MAT240: Algebra I


Course information

Code: MAT240F
Instructor: Marco Gualtieri
Class schedule: T11-1 and R12, starting Thursday September 8th, 2022. You should have received a zoom link through Quercus.
Office Hours: online T1-2, after class.
Class location: Live and recorded, on Zoom and/or livestreaming, links to be sent through Quercus
Corequisite: MAT157Y1 is a co-requisite as stated in the calendar. I will not be giving exemptions to get around the rules.
Assessments: Due to the online nature of the course, assignments will be done exclusively through crowdmark and quercus. There will be an in-person mid-term and final exam.

Official syllabus


Without a UTORID and UofT email address, and unless you have enrolled you will not be able to access any class materials. Follow these instructions before semester begins. Do not contact TAs or the instructor if you are having technical difficulties with the UTORID system, we can’t help you with this.

Teaching Assistants

Each student will be assigned to a TA for this course. There will be TA office hours. If you have a mathematical question which is not addressed during class, you may ask during any of the office hours.

If you have a question about assessments or grading, ask your TA, nicely, during their office hour. Be very careful when asking for re-grades: these should be for errors in applying the TA’s own grading method, and should not be about arguing about the grade allocation method itself.

Isabel Beach (Beginning week of Sept 19)

Samprit Ghosh (Beginning week of Sept 19)

Matthew Koster (Beginning week of Sept 19)

C Yu (Beginning week of Sept 19)

Course description

This course is an introduction to linear algebra, with a focus on the conceptual structure of the subject in addition to its computational aspects.

Text Book: Linear Algebra Done Right, by S. Axler (third edition)

This is the textbook I will refer to when assigning reading. We will cover chapters 1 (Vector spaces), 2 (Finite-dimensional vector spaces), 3 (Linear maps), 4 (Polynomials), and 5 (Eigenvalues, eigenvectors and invariant subspaces). I will provide extra reference material for special topics.

Linear algebra is a very standardized topic; buying the textbook is not strictly necessary. With the guidance given in class, a student could use any of the following alternative references to learn the material:

  • Linear Algebra, by Hoffman and Kunze
  • Linear Algebra, by Friedberg, Insel and Spence
  • Linear Algebra done Wrong, by Treil
  • Introduction to Linear Algebra, by Lang
  • Linear Algebra and Its Applications, by Strang.


Assignments will be sent to you via Crowdmark via emailed link. Never forward your link to others - it is personalized. Since you must upload your assignment, make sure you leave plenty of time to complete the upload. Late assignments will not be accepted.

While you can certainly discuss homework with classmates, you have to write up the solutions yourself, in your own words. Otherwise it is considered unauthorized aid or assistance (working too closely with another student on an individual assignment so that the end result is too similar), which is an academic offence under the University’s Code of Behaviour on Academic Matters. If you find the solutions in books or on the internet, you must quote your source and write it up in your own words.

About online homework-completion services: we have a team which regularly combs these sites, and have caught many plagiarists this way. If a submitted assignment resembles the answers given online (which are more often wrong than not), it will be escalated to the dean’s office.

* Assignment 1 Crowdmark Link (since some people still don’t have UofT emails) * Assignment 1 temporary PDF

Course notes

Course notes for special topics will be sent to you via Quercus. All course materials (problem sets, lecture notes, etc) are provided for the use of enrolled students only. Registered students are not allowed to post, share, or sell course materials.


Marking Scheme:

There will be 10 assignments, equally weighted. The lowest two scores will be dropped. There will be no accommodations for lateness or missed assessments, for any reason. Be careful since uploading to Crowdmark can be tricky if you are not accustomed to it.

There will be an in-person term exam, Nov 1 11-1, EX 200 (Exam Centre)

There will also be an in-person final exam, date TBA.

The assignments are collectively worth 40%, the term exam is worth 20%, while the final exam is worth 40%.

Code of Behaviour / Plagiarism

Students should become familiar with and are expected to adhere to the Code of Behaviour on Academic Matters. Do not share your written work with anyone – if you do, there is a good chance your assessment will be zeroed out.

How to do well in this class

This class is about training your mind to think in a more modern mathematical way, and in this sense it is like learning a language: you need to spend focused time with the material and you need to practice. In addition to the 3 hours of lectures, you should be spending at least 4-5 hours a week thinking about the material, reading the suggested texts, and meditating upon the nature of n-dimensional space.