Computational Linear Algebra is a pilot first-semester, first-year undergraduate course that shows how mathematics and computation are unified for reasoning about data and making discoveries about the world.
This course ran in Fall 2020 at the University of Michigan Robotics Institute.
Engineering math education is stuck in the Sputnik era: we force students to do four semesters of calculus before they can do anything interesting in engineering. ROB 101 seeks to break through with new ideas. Students will see how engineers are using mathematics and computing to solve large and important problems. Students will still do drill problems to firm up concepts with teeny tiny problems with two or three variables, but they will also solve problems in the Julia programming language with hundreds of variables.
Students will have a palpable understanding that computation and mathematics are friends, instead of hoops to be jumped through on the way to a degree.
All lecture and recitation videos are available on YouTube:
ROB 101 Videos
And lecture notes here.
The textbook, Notes for Computational Linear Algebra, continues to be updated.
Three main projects that accompany the course are available here.
| Lecture | Topic | Youtube | Textbook Chapters | Assignments due |
|---|---|---|---|---|
| 1 | Introduction | Video | 1.1 - 1.2 | |
| 2 | Linear Equations & Matrices | Video | 1.3 - 2.5 | |
| 3 | Matrix Determinant | Video | 2.5 - 2.6 | |
| R1 | Recitation: Linear Systems & Quadratic Equation | Video | ||
| 4 | Determinant & Triangular Systems | Video | 2.6 - 3.4 | |
| 5 | Triangular Systems: Substitution | Video | 3.5 - 4.1 | Homework 1 |
| 6 | Matrix Multiplication | Video | 4.2 - 4.4 | |
| 7 | Matrix Multiplication II | Video | 4.4 - 5.2 | |
| 8 | LU Factorization | Video | 5.3 | Homework 2 |
| 9 | LU Factorization II | Video | 5.3 - 5.5 | |
| R2 | Recitation: Triangular Matrices & Substitution | Video | ||
| 10 | Matrix Transpose & Inverse | Video | 6.1 - 6.3 | |
| 11 | Vector Space R^n | Video | 6.3, skip to 7.1 | |
| 12 | Linear Independence | Video | 7.2, 7.4 | Homework 3 |
| R3 | Recitation: Matrix Multiplication & LU Decomposition | Video | ||
| 13 | Linear Independence II | Video | 7.4.5, 7.3, 7.5 | |
| 14 | Linear Independence III | Video | 7.6 - 7.7 | Project 1 |
| 15 | Linear Independence IV | Video | 7.7, skip to 8.1 - 8.2 | |
| R4 | Recitation: Vectors in R^n & Linear Independence | Video | ||
| 16 | Norm of a Vector | Video | 8.2 - 8.3 | |
| 17 | Least Squares | Video | 9.1 - 9.2 | Homework 4 |
| 18 | Subspaces | Video | 9.2, 9.4 | |
| R5 | Recitation: Linear Independence of Vectors | Video | ||
| 19 | Subspaces II | Video | 9.3 - 9.4 | |
| 20 | Rank & Nullity of a Matrix | Video | 9.5 - 9.6 | Homework 5 |
| 21 | Dot Product & Orthogonal Vectors | Video | 9.6 | |
| R6 | Recitation: Existence & Uniqueness of a Solution | Video | ||
| 22 | Orthonormal Vectors | Video | 9.7 | |
| 23 | QR Factorization | Video | 9.9 - 10.1 | Homework 6 |
| 24 | Orthogonal Matrices & Roots of Nonlinear Equations | Video | 10.1 - 10.2 | |
| R7 | Recitation: LU Factorization | Video | ||
| 25 | Bisection Algorithm | Video | 10.3 - 10.4 | |
| 26 | Newton's Method | Video | 10.4 - 10.5 | Homework 7 |
| 27 | Partial Derivatives & Roots | Video | 10.5 | |
| R8 | Recitation: Subspaces, Null Space, Gram-Schmidt, QR Factorization | Video | ||
| 28 | Gradient & the Jacobian | Video | 10.5 - 10.6 | |
| 29 | Newton-Raphson Algorithm | Video | 11.1 - 11.2 | Homework 8 |
| 30 | Optimization | Video | 11.3 - 11.4 | |
| R9 | Recitation: Non-linear Equations, Bisection, Newton Methods | Video | ||
| 31 | Gradient Descent | Video | 11.5 - 11.6 | |
| 32 | Optimization II | Video | 11.6, skip to A.1 | Project 2 |
| 33 | Affine Spaces | Video | A.1, skip to 11.8 - 11.9 | |
| R10 | Recitation: Gradients & Gradient Descent | Video | ||
| 34 | Hyperplanes | Video | 11.9, A.4 | |
| 35 | Quadratic Program | Video | A.4 extensions | Homework 9 |
| 36 | Quadratic Program II | Video | B.1 - B.1.3 | |
| R11 | Recitation: Ordinary Differential Equations (ODEs) | Video | ||
| 37 | Complex Numbers | Video | B.1.4 | |
| 38 | Eigenvalues & Eigenvectors | Video | B.1.4 - B.1.5 | |
| 39 | Final class & convolution | Video | Not yet in book. | Project 3 |
Students thoughts on the course for Fall 2020 can be read in the teaching evaluations.
- Chad Jenkins, Associate Director of Undergraduate Programs, Michigan Robotics
- Jessy Grizzle, Director, Michigan Robotics
- Maani Ghaffari, Assistant Professor, Naval and Marine Architecture, U-M
- Kira Biener
- Tribhi Kathuria
- Madhav Achar
- Fangtong (Miley) Liu
- Shaoxiong Yao
- Eva Mungai
- Bruce JK Huang
- Grant A. Gibson
- Oluwami Dosunmu-Ogunbi
- Lu Gan
- Ray Zhang