The material is organized by themes into two week blocks.
Blank spaces in the schedule are there because either: (i) I haven't decided exactly what to do on that day, and/or (ii) I think that the earlier topics will require more time than allotted, and I'm saving those days as extra space.
Assignments are due on Tuesdays at the beginning of class. The row that the assignment appears on is the day that it is due, (so for example assignment 1 is due on Sept 21). The assignments are available in either .ps or .pdf formats. The assignments can be downloaded from this page. The links to the assignment will appear a week before the assignment is due.
The practice problems are just that: suggested problems to practice the ideas in that day's lecture. They won't be collected, but they are a good way to ensure that you are understanding what is going on the course. My recommendation: Do them!
The tutorials are a chance to go over some of the ideas in the class that week; there will be a small presentation about one of the topics, some practice problems, and people who can answer questions about these problems and the ideas in class. The tutorial is not meant to answer specific questions about the homework.
| Date | Topic | Book | Homework | Practice Problems | Tutorial Topic | ||
|---|---|---|---|---|---|---|---|
| Sept. | 14 | Introduction to Course | §1.1 | 4, 5, 6, 14, 26, 33 | |||
| 15 | Solving linear equations with matrices I. | §1.2 | 4, 5, 18, 22, 27, 29 | ||||
| 17 | Solving linear equations with matrices II. | §1.2 | 40, 42, 46, 60, 64, 65 | RREF | |||
| 21 | Rank, relation to solving equations. | §1.3 | H1 .pdf .ps | 1, 5, 9, 13, 14, 22 | |||
| 22 | Vectors, Rn, linear combinations. | §1.3 | A1 .pdf .ps | 23, 24, 27, 28, 36, 37 | |||
| 24 | More about Linear Combinations | Lin. Comb. .pdf .ps | |||||
| 28 | Functions and Linear transformations, representation by matrices | §2.1 | H2 .pdf .ps | 1, 3, 5, 6, 7, 23, 37 | |||
| 29 | Some geometric linear transformations. | §2.2 | A2 .pdf .ps | 1, 4, 5, 10, 11, 24, 28, 35 | |||
| Oct. | 1 | More geometric transformations. | §2.2 | Lin. Trans. .pdf .ps | |||
| 5 | Matrix products. | §2.4 | H3 .pdf .ps | 1, 3, 10, 13, 17, 44, 48, 50 | Solutions: .pdf .ps | ||
| 6 | Invertible functions. | §2.3 | A3 .pdf .ps | 3, 7, 13, 25, 31, 34, 40 | |||
| 8 | Invertible linear transformations; computing the inverse. | Inverses; Matrix multiplication .pdf .ps | |||||
| 12 | Linear Transformations Redux. | H4 .pdf .ps | Solutions: .pdf .ps | ||||
| 13 | Image and Kernel. | §3.1 | A4 .pdf .ps | 8, 15, 17, 18, 19, 33, 38, 50 | |||
| 15 | More image and kernel | Image and Kernel .pdf .ps | |||||
| 19 | Subspaces of Rn. Basis and linear independence | §3.2 | H5 .pdf .ps | 1, 7, 8, 16, 17, 26, 36, 37 | Solutions: .pdf .ps | ||
| 20 | Dimension of a Subspace | §3.3 | A5 .pdf .ps | 7, 21, 22, 26, 30, 34, 39 | |||
| 22 | Review for Midterm. | Review | |||||
| 26 | Discussion of Midterm. | ||||||
| 27 | Dimension and Subspaces. | §3.3 | H6 .pdf .ps | ||||
| 29 | Two Examples. | A6 .pdf .ps | Question Session | ||||
| Nov. | 2 | Introduction to mathematical proofs. | |||||
| 3 | Induction | H7 .pdf .ps | |||||
| 5 | Dividing space with planes | A7 .pdf .ps | Induction | ||||
| 9 | Set theoretic vocabulary | ||||||
| 10 | Return to linear algebra | H8 .pdf .ps | |||||
| 12 | Basis and dimension | A8 .pdf .ps | |||||
| 16 | Introduction to abstraction. | ||||||
| 17 | Abstract Vector spaces | §4.1 | H9 .pdf .ps | ||||
| 19 | Examples of abstract vector spaces | §4.1 | A9 .pdf .ps | ||||
| 23 | Linear recurrence equations. | ||||||
| 24 | Linear transformations. | §4.2 | H10 .pdf .ps | ||||
| 26 | Isomorphisms and equality. | §4.2 | A10 .pdf .ps | Fibonacci numbers. | |||
| 30 | Coordinates and Bases. | §4.3 | |||||
| Dec. | 1 | Linear transformations in different bases. | §4.3 | H11 .pdf .ps | |||
| 3 | Review for December exam. | A11 .pdf .ps | |||||
| 7 | H12 .pdf .ps | ||||||
| A12 .pdf .ps | |||||||