16-811 Mathematical Fundamentals for Robotics
Spring 1998

Instructor: Yan-Bin Jia (jia@cs.cmu.edu)
Students (CMU access only)
Location: Doherty Hall 1209
Time: TR 3:00-4:20
URL: http://www.cs.cmu.edu/~jia/16-811.html

Final Exam (Solutions)

Assignment 1 (Sample Solutions)

Assignment 2 (Sample Solutions)

Assignment 3 (Sample Solutions)

This course, originally developed by Mike Erdmann, covers selected topics in applied mathematics which have proven very useful in today's robotics research. This year I have expanded Mike's course syllabus in the past so that the current syllabus has more algorithmic flavor and covers twelve topics:

1. Polynomial Interpolation and Approximation
2. Solution of Nonlinear Equations
3. Roots of Polynomial, Resultants
4. Solution of Linear Equations
5. Approximation by Orthogonal Functions (including Fourier series)
6. Fast Fourier Transform
7. Integration of Ordinary Differential Equations
8. Optimization
9. Linear Programming
10. Calculus of Variations (with applications to Mechanics)
11. Dynamic Programming
12. Probability and Stochastic Processes (Markov chains)

Historical note. Linear programming and dynamic programming were taught in the two GSIA minicourses Linear Programming and Operations Research in Robotics, which used to constitute half of the math qualifier for the Robotics Ph.D. program in its very early years. I consider reintroducing some of these "old" topics to this year's course merely for their relevance to applications in robotics .

Course Activity

• A certain level of self-study expected.

  This is a graduate course. You are thus expected to pursue ideas and topics discussed in this course on you own beyond the level of the lectures.
  
  

• Occasional general assignments.

  Such assignments, for all students, will entail solving some problems on paper or implementing some of the algorithms discussed in the course.
  
  

• A final exam (no midterm).

  I have not decided on its form (in-class or take-home) yet.
  
  

Bibliography

• W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C. Cambridge University Press. 1988.

1. S. D. Conte and C. de Boor. Elementary Numerical Analysis. Third edition. McGraw-Hill. 1980. (on the reserve stack in E&S library.)
   
   
2. J. Stoer and R. Bulirsch. Introduction to Numerical Analysis. Second edition. Springer-Verlag. 1993.
   
   
3. D. G. Luenberger. Introduction to Linear and Nonlinear Programming . Addison-Wesley. 1973.
   
   
4. G. Strang. Introduction to Applied Mathematics. Wellesley-Cambridge Press. 1986.
   
   
5. R. Courant and D. Hilbert. Methods of Mathematical Physics. Volume I. John Wiley and Sons. 1989. (Reprint of 1953 Interscience edition.)
   
   
6. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. The MIT Press and McGraw-Hill. 1990.
   
   
7. William Feller. An Introduction to Probability Theory and Its Applications , Vol 1. John Wiley & Sons. 1968
   
   
8. R. Weinstock. Calculus of Variations. Dover Publications. 1974. (Reprint of 1952 McGraw-Hill edition.)
   
   
9. W. Yourgrau and S. Madelstam. Variational Principles in Dynamics and Quantum Theory . Dover Publications. 1979. (Reprint of a 1968 edition.)
   
   
10. G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins University Press. 1983.
    
    
11. G. E. Forsythe, M. A. Malcolm, and C. B. Moler. Computer Methods for Mathematical Computations. Prentice-Hall. 1977.
    
    
12. B. L. van der Waerden. Algebra. Volume I. Springer-Verlag. 1991.

Yan-Bin Jia