16-811: Math Fundamentals for Robotics, Fall 2015

Professor: Michael Erdmann (me at -nospam- cmu.edu)
Teaching Assistants:   Sankalp Arora  (asankalp -nospam- andrew.cmu.edu)
                                      Chung-Yao Chuang  (chungyac at -nospam- andrew.cmu.edu)
                                      Yen-Chia Hsu  (yenchiah at -nospam- cs.cmu.edu)
Location: HH B103 (Hamerschlag Hall)
Time: TR 3:00-4:20

Michael Erdmann's Office Hours: After class or by appointment (office is GHC 9203).
Sankalp Arora's Office Hours: TBA
Chung-Yao Chuang's Office Hours: TBA
Yen-Chia Hsu's Office Hours: TBA


Copies of (handwritten) lecture notes are available online here.


This course covers selected topics in applied mathematics, taken from the following list:
1. Solution of Linear Equations.
2. Polynomial Interpolation and Approximation.
3. Solution of Nonlinear Equations.
4. Roots of Polynomials, Resultants.
5. Approximation by Orthogonal Functions (includes Fourier series).
6. Integration of Ordinary Differential Equations.
7. Optimization.
8. Calculus of Variations (with applications to Mechanics).
9. Probability and Stochastic Processes (Markov chains).
10. Computational Geometry.
11. Differential Geometry.

Course Activity

This is a graduate course. You are thus expected to pursue ideas and topics discussed in this course on your own beyond the level of the lectures. My aim is to cover some of the easy early material quickly, then spend more detailed time on the later material. My goal throughout the course is to acquaint you with fundamental algorithms and mathematical reasoning, as well as give you some implementation experience.

The course grade will be determined by performance on assignments, participation in class, and a class project. Class assignments will entail solving some problems on paper or implementing some of the algorithms discussed in the course.

The term project should take about a month of work (40 hours). It should pursue a mathematical topic (such as a robotics project with a strong mathematical component) that is not otherwise covered in detail in the course. Ideally, the project should be connected to your research. If you are a first year graduate student, you should view the project as a springboard to research involvement. Project writeups should be 5 pages long. Project writeups are due at the end of the last presentation. Project presentations will occur near the end of the term, depending on room availabilities.


In order to pass this course you must do all the work required. That entails coming to class, submitting solutions for the assignments, and doing the project. You must submit a solution for every problem on an assignment by that assignment's due date. Assignments are graded on a "minus, check, plus" scale. You must receive a "check" or a "plus" on every assignment in order to pass the course. If you obtain a "minus" on an assignment, you may and must submit correct solutions by the resubmission deadline for that assignment, in order to try to raise your assignment grade to a "check". (The resubmission deadline is not an alternate deadline for the original assignment; you need to attempt every problem by the original deadline.) For the project, you should submit a project proposal, a project writeup, and present your project publicly (it remains to be determined whether we will have short talks or a poster session).


There is no required text for this course. The lecture material is available online (as scans of handwritten notes). The following is a suggested reading list. Much of the lecture material is taken from these books.
1. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C. Cambridge University Press. (Any edition.)

2. G. Strang. Introduction to Applied Mathematics. Wellesley-Cambridge Press. 1986.

3. G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins University Press. 1983.

4. S. D. Conte and C. de Boor. Elementary Numerical Analysis. Third edition. McGraw-Hill. 1980.

5. G. E. Forsythe, M. A. Malcolm, and C. B. Moler. Computer Methods for Mathematical Computations. Prentice-Hall. 1977.

6. D. G. Luenberger. Introduction to Linear and Nonlinear Programming. Addison-Wesley. 1973.

7. J.-C. Latombe, Robot Motion Planning, Kluwer Academic Publishers, Boston, 1991.

8. R. Weinstock. Calculus of Variations. Dover Publications. 1974. (Reprint of 1952 McGraw-Hill edition.)

9. R. Courant and D. Hilbert. Methods of Mathematical Physics. Volume I. John Wiley and Sons. 1989. (Reprint of 1953 Interscience edition.)

10. W. Feller. An Introduction to Probability Theory and Its Applications. Volume 1. Third edition. John Wiley and Sons. 1968.

11. F. P. Preparata and M. I. Shamos, Computational Geometry, Springer-Verlag, New York, 1985. (Corrected and expanded printing: 1988.)

12. B. O'Neill, Elementary Differential Geometry, Academic Press, New York, 1966. 2nd Edition: 1997.