Then, students should schedule a follow-up meeting with their instructor to determine relevant details such as what role SAS or its Testing Center may play in accommodation implementation. This process works best for everyone when completed as early in the quarter as possible. If students have questions about whether they are eligible for accommodations or have concerns about the implementation of their accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.

    Religious Observances

    Dartmouth has a deep commitment to support students’ religious observances and diverse faith practices. 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 — before the end of the second week of the term at the latest — to discuss appropriate course adjustments.

    Mental Health and Wellness

    The academic environment 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: the Counseling Center which allows you to book triage appointments online, the Student Wellness Center which offers wellness check-ins, and your undergraduate dean. The student-led Dartmouth Student Mental Health Union and their peer support program may be helpful if you would like to speak to a trained fellow student support listener. If you need immediate assistance, please contact the counselor on-call at (603) 646-9442 at any time. Please make me aware of anything that will hinder your success in this course.

    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 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.