| Date | Section and Topic | Read before class | Homework (problems in boldface are to hand in) |
| August 28 | Organization and introduction | Section 1.1 | HW 1 from 1.1 due Sept 1: 1, 2, 4, 6, 7, 9, 11, 21 |
| August 30 | More on Vectors | Section 1.1 | |
| Sept 1 | Dot products | Section 1.2 | HW 1 due today; HW 2 from 1.2 due Sept 8: 2, 3, 9, 10, 11, 14, 16, 22 | September 6 | Projections, methods of proof | Section 1.3 | HW 3 due Sept 11; 1.2, 17, 18; 1.3, 3, 5b, 7, 11, 13, 16 |
| September 8 | Matrices | Section 1.4 | HW 4 due Sept 13; 1.4, 1d, j, m, 2, 3, 4, 5, 7, 13b |
| September 11 | Matrix Multiplication | Section 1.5 | HW 5 due Sept 15; 1.5, 1 a, d, h, i, k, m, o, 2 b, e, 10 b, d, 11 b, 13, 14, 18 , 24, 26 |
| September 13 | Systems of linear equations | Section 2.1 | HW 6 due Sept 18; 2.1, 1 b, f, h, 2 b, d, 3, 5, 7, 8a, 10 |
| September 15 | Gaussian elimination | Section 2.1 | |
| September 18 | Gauss-Jordan elimination | Section 2.2 | HW 7 due Sept 22: 2.2, 2 d, f, 4 b, 5 b, d, 7 b, 10, 11, 13 |
| September 20 | Equivalent systems, rank, row space | Section 2.3 | HW 8 due Sept 27: 2.3, 1 b, 2, 4, 5 b, d, f, 8 b, d, f, h, 11 b, 16 |
| September 22 | Exam 1 | Sections 1.1-2.2 | |
| September 25 | Inverses of matrices | Section 2.4 | HW 9 due Sept 29: 2.4, 1 a, 2 b, d, 3 b, d, 4 b, d, 6, 7 b, 8 a, 13, 14, 20 Optional: Suppose in #20 that the limit as k approaches infinity of A^k is 0 (i.e., all its entries have a limit of 0). What does this say about the inverse of (A-I)? This is used in real life to approximate the inverses of certain big matrices. |
| September 27 | More on inverses: intro to determinants | Section 3.1 | HW 10 due Oct 2: 3.1, 1 b, d, f, h, 2 b, 3 b, 5 b, c, 8, 10, 13 |
| September 29 | More on determinants | Section 3.2 | HW 11 due Oct 4: 3.2, 1 b, d, 2 b, d, 3 b, 4 b, 7, 8, 13, 15 |
| October 2 | Properties of Determinants | Section 3.3 | HW 12 due Oct 6: 3.3, 2 b, d, 3 b, 5, 9, 10, 13, 17, 18 |
| October 4 | Eigenvalues and diagonalization | Section 3.4 | |
| October 6 | Formula for the Fibonacci numbers | Section 3.4 | HW 13 due Oct 11: 3.4, 1 d, 2 b, 3 d, f, 4 e, 5 d, 6, 13, 17. Read but don't do 23. |
| October 9 | Vector Spaces | Section 4.1 | HW 14 due Oct 13: 4.1, 2, 3, 4, 9, 11, 13, 16, 17 |
| October 11 | Subspaces | Section 4.2 | HW 15, due Oct 16: 4.2, 3 c, d, f, h, 4, 6, 7 c, d, 8, 13, 18, 19 |
| October 13 | Spanning | Section 4.3 | HW 16, due Oct. 18: 4.3, 1 b, d, 2 b, 3 b, 5, 6, 8, 13, 17, 26 |
| October 16 | Linear Independence | Section 4.4 | HW 17 due Oct 20: 4.4; 2 c, d, 3 b, d, 5, 8, 13 a, c, 16, 17 a, c, 19 |
| October 18 | Basis and dimension | Section 4.5 | |
| October 20 | Exam 2 | Sections 2.3-4.4 | Have a good weekend! |
| October 23 | More on bases | Sect 4.5 | HW 18 due Oct 27: 4.5; 1a, c, 2, 3, 6, 7, 10a, 13, 15, 21, 23 |
| October 25 | Special Bases | Sect 4.6 | HW 19 due Oct 30: 1b, 4b, 5b, 10b, 12b, 15 (very important: we'll see it again), 17a , 18a, 20 |
| October 27 | Coordinates | Sect 4.7 | HW 20: Due Nov. 3: 1b, 2c, 3, 4b, 8, 9, 10, 11, 15, 16 |
| October 30 | Change of coordinates | Sect 4.7 | |
| November 1 | Introduction to Linear Transformations | Sections 5.1 | HW 21: Due Nov 6: 1 c, i, 4, 7, 8, 9, 12, 14, 20, 33 |
| November 3 | Matrix of a linear transformation | Sect 5.2 | HW 22: Due Nov 10: 1, 2 b, d, 3 b, d, 4 c, 6 c, 8 b, 20, 12, 22 |
| November 6 | Changing bases for linear transformations | Sect 5.2 | |
| November 8 | The dimension theorem | Sect 5.3 | HW 23: Due Nov. 13: 3 b, c, 4 b, e, 5, 9, 11, 13, 18 |
| November 10 | One-to-one and onto linear transformations | Sect 5.4 | HW 24: Due Nov. 15: 1 b, d, f, 2 b, 4, 5, 6, 8, 9, 10 |
| November 13 | Isomorphism | Sect 5.5 | HW 25: Due Nov. 17: 2, 3, 4, 5, 6, 8, 13, 14 |
| November 15 | The general dimension theorem | Sect 5.5 | |
| November 17 | Exam 3 | Sect 4.5-4.7, 5.1-5.5 | Have a good break! |
| November 27 | Eigenvalues and eigenvectors of linear operators | Sect 5.6 | HW 26: Due Dec. 1: 1 b, e, 2 a, e, 5, 8 , 10, 13 , 15, 16. |
| November 29 | Diagonalization of linear operators | Sect 5.6 | |
| December 1 | Gram-Schmidt orthogonalization | Sect 6.1 | HW 27: Due Dec 6: 1 b, d, 3 b, 4 b, d, 5 d, 9, 10 |
| December 4 | Orthogonal matrices | Sect 6.1 | HW 28: Due Dec 8: 2 b, d, 7 d, 15 , 16 a, 18 , 19, 20 |
| December 6 | Orthogonal complements | Sect 6.2 | HW 29: Due Dec 11: 1 b, d, 2 c, d, 3 b, c, 4 b, c , 8, 12, 20, 21 |
| December 8 | Orthogonal diagonalization | Sect 6.3 | HW 30: Due Dec 13: 1 b, c, 2 b, c, 3 b, 5 b, 8, 11 |
| December 11 | Complex Numbers | Handout | |
| December 13 | Complex vector spaces | Chapter 7 | Review session at 4pm in MATH 245 |
| December 15 | Extended office hours from 11 am - 1 pm | ||
| December 17 | Final Exam: 7:30-10 pm | Chapters 1-6 + basics of complex numbers |