Mathematical Methods for Computer Vision, Robotics, and Graphics (Fall 2011)
Course Announcements
| Date | Contents |
|---|---|
| 2011-11-29 | Homework 9 (Last year's second midterm) has been posted and is due next Tuesday. |
| 2011-11-29 | Important: The second midterm will be on Dec. 8 (next Thursday)! |
| 2011-11-18 | Grades of homework 6 are uploaded. Two copies have no names on them. |
| 2011-11-15 | Homework 8 posted. |
| 2011-11-09 | Homework 7 posted. |
| 2011-11-03 | Midterm 1 Statistics posted. Review Session 6 posted. Class 8 and 12 notes updated. |
| 2011-11-01 | Midterm 1 Solutions posted. Homework 5 Solutions posted. Homework 6 posted. |
| 2011-10-31 | Midterm 1 has been graded. Check Coursework for grades. Midterms will be available for pickup tomorrow, in class. |
| 2011-10-26 | Coursework website has been set up for viewing grades. |
| 2011-10-26 | Class 11 notes posted. Review 5 notes posted. |
| 2011-10-25 | Midterm 1 was today. Homework 5 and Class 10 Notes have been posted. (Class 9 is the same as Class 10) |
| 2011-10-06 | Class 5 notes posted. Review 2 notes posted. |
| 2011-10-04 | Homework 2 Assigned - Due 10-11-2011. Homework_1 solution posted. |
| 2011-9-27 | Homework 1 Assigned - Due 10-04-2011. Office hours and discussion section times posted. |
| 2011-9-25 | Site Created |
Summary
This course will focus on the continuous mathematics used in computer science (and EE) with a particular emphasis on the issues associated with designing, implementing and/or using numerical algorithms to solve equations. An underlying theme concerns the approximation issues associated with using floating-point numbers (as opposed to integers) in numerical algorithms.
Staff
- Instructor
- Ron Fedkiw (fedkiw@cs.stanford.edu)
- Office: Gates 207
- Office hours: TBD, no homework questions
- Course Assistant
- Linhai Qiu (lqiu@stanford.edu)
- Office: Gates 209
- Office hours: Monday, 4:00PM - 6:00PM in Gates 209
- Course Assistant
- Rahul Sheth (rbsheth@stanford.edu)
- Office: Gates 210
- Office hours: Monday, 11:00AM - 1:00PM in Gates 210
Please refer all questions about course material and practices to the CAs before contacting Professor Fedkiw. If you have a question for the CAs, please make sure that it isn't answered on this webpage before contacting them. Also, please do not show up outside of scheduled office hours without first making an appointment. When emailing the CAs, make sure to include "CS205" somewhere in the subject of your message.
Meeting Times
- Class: Tuesday and Thursday, 9:30AM - 10:45AM in Hewlett 201
- Discussion: Friday, 11:00AM - 11:50AM in 370-370
Required Texts
- Scientific Computing: An Introductory Survey (2nd edn)
by Michael T. Heath, McGraw-Hill publishing, New York, 2002 (class textbook) (Amazon Link)
Useful Texts
- An Introduction to the Conjugate Gradient Method Without the Agonizing Pain (notes)
by Jonathan R. Shewchuk, August 1994 (http://www.cs.cmu.edu/~jrs/jrspapers.html)
Please note that you may be able to take the course without owning the textbook but you are still required to be able to access a copy if needed. It is also an excellent resource (it was written by a Stanford graduate) and thus highly recommended.
