Syllabus for MAT240: Algebra I

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, we can’t help you with this.

https://tcard.utoronto.ca/

Each student will be assigned to a TA for this course. There will be online TA office hours. If you have a mathematical question, post it to the Forum (see below) or discuss in office hours. If you have a question about assessments or grading, ask your TA.

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.

Assignment 1 Crowdmark Link (since some people still don’t have UofT emails) Assignment 1 temporary PDF (if you are not yet enrolled in crowdmark)

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.

Part I: Sets and maps

Part II: Algebraic structures and Fields

Part III: Vector spaces and subspaces

Part IV: Subspaces and Linear dependence

Gaussian Elimination

Part V: Applications of Gaussian Elimination

Part VI: Linear maps

Matrices and matrix multiplication

Part VII: The dual space

Part VIII: Linear operators

Jordan Canonical Form

There will be a Piazza forum for this course. You will receive an email invitation to the forum. Join the forum, ask as many questions as you like, and try answering some too – we often learn a lot by trying to explain things to others. The TAs and I will check the forum and answer some of the questions, and your classmates will hopefully do the same. The forum is purely to facilitate discussion among the students and has no direct impact on grades at all.

Marking Scheme:

There will be 11 assessments, equally weighted. The lowest two will be dropped. There will be no accommodations for lateness or missed assessments, for any reason.

There will also be in-class mini-quizzes, which are worth 15% of the final grade. At most two absences will not be counted. Again, no accommodations of any kind for missed assessments, for any reason.

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.

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.