One semester course on linear algebra. Assuming a basic acquaintance with vectors and matrices, the course goes on to study linear algebra and matrix theory in greater depth as well as covering some applications. Topics include Gauss elimination, linear transformations, vector spaces, bases and dimension, determinants, orthogonality, Gram-Schmidt method, QR factorization, eigenvalues, symmetric matrices and quadratic forms.
Linear Algebra with Applications, 3E. by Otto Bretscher. We will cover chapters 1-8. Covering this much material is only possible because some of the material should already be familiar from previous courses. Since the class meets only once a week, you will have to work hard on your own outside class.
There will be grades for quizzes, two midterm exams and a final exam. For a general university policy statement about grades, academic honesty and workload, go to: University Grading Policy Statement.
| Quizzes | 20 % |
| Midterm Exams (20 % each) | 40 % |
| Final Exam | 40 % |
| Midterm I | Wednesday, February 23 |
| Midterm II | Wednesday, April 6 |
| Final | Wednesday, May 11 |
Homework will be assigned but not collected. Instead there will be weekly quizzes consisting of problems very similar to the homework problems. If you can do the homework problems you should have no trouble with the quizzes. One quiz score will be dropped to allow for an absence or just a "bad day." To see the assignments, click on the link above.
| Week | Topic | Reading |
| 1/19 | Linear equations, Gauss elimination | 1.1-1.3 |
| 1/26 | Linear transformations, inverses | 2.1-2.3 |
| 2/2 | Matrix arith., bases, linear independence | 2.4, 3.1-3.2 |
| 2/9 | Dimension, Coordinates | 3.3-3.4 |
| 2/16 | Determinants | 6.1-6.2 |
| 2/23 | Midterm I | |
| 3/2 | Abstract vector spaces and transformations | 4.1-4.3 |
| 3/9 | Orthogonality, Gram-Schmidt, QR | 5.1-5.2 |
| 3/16 | Spring Break | |
| 3/23 | Orthogonal transformations, Least squares | 5.3-5.4 |
| 3/30 | Inner products, more determinants | 5.5, 6.3 |
| 4/6 | Midterm II | |
| 4/13 | Eigenvalues and eigenvectors | 7.1-7.3 |
| 4/20 | Diagonalization, complex eigenvalues | 7.4-7.6 |
| 4/27 | Symmetric matrices, quadratic forms | 8.1-8.2 |
| 5/7 | Singular values | 8.3 |
| 5/11 | Final Exam |
Here are two do-it-yourself computer labs to see how Matlab can be used to numerically solve linear algebra problems. The links below allow you to download the instructions for the labs which can be done on any computer running Matlab. This is purely for enrichment -- no grades.
Lab 1 Lab 2