Class Notes
| Notes | |
|---|---|
| Class | |
| Class 1 - 09-27-2011 | |
| Class 2 - 09-29-2011 | |
| Class 3 - 10-04-2011 | |
| Class 4 - 10-06-2011 | |
| Class 5 - 10-11-2011 | |
| Class 6 - 10-13-2011 | |
| Class 7 - 10-18-2011 | |
| Class 8 - 10-20-2011 | |
| Class 9 - 10-25-2011 (Midterm 1) | |
| Class 10 - 10-27-2011 | |
| Class 11 - 11-01-2011 | |
| Class 12 - 11-03-2011 | |
| Class 13 - 11-08-2011 | |
| Class 14 - 11-10-2011 | |
| Class 15 - 11-15-2011 | |
| Class 16 - 11-17-2011 | |
| Class 17 - 11-29-2011 | |
| Class 18 - 12-01-2011 | |
| Class 19 - 12-06-2011 | |
| Class 20 - 12-08-2011 (Midterm 2) | |
Old Class Notes
| Notes | |
|---|---|
| Class | |
| Class 1 | |
| Class 2 | |
| Class 3 | |
| Class 4 | |
| Class 5 | |
| Class 6 | |
| Class 7 | |
| Class 8 | |
| Class 9 | |
| Class 10 | |
| Class 11 | |
| Class 12 | |
| Class 13 | |
| Class 14 | |
| Class 15 | |
| Class 16 | |
Discussion Session Notes
| Class |
|---|
| Review 1 - 09-30-2011 |
| Review 2 - 10-07-2011 |
| Review 3 - 10-14-2011 |
| Review 4 - 10-21-2011 - Midterm 1 Review |
| Review 5 - 10-28-2011 |
| Review 6 - 11-04-2011 |
| Review 7 - 11-11-2011 |
| Review 8 - 11-18-2011 |
| Review 9 - 12-02-2011 - Midterm 2 Review |
Tentative Schedule
| Topic | Estimated Length |
|---|---|
| Sources and measure of numerical errors. Accuracy and stability of numerical calculations |
1 class |
| Linear Systems. Existence and uniqueness of a solution. Gaussian elimination and LU factorization. Pivoting. |
1 1/2 classes |
| Matrix norms and condition number | 1/2 class |
| Cholesky factorization | 1/2 class |
| Overconstrained systems. Normal Equations | 1/2 class |
| QR factorization. Gram-Schmidt orthonormalization. Householder transform |
1 class |
| Eigenvalue problems. Characteristic Polynomial. Similarity transforms. Jordan forms. Power Method | 1 1/2 classes |
| Singular Value Decomposition | 1/2 classes |
| Nonlinear equations. Fixed point iteration. Newton, secant and bisection methods. Convergence rate. Systems of nonlinear equations. | 1 1/2 classes |
| Unconstrained optimization. Golden section search. Newton iteration. Steepest descent method. | 1 class |
| Conjugate Gradients Method | 2 1/2 classes |
| Preconditioning | 1/2 class |
| Constrained optimization. Lagrange multipliers | 1/2 class |
| Function interpolation. Polynomial interpolants. Lagrange and Newton interpolation. Splines | 1 class |
| Numerical quadrature. Newton-Cotes and Gaussian quadrature. | 1/2 class |
| Initial value ODE problems. Stability and accuracy. | 1/2 class |
| Forward and Backward Euler, Trapezoidal Rule. Runge-Kutta, TVD and multistep methods. | 1 class |
| Newmark integrators. Staggered position/velocity grids. | 1 class |
| Boundary value PDE problems. Discretization and solution of the Laplace Equation. The Heat Equation. CFL condition and stability. | 1 class |
Assignments
There will be a problem set assigned each week. The homework is due the following Tuesday, and solutions will be posted promptly at that time. Late homework will receive no credit, with absolutely no exceptions.
Homework will be graded in coarse, half-point increments between 0 and 2 points. A sample midterm will be assigned in lieu of normal problems the week before each midterm and graded coarsely out of 3 points.
You may collaborate on homework assignments provided each student writes up his or her own solutions and clearly lists the names of all the students in the group.
Submission:
Homework must be submitted by the beginning of each Tuesday's class, in one of three ways:
1) On the desk in front of class (Tuesday only)
2) In the dropbox outside Gates 209 - NOT the pickup box outside 210 (Anytime)
3) Via Coursework drop box (Anytime)
We do not give any homework extensions, but you can hand assignments in late for no credit. We will grade them, and record the grades for future reference. If your final class grade is borderline between two grades, we may take a single late homework into account. It is highly unlikely that we would ever consider more than one late homework, however.
Note: If submitting electronically, please request a confirmation. If you do not receive a confirmation message from either CA before class starts, your submission will not count.
Graded Homework Pickup:
1) In class of Tuesday of the following week after submitting the homework.
2) The box outside Gates 210. On the box, it says "graded homework pickup".
Examinations
There will be two in-class midterm examinations on October 25th and December 8th. Additionally there will be an optional cumulative final. If you choose not to take the final, your final exam grade will be determined by averaging your two midterm scores. All exams are closed book and closed notes.
SVD: You are not required to know algorithms for finding the SVD of an arbitrarily complex matrix, but should be able to find the SVD for simple matrices such as those on the practice midterm. Keep in mind that the singular values of A are the square-roots of the eigenvalues of A^T A or A A^T. More generally, the columns of U and V are the eigenvectors of A A^T and A^T A, respectively.
| Midterms |
|---|
| Midterm 1 - 10-25-2011 |
| Midterm 1 Solutions |
| Midterm 2 - 12-08-2011 |
Midterm 1 Statistics
Mean: 25 Median: 26 Mode: 22
Grading
| Section | Proportion |
|---|---|
| Homework | 20% |
| Midterm Exam 1 | 20% |
| Midterm Exam 2 | 20% |
| Final Exam | 40% |
The Final Exam is optional. If you choose not to take the final exam, your final grade will be computed from Homework (20%), Midterm Exam 1 (40%) and Midterm Exam 2 (40%).