Instructor: Johan Asplund, johan.asplund[at]stonybrook.edu, Office: Math Tower 4-105.
Class time and location:
MW 3:30–4:50pm, Physics P112.
Office hours:
MW 2:30–3:30pm (Math Tower 4-105) and Tu 5–6pm (MLC via Zoom).
Grader: Daniel Johnson, Daniel.A.Johnson[at]stonybrook.edu.
Syllabus: Here.
Textbook: Linear Algebra with Applications (5th edition) by Otto Bretscher.
Quizzes and suggested problems: Most weeks there will be an in-class quiz. It will be held at the end of the class at the dates indicated in the tentative schedule below. Each quiz consists of one or two problems.
| Date | Topic | Read | Problems | Quiz |
|---|---|---|---|---|
| Mon Aug 24 | Linear systems, matrices and vectors | 1.1, 1.2 (notes) | 1.1.9, 1.2.4, 1.2.5, 1.2.11 | |
| Wed Aug 26 | Gauss–Jordan elimination, matrix operations | 1.2, 1.3 (notes) | 1.2.21, 1.3.4, 1.3.14, 1.3.20 | |
| Mon Aug 31 | Linear transformations | 2.1 (notes) | 2.1.2, 2.1.3, 2.1.5, 2.1.20 | Quiz 1 |
| Wed Sep 2 | Linear transformations in geometry | 2.2 (notes) | 2.2.2, 2.2.4, 2.2.19, 2.2.20 | |
| Mon Sep 7 | No class (Labor day) | |||
| Wed Sep 9 | Matrix products | 2.3 (notes) | 2.3.3, 2.3.4, 2.3.14, 2.3.20 | Quiz 2 |
| Mon Sep 14 | Inverses of linear transformations | 2.4 (notes) | 2.4.3, 2.4.6, 2.4.18, 2.4.32 | |
| Wed Sep 16 | Image and kernel of linear transformations | 3.1 (notes) | 3.1.5, 3.1.14, 3.1.21, 3.1.24 | Quiz 3 |
| Mon Sep 21 | Subspaces and bases | 3.2 (notes) | 3.2.1, 3.2.5, 3.2.14, 3.2.27 | |
| Wed Sep 23 | Dimension | 3.3 (notes) | 3.3.3, 3.3.11, 3.3.22, 3.3.27 | Quiz 4 |
| Mon Sep 28 | Coordinates | 3.4 (notes) | 3.4.5, 3.4.10, 3.4.15, 3.4.23(a) | |
| Wed Sep 30 | Orthogonal projections | 5.1 (notes) | 5.1.2, 5.1.5, 5.1.10, 5.1.15 | Quiz 5 |
| Mon Oct 5 | Midterm review | 1.1–3.4 | ||
| Wed Oct 7 | Midterm I (In class) | |||
| Mon Oct 12 | No class (Fall break) | |||
| Wed Oct 14 | Gram–Schmidt process | 5.2 (notes) | 5.2.5, 5.2.7, 5.2.29, 5.2.32 | |
| Mon Oct 19 | Orthogonal transformations | 5.3 | 5.3.3, 5.3.7, 5.3.8, 5.3.15, 5.3.16 | |
| Wed Oct 21 | Least squares | 5.4 | 5.4.1, 5.4.3, 5.4.5, 5.4.8(e) | Quiz 6 |
| Mon Oct 26 | Inner product spaces | 5.5 | 5.5.1, 5.5.5, 5.5.8, 5.5.22 | |
| Wed Oct 28 | Determinants | 6.1 | 6.1.4, 6.1.9, 6.1.23, 6.1.28 | Quiz 7 |
| Mon Nov 2 | More determinants | 6.2 | 6.2.3, 6.2.8, 6.2.17, 6.2.38 | |
| Wed Nov 4 | Cramer's rule | 6.3 | 6.3.1, 6.3.22, 6.3.25 | |
| Mon Nov 9 | Midterm review | 5.1–6.2 | ||
| Wed Nov 11 | Midterm II (In class) | |||
| Mon Nov 16 | Diagonalization | 7.1 | 7.1.1, 7.1.4, 7.1.8, 7.1.15 | |
| Wed Nov 18 | Eigenvalues | 7.2 | 7.2.3, 7.2.9, 7.2.11, 7.2.17 | Quiz 8 |
| Mon Nov 23 | Eigenvectors | 7.3 | 7.3.4, 7.3.10, 7.3.22, 7.3.24 | |
| Wed Nov 25 | No class (Thanksgiving) | |||
| Mon Nov 30 | Applications of diagonalization | 7.4 | 7.4.2, 7.4.9 | Quiz 9 |
| Wed Dec 2 | Final review/Buffer | 1.1–7.4 | ||
| Mon Dec 7 | Final review/Buffer | 1.1–7.4 | ||
| Mon Dec 14 | Final Exam: 11:15am–1:45pm, TBA | |||