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Robotics 501: Mathematics for Robotics

ROB 501: Mathematics for Robotics, is a graduate-level course at the University of Michigan that introduces applied mathematics for robotics engineers.

Topics include vector spaces, orthogonal bases, projection theorem, least squares, matrix factorizations, Kalman filter and underlying probabilistic concepts, norms, convergent sequences, contraction mappings, Newton Raphson algorithm, local vs global convergence in nonlinear optimization, convexity, linear and quadratic programs.

This offering of the course is from Fall 2018.


It is assumed that students know basic matrix algebra, such as how to multiply and invert matrices, what is the rank of a matrix, and how to compute eigenvectors; know how to compute means and variances given a density of a continuous random variable, and conditional probability and how to compute it; know vector calculus and will review how to compute gradients of functions and what is the method of Lagrange multipliers; simple properties of complex numbers; and how to use MATLAB, including plotting, various types of multiplication, such as * vs .* (star vs dot star), writing a for loop, or finding help.

Lecture Videos, Textbook & Notes

All lecture videos are available on YouTube:
ROB 501 Fall 2018 videos

Also, the textbook, lecture notes and handouts are available.


Recitation questions and answers are both available.

Course Plan

Lecture Topic YouTube Assignments Due
1 Intro & Proofs Video
2 Induction, Fundamental Theorem, & Contradiction Video
3 Abstract Linear Algebra Video
4 Subspaces & Linear Independence Video Homework 1
5 Basis Vectors & Dimension Video
6 Linear Operators & Eigenvalues Video Homework 2
7 Similar Matrices & Norms Video
8 Inner Product Spaces Video Homework 3
9 Projection Theorem & Gram-Schmidt Video
10 Normal Equations & Least Squares Video Homework 4
11 Symmetric & Orthogonal Matrices Video
12 Positive Semi-Definite Matrices & Schur Complement Theorem Video Homework 5
13 Recursive Least Squares & Kalman Filter Video
14 Least Squares & Probability Video
15 Best Linear Unbiased Estimator Video Homework 6
16 QR Factorization Video Exam 1
17 Modified Gram-Schmidt & Minimum Variance Estimator Video
18 Probability Space & Random Variables Video
19 Gaussian Random Vectors Video Homework 7
20 Real Analysis & Normed Spaces Video
21 Real Analysis & Interior of a Set Video Homework 8
22 Newton-Raphson Algorithm Video
23 Cauchy Sequences Video Homework 9
24 Continuous Functions Video
25 Weierstrass Theorem Video
26 Final Class & Linear Programming Video Homework 10 & Exam 2

A more detailed course plan is available.


  • Jessy Grizzle, Director, Michigan Robotics
  • Nils Smit-Anseeuw


All code is licensed under the GNU General Public License v3.0.

All other content, including textbooks, homeworks, and video, is licensed under the Creative Commons Attribution-NonCommericial 4.0 (CC BY-NC 4.0).

For more