Course Content
The textbook for the class is Matrix Theory and Linear Algebra, by Peter Seliger. This book is available from the Dalhousie Bookstore and from the author's webpage.Additional resources
- Essence of linear algebra, video series by 3blue1brown. (EoLA)
- Interactive Linear Algebra, by Dan Margalit & Joseph Rabinoff. Online books with lots of visuals.
- Jupyter Guide to Linear Algebra, by Ben Vanderlei. Useful to see the concepts we see in class implemented in Python.
Approximate content of lectures
- May 05: Check-in & syllabus overview. Linear systems. Sections 1.1-1.2.
- May 07: Elementary operations. Augmented matrix notation. Sections 1.3-1.4.
- May 09: Row reduction (Gaussian elimination). Gauss-Jordan elimination. Reduced row echelon form. Sections 1.4-1.5.
- May 12: Systems over Z_p. Section 1.8.
- May 14: Homogeneous systems. Intro to vectors. Sections 1.7 & 2.1-2.3.
- May 16: asynchronous activity - solving Lights Out, balancing linear equations.
- May 19: Victoria Day.
- May 21: Linear combinations & lengths. Sections 2.4-2.4.
- May 23: Dot products. Section 2.5.
- May 26: Cross products. Section 2.6.
- May 28: Matrix algebra, including matrix multiplication. Sections 4.1-4.4.
- May 29: Midterm test.
- May 30: Matrix inverses. Spans. Section 4.5 & 5.1.
- Jun 02: Basis and dimension. Subspaces: column space & null space.. Section 5.2-5.5.
- Jun 04: Linear transformations. Sections 6.1-6.2.
- Jun 06: More on linear transformations. Sections 6.2-6.4.
- Jun 09: Determinants. Chapter 7.
- Jun 11: Eigenvectors and eigenalues. Sections 8.1-8.2..
- Jun 13: Diagonalization. Section 8.4.
- Jun 16: Review.
- Jun 18: no class.
- Jun 20: Final exam.
Assessment
Midterm test: exam
- Homework: assigned weekly through WebWork via Brightspace. Sets will tipically open on Saturday, end of day, and be due on the Monday of the following week, end of day. (e.g. HW2 opens on May 10 and is due on May 19)
- Midterm: the test will open on Brightspace on May 29 and be due on May 30. I encourage you to simulate an exam environment on this test, as means to train you for the final exam. In any case, this is an individual assignment: blatant plagiarism will not be tolerated.
- Final exam: this test will be held in person on June 20, 12-3:00pm Tupper Theatre B. If you do the homework assignments, you should be prepared for the final. A practice exam will also be posted.
- Participation: the points is to get you started in engaging with the class, both during and off class time. Some ways to participate are by asking or answering questions in class, coming to office hours, asking and answering questions on the course Brightspace forum, and sending emails to your instructor.
- Applications of linear algebra: Many of concepts and theorems that we will see in this course are important to various applied science fields. Here we take the opportunity to highlight such applications by writing a prompt on a topic that interests you. You can send your submission to daniel.teixeira@dal.ca, or submit it through Brightspace. Periodically, submissions will be posted for other students to learn about such applications. You can ask your instructor for topic suggestions.