CS 205A
Mathematical Methods for Computer Vision, Robotics, and Graphics (Fall 2007)

Course Announcements

DateContents
2007-9-26Homework 1 has been posted
2007-10-1Jon's Office Hours have been posted
2007-10-04Homework 2, Review 2 has been posted
2007-10-04Nipun's Office Hours have been updated
2007-10-05Homework 1 solution has been posted
2007-10-08Homework 1 has been graded and is available for pickup.
2007-10-08Homework 3, Review 3 has been posted.
2007-10-15Homework 2 solution has been posted
2007-10-17Homework 2 has been graded and is available for pickup.
2007-10-18Homework 4, Review 4, another practice midterm have been posted.
2007-10-18Review 4 tomorrow will be just a question answer session.
2007-10-18There will be additional office hours on Monday, in Gates 200, from 4PM until 5PM
2007-10-19Homework 3 solution has been posted
2007-10-23Midterm 1 has been posted. SCPD students are supposed to submit this by tonight if they were unable to make it to the exam in class.
2007-10-26Homework 5 has been posted
2007-10-29Midterm 1 has been graded with an average score of 14.18 out of 20
2007-11-01Review 6, homework 6, homework 4 solutions have been posted
2007-11-02Homework 3 has been graded, Homework 5 solutions have been posted
2007-11-05Homework 4 has been graded
2007-11-09Review session notes, Homework 6 solutions, and Homework 7 have been posted
2007-11-18Homework 8 is posted, and is due 11/29/2007. Happy Thanksgiving break
2007-11-27Nipun's Office Hours have been updated
2007-11-28Final date has been updated
2007-11-29Homework 6 has been graded
2007-11-29Homework 9 has been posted
2007-12-03Another practice midterm has been posted
2007-12-04Lecture 19 has been posted

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

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

Useful Texts

Please note that the textbook is not required. However, it is an excellent resource (it was written by a Stanford graduate) and thus highly recommended.

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
Class 17
Class 18
Class 19

Discussion Session Notes

ClassDescription
Review 1Homework 1 hints and the method of normal equations
Review 2Homework 2 hints, fundamental subspaces
Review 3Homework 3 hints, eigenanalysis
Review 4Q/A session for midterm
Review 5Homework 5 hints, secant method, mean value theorem, metric tensors
Review 6Homework 6 hints, more norms, inner products
Review 7Homework 7 hints, matrix decompositions and subspace decompositions
Review 8Homework 8 hints, first order ODEs

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 which will be posted on Thursday at 11:59 PM. The homework is due the following Thursday by 11:59 PM, and solutions will be posted promptly at that time. Homework is considered late if it is not in the box at the time the solutions are posted to the webpage, and 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.

Homework
Homework 1 (Solution)
Homework 2 (Solution)
Homework 3 (Solution)
Homework 4 (last year midterm) (Solution)    (another practice midterm --not due)
Homework 5 (Solution)
Homework 6 (Solution)
Homework 7 (Solution)
Homework 8 (Solution)
Homework 9 (last year midterm)    (another practice midterm --not due)

Submission: Homework must be submitted physically in the bin outside Gates 210. If it is after hours and you cannot get onto the second floor of gates you can use your Student ID to get into the basement. There is a dropoff bin inside the Pup cluster. Please only use the bin in the pup cluster if it is after hours. You can also turn in homework the Thursday they are due in class.

No, we do not have a stapler that you can use. Don't even ask.

Homework is available for pickup in Gates 377 in the filing cabinet.

Examinations

There will be two in-class midterm examinations on October 23 (Class 9) and December 6 (Last Class). Additionally there will be an optional cumulative final on December 14th. If you choose not to take the final, your final exam grade will be determined by averaging your two midterm scores.

Exams
Midterm 1
Midterm 2

Grading

SectionProportion
Homework20%
Midterm Exam 120%
Midterm Exam 220%
Final Exam40%