16-811: Math Fundamentals for Robotics


Here are scanned copies of my handwritten notes (as well as those of two former robograds who taught some of the lectures in the past).
The notes appear in chronological order.

Many thanks to Alexander Gutierrez, who scanned many of these notes while taking the course during Fall 2004.

  • Solving Linear Equations
  • Polynomial Approximations - Interpolation
  • Solution of Nonlinear Equations
  • Roots of Polynomials
  • Resultants and Elimination Theory
  • Approximation
  • Differential Equations
  • Optimization    (with thanks to Tamara Abell for her lecture notes on constrained optimization)
  • Calculus of Variations
  • Markov Chains    (with thanks to Yan-Bin Jia for his notes from the year he taught 16-811)
  • Two-Dimensional Configuration Space    (added Fall 2010; slides scanned in from a short course I gave at a workshop long ago)
  • Convex Hull    (added Fall 2010; these are just rough notes to myself, so apologies for poor handwriting and any errors)
  • Two-Dimensional Voronoi Diagram    (added Fall 2010; slides)
  • Differential Geometry: Frenet Frames and Surface Curvature    (added Fall 2017; again, originally just intended as notes to myself)
  • Caution: these notes were written a while ago. They form the basis for my lectures, but may contain some errors. I correct typos and other minor errors during lecture. And a lot of the pictures I draw to convey intuition are not in these notes; they occur to me while I am lecturing. On the flip side, I have been known to confuse myself while lecturing, especially after a long sleepless night. Moral: read the notes, come to lecture, and think!

    The following copyright applies to all these notes (with exception for the notes by Tamara Abell and Yan-Bin Jia, who each retain their own copyright):

    Copyright Michael Erdmann 1992, 2004, 2010, 2017, 2023

    These notes are not intended for widespread distribution. Of course, feel free to make copies for your own use. If you use these notes or any material derived from them, for instance in teaching another course, please give proper credit, along with a mention of my notes. Proper credit generally goes to one of the sources listed in the course bibliography. Thank you.

    Back to the webpage for 16-811