Computational Linear Algebra is a first-semester, first-year undergraduate course that shows how mathematics and computation are unified for reasoning about data and making discoveries about the world.
The second iteration of the course ran in Fall 2021 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.
The entire course is available for the terms:
The links below are for the Fall 2021 term.
All lecture and lab videos are available on YouTube:
ROB 101 Fall 2021 videos
And lecture notes as well as recitation questions and answers are available.
Lab videos may also contain recitation sections.
The textbook, Notes for Computational Linear Algebra, continues to be updated.
Three main projects that accompany the course are available here.
Lecture | Topic | Youtube | Assignments due |
---|---|---|---|
1 | Introduction & Linear Equations | Video | |
L1 | Lab: Setting Up Julia | Video | |
2 | Matrices & Matrix Determinant | Video | |
L2 | Lab: Plotting in Julia | Video | |
3 | Determinant & Triangular Systems | Video | |
4 | Matrix Multiplication | Video | Homework 1 |
L3 | Lab: Intro to Algorithms | Video | |
5 | LU Factorization | Video | |
6 | LU Factorization II | Video | Homework 2 |
L4 | Lab: Intro to Functions | Video | |
7 | Matrix Transpose & Inverse & Vector Space R^n | Video | |
8 | Linear Independence | Video | Homework 3 |
9 | Linear Independence II | Video | |
10 | Linear Independence III | Video | Project 1 |
L5 | Lab: Linear Independence | Video | |
11 | Norm of a Vector & Least Squares | Video | |
12 | Subspaces | Video | Homework 4 |
L6 | Lab: Vector Space Fundamentals & Project 2 | Video | |
13 | Dot Product & Orthogonal Vectors | Video | |
14 | QR Factorization | Video | |
15 | Basis Vectors & Coordinates for Subspaces | Video | Homework 5 |
L7 | Lab: Graham-Schmidt & Subspaces | Video | |
16 | Eigen & Rank & Nullity of a Matrix | Video | |
17 | Roots of Nonlinear Equations & Bisection Algorithm | Video | Homework 6 |
L8 | Lab: Basis Vectors & Dimension | Video | |
18 | Bisection Algorithm & Newtown's Method | Video | |
19 | Partial Derivatives & Roots & Gradient & the Jacobian | Video | Homework 7 |
20 | Newton-Raphson Algorithm | Video | |
21 | Optimization & Gradient Descent | Video | Project 2 |
L9 | Lab: Optimization & Project 3 | Video | |
22 | Gradient Descent II | Video | |
23 | Affine Spaces | Video | Homework 8 |
24 | Hyperplanes & Quadratic Program | Video | |
25 | Soft Margin Classifier & Gaussian Support Vector Machine | Video | |
26 | Convolution | Video | Homework 9 & Project 3 |
Students thoughts on the course for Fall 2021 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
- John Pye
- Madhav Achar
- Fangtong (Miley) Liu
- Shaoxiong Yao
- Eva Mungai
- Bruce JK Huang
- Grant A. Gibson
- Oluwami Dosunmu-Ogunbi
- Lu Gan
- Ray Zhang