One semester course on linear algebra. Assuming a basic acquaintance with vectors and matrices, the course goes on to study matrix theory in greater depth as well as some of its applications. Topics include Gauss elimination, LU factorization, row, column and null spaces and their dimensions, orthogonality, Gram-Schmidt method, QR factorization, determinants, eigenvalues, symmetric and Hermitian matrices and linear transformations. Applications include Markov chains, linear differential and difference equations, method of least squares, principle axes for conic sections, etc. There will be two computer lab sessions where you can try out some linear algebra software.
Introduction to Linear Algebra by Gilbert Strang. We will cover most of the topics in the book. This is only possible because some of the material should already be familiar from previous courses. Specifically, you should already know about matrix multiplication, determinants of small matrices, and probably at least heard of eigenvalues.
There will be two 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
| Homework | 20 % |
| Midterm Exams (20 % each) | 40 % |
| Final Exam | 40 % |
| Midterm I | Wednesday, February 25 |
| Midterm II | Wednesday, April 7 |
| Final | Wednesday, May 12 |
Assignments are due most Wednesdays. Late homework will be accepted by Friday of the week they are due at a penalty of 20%; after that only if you have a valid excuse. The assignments contain many problems to practice but you hand in only the starred problems. Even so, the grader may not grade all of the problems you hand in. You may discuss homework with other students but then you should each write up your own solutions. Click the link above to see the assignments.
| Week | Topic | Reading |
| 1/21 | Gauss elimination, inverses | 2.1-2.4 |
| 1/28 | LU, LDU | 2.5-2.7 |
| 2/4 | Row, col. and null spaces, rank | 3.1-3.3 |
| 2/11 | Basis, dimension, networks | 3.4-3.6 |
| 2/18 | Determinants | 5.1-5.3 |
| 2/25 | Midterm I, Lab I | |
| 3/3 | Eigenvalues, diagonalization, similarity | 6.1-6.2, 6.6 |
| 3/10 | Applications to diff. eqs., Markov chains | 6.3. 8.3 |
| 3/17 | Spring Break | |
| 3/24 | Orthogonality, projections, networks | 4.1-4.2,8.2 |
| 3/31 | Least squares,Gram-Schmidt, Fourier series | 4.3-4.4, 8.5 |
| 4/7 | Midterm II, Lab II | |
| 4/14 | Symm. and Hermitian matrices, apps. | 6.4, 10.2 |
| 4/21 | Positive definiteness, SVD | 6.5, 6.7 |
| 4/28 | Linear transformations | 7.1-7.2,8.6 |
| 5/5 | Linear transformations, apps. | 7.3-7.4 |
| 5/12 | Final Exam |