16-811: Math Fundamentals for Robotics, Fall 2012
Professor: Michael Erdmann (me at -nospam- cmu.edu)
Debadeepta Dey (debadeep at -nospam- cs.cmu.edu)
Robbie Paolini (rpaolini at -nospam- cmu.edu)
Location: Wean Hall 5409
Time: TR 3:00-4:20
Michael Erdmann's Office Hours: After class or by appointment (office is GHC 9203).
Copies of (handwritten)
lecture notes are available online here.
Debadeepta Dey's Office Hours: Wednesdays, 10am, in EDSH 222.
Robbie Paolini's Office Hours: Mondays, 3pm, in NSH 4209.
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.
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
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 in detail 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.
Typical project writeups are 5-10 pages long. Projects are due the
last day of class. Project presentations will occur either during the
last few lectures or during the final exam period.
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
- 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,
- 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
- 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.