16-811: Math Fundamentals for Robotics, Fall 2003

Instructor: Michael Erdmann (me@cs.cmu.edu)
TA: Gita Sukthankar (gitars@ri.cmu.edu)
Location: Doherty Hall 1217
Time: TR 3:00-4:20

TA Office Hours: Wednesday, 3-5pm, Newell-Simon 1604A, phone x8-8283

Assignments

Topics

1. Polynomial Interpolation and Approximation.

2. Solution of Nonlinear Equations.

3. Roots of Polynomials, Resultants.

4. Solution of Linear Equations.

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 Computational and Differential Geometry topics are recent additions to the course. That material used to be part of a separate course on geometry which is no longer offered.

The course grade will be determined by performance on assignments, participation in class, and possibly some quizzes. Assignments will be of two types: First, there will be occasional general assignments for all. Such assignments will entail solving some problems on paper or implementing some of the algorithms discussed in the course. Second, from time to time I will assign specific problems to each of you individually. These problems will range from simple elucidation of confusing points in the lectures to independent pursuit of some subtopics. You will be expected to write up your solution within a week or so. I will make copies of your writeup and distribute those to the entire class. (You should write up at least one such assignment during the course of the term.)

Bibliography

• W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C. Cambridge University Press. 2nd Edition, 1992.

Secondary references include (in approximate order of the material covered):

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

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

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

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

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

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

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

8. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer-Verlag, Berlin, 1987.

9. W. M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, New York, 1975.

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

11. M. Spivak, Differential Geometry, Publish or Perish, Berkeley, 1979.

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

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

14. W. Yourgrau and S. Madelstam. Variational Principles in Dynamics and Quantum Theory. Dover Publications. 1979. (Reprint of a 1968 edition.)