| Monday, 3/26 | Intro to the course. Systems of linear equations (Section 1.1) and solving them via row operations on matrices. |
| Wednesday, 3/28 | Matrices, Gauss-Jordan elimination (Section 1.2). Read: Sections 1.1 and 1.2. |
| Friday, 3/30 | The number of solutions to a linear system; matrix algebra (Section 1.3). Read: Section 1.3. HW #1 due: Section 1.1, #6, 7, 15, 17, 25, 32, 48. Section 1.2, #4, 6, 7, 22, 26, 27, 36, 69, 72. |
| Monday, 4/2 | Linear Transformations (Section 2.1) Read: Section 2.1 |
| Wednesday, 4/4 | Linear Transformations in Geometry (Section 2.2). Read: Section 2.2. |
| Friday, 4/6 | Matrix multiplication (Section 2.3). Read: Section 2.3 HW #2 due: Section 1.3, #4, 18, 23, 24, 25, 26, 28, 47, 58. Section 2.1, #5, 6, 7, 31, 32, 40, 43. Section 2.2, 4, 8, 10, 19, 20. |
| Monday, 4/9 | Inverse transformations and their matrices (Section 2.4). Read: Section 2.4. |
| Wednesday, 4/11 | A few more words on inverses (2.4). The image and kernel of a linear transformation (3.1). Read: Section 3.1. HW #3 due: Section 2.2, #27, 28. Section 2.3, #1, 3, 5, 7, 9, 17, 18, 34, 36, 37, 42-48. Section 2.4, #2, 4, 6. |
| Friday, 4/13 | No class |
| Monday, 4/16 | More on kernel and image (3.1). Read Section 3.1. HW #4 due: Section 2.4, #10, 13, 29, 34, 41, 67, 68, 75 (for #34, a diagonal nxn matrix is one with all 0s outside of the main diagonal, which goes from the upper left to the lower right). Section 3.1, #6, 7, 8, 12. |
| Wednesday, 4/18 | Subspaces of R^n. Linear Independence (Section 3.2). Read Section 3.2. |
| Friday, 4/20 | More linear independence. Bases (Section 3.2) Read: Give Section 3.2 one more go-round. HW #5 due: Section 3.1, #18, 22, 23, 24, 30, 39, 40, 49, 51. Section 3.2, #2, 3, 6, 12, 36, 37, 39. |
| Monday, 4/23 | More on bases (Section 3.2). Review. |
| Wednesday, 4/25 | Midterm 1 |
| Friday, 4/27 | Dimension (Section 3.3) Read: Section 3.3. |
| Monday, 4/30 | Mid-term break |
| Wednesday, 5/2 | The rank-nullity theorem. Finding bases for the kernel and image of a matrix. (Section 3.3) Read: take another look at Section 3.3. |
| Friday, 5/4 | A few more words on the rank-nullity theorem. Introduction to the determinant. HW #6 due: Section 3.2, #24, 34. Section 3.3, #9, 17, 19, 20, 21, 22, 25, 29, 30, 36, 37, 38, 39, 62, 63, 64, 80. |
| Monday, 5/7 | Determinants and their properties. Similar matrices. (Section 6.2) Read: Section 6.2 |
| Wednesday, 5/9 | Eigenvectors and Eigenvalues (Sections 7.1 and 7.2) Read: Definition 7.1.2. First three pages of Section 7.2. HW#7 due: Section 3.3, #82, 83, 85. Section 6.2, #6, 8, 9, 10, 14, 15, 30. |
| Friday, 5/11 | Finding eigenvalues and eigenvectors. Algebraic and geometric multiplicity of eigenvalues. Read: Rest of Section 7.2 |
| Monday, 5/14 | Eigenbases and how to find them. Read: Section 7.3. Project I due. |
| Wednesday, 5/16 | Eigenbases and connections to diagonal matrices. HW #8 due: Section 6.2, #37. Section 7.1, #1, 3, 6, 46, 47. Section 7.2, #3, 9, 15, 18, 38, 45. Section 7.3, #3, 9, 11, 14, 18, 22, 42 (For the problems in this section, interpret "diagonalize A" to mean "find an eigenbasis for A" and "diagonalizable" to mean "has an eigenbasis"). |
| Friday, 5/18 | Dynamical systems. Review for exam. |
| Monday, 5/21 | Midterm 2, in Weitz 133 |
| Wednesday, 5/23 | A few words on dynamical systems (Section 7.4). Linear Spaces (Section 4.1). Read: Section 4.1. |
| Friday, 5/25 | No class |
| Monday, 5/28 | Linear Transformations and isomorphisms (Section 4.2). Read: Section 4.2. HW #9 due: Section 7.4, #3, 4, 14, 15. Section 4.1 #1-6, 9, 10, 25, 26, 27, 28. |
| Wednesday, 5/30 | More on isomorphisms. The coordinate mapping. (Sections 4.2 and 4.3) Project 2 due. |
| Monday, 6/4 | Final Exam, 3:30-6:00 pm, in Weitz 133 |