Syllabus for MAT240: Algebra I

The wait listing period ends on September 13th, 2019. Summaries of the course material before this date will be made available publicly here.

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.

Assignment 1 (To be completed via Crowdmark, not physically handed in) Due date: Sunday September 15, 2019 11:59 PM

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.

No B.S. Bonus: If you write absolutely nothing false on an assignment (including “trivial” numerical errors) you will be awarded a 10% bonus. This is intended to disincentivize the writing of utter nonsense.

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 without the instructor’s permission.

Sep 5, 2019

Sep 10, 2019

Gaussian Elimination

Notes on Matrices

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 one 2h term test (20% of the total grade), a 3h final exam (50%), and about 9 homework assignments (30%).

If you cannot show up for a test because of illness or any other special reason, you MUST email your instructor a completed UofT medical certificate, which can be downloaded here. There will be NO make-up tests. The marking scheme will be adjusted appropriately for students who have missed a test because of illness or any other (approved) legitimate reason.

Students should become familiar with and are expected to adhere to the Code of Behaviour on Academic Matters.

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.

The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible:

https://www.studentlife.utoronto.ca/as