CMPUT 499/609: Honours Numerical Analysis
New course alternatives in numerical methods: cmput340 or cmput499
To account for the diverse interests and varying mathematical skills of students, we have split our numerical methods course, and now offer it in a regular and an honours version.In the basic course the focus is on how to use numerical methods to solve real world mathematical problems. It builds on your linear algebra and calculus courses, and combines math with algorithms into scientific problems solving.
In the honours version, the focus is also on solving real world problems numerically, but we will also study more about mathematical properties of numerical methods, how they interrelate and how to derive them. The course is especially helpful for those interested in mathematics intensive areas such as machine learning, imaging and vision, robotics etc, or for anyone planning to pursue graduate studies.
In a nutshell, the difference between the regular and honours version could be summarized as: In the regular course you learn recipes for solving problems. In the honours version you also learn enough to compose your own recipes, and gain a deeper understanding of how the different numerical methods relate. In short a better understanding of the whole, not just the pieces.
Course Outline
General Information
Term: Fall 2007
Date and Time: Tue, Thu 3:30PM-4:50PM
Location: CSC B10
Optional seminar: Wed 9:00AM-9:50AM, DP 2099
Number of credits: 3 credits
Contact
Instructor: Martin Jagersand
Office: ATH 401
E-mail: c499@ugrad.cs.ualberta.ca
Office Hours: after class
Teaching Assistant:
Parisa Mosayebi
mosayebi @ cs.ualberta.ca
Baidya Saha
baidya @ cs.ualberta.ca
Newsgroup: CMPUT
499 Newsgroup
Mailing List: c499@ugrad.cs.ualberta.ca
View more contact information.
Overview
Some of the most challenging computing problems involve the numerical calculation of solutions to problems from continuous mathematics. Examples include predicting the weather, simulating the space shuttle's reentry into the atmosphere, calculating the strengths of structures (bridges, houses, airplanes etc).
Three main goals in this course are
- (1) to learn how to go from a real world problem to a mathematical model,
- (2) to learn about methods and algorithms to compute numerical solutions to mathematical problems and
- (3) how to analyze the errors in numerical computation.
Objectives
To obtain a working knowledge of how to apply numerical methods to real-world problems and a basic understanding of the mathematics and properties of these methods.
Pre-requisites
We recommend that you take the better quality linear algebra (ie math 125, or 120+225), and the honours math (math 117 and 118). You will also be assumed to know a bit about integration and differential equations. 214 (and 215) or the corresponding honours courses are recommended. That said, while this course does depend on the fundamentals of linear algebra and calculus, most important is a level of mathematical maturity coming more from practice than from any one particular course.
If you are not sure whether you can take this honours version or the regular cmput340, you can sit in on both, or you can start with this one and if it is not right for you, switch to 340 (before the deadline).
Course Topics
Numerical Computing basics Numerical representations, Computational accuracy and stability, software and hardware for numerical computing.
Linear Equations Some real world applications and motivations, Gauss and Gauss-Jordan Elimination, LU factorization, Sensitivity and Conditioning, Overdetermined systems and Linear Least Squares, Linear Regression, Data Fitting and Interpolation, Eigenvalue Problems.
Nonlinear Equations and Optimization Basic 1D search methods with and without derivatives. Convergence rates and stopping criteria, Multidimensional root finding. Conditions for extrema, local and global min and max. Unconstrained optimization. Constrained optimization, Comparison of root finding and optimization, Trust region methods, Homotopy methods and Embeddings.
Numerical Integration and Differentiation Numerical Quadrature, Numerical Differentiation, Richardson Extrapolation.
Differential Equations Numerical methods for ODE's, Boundary Value problems and the shooting method, Intro to PDE's, finite difference and finite element methods.
Course Work and Evaluation
| Course Work | Date | Weight |
|---|---|---|
| Exam 1 | Tue Oct 16 | 24% |
| Exam 2 | Tue Dec 4 | 24% |
| Written assignments (4) | see schedule | 24% (6% each) |
| Lab assignments (4) | see schedule | 28% (6-8% each) |
| Project: Optional | - | substitute one/more labs/assignments |
See the course schedule for specific information, assignments and dates for course work.
Grading System
A note on grading. Some students think that taking a more challenging course will mean they likely get a lower grade. However, just as in the math honours courses grading will be fair over courses. Grading is absolute, based on your what you have learned, and not on a curve compared to your classmates.
Course Materials
-
Michael T. Heath:
Scientific Computing. An Introductory Survey,
2nd Ed McGraw Hill 2002
Heath provides a mathematically careful treatment of core topics.
-
(Optional) W. Press, S. Teukolsky, W.Vetterling and B. Flannery.
Numerical Recipes in C Cambridge University Press, 1996.
A standard reference for scientists and engineers, Numerical Recipes contains both methods and algorithms implemented in C.
In addition, the core topics in the course are covered in most books on Numerical Analysis (call number QA 297) or on Scientific Computing (call number QA 183) such as:
- Schilling, R. and Harris, S.(2000) Applied Numerical Methods for Engineers. Brooks/Cole Publishing.
- Borse, G.(1997) Numerical Methods with MATLAB, ITP Books.
- Cheney, W. and Kincaid, D.(1999) Numerical Mathemetics and Computing(4th Ed.). ITP Books.
- Alfio Quarteroni, Riccardo Sacco and Fausto Saleri: Numerical MathematicsSpringer Verlag, 2000.
Policy
Course Outlines
Policy about course outlines can be found in Section 23.4(2) of the University Calendar.
Academic Integrity
The University of Alberta is committed to the highest standards of academic integrity and honesty. Students are expected to be familiar with these standards regarding academic honesty and to uphold the policies of the University in this respect. Students are particularly urged to familiarize themselves with the provisions of the Code of Student Behaviour (online at www.ualberta.ca/secretariat/appeals.htm) and avoid any behaviour which could potentially result in suspicions of cheating, plagiarism, misrepresentation of facts and/or participation in an offence. Academic dishonesty is a serious offence and can result in suspension or expulsion from the University. (GFC 29 SEP 2003)
Collaboration
Assignmnets and labs are expected to be done indivitualy.
University Policies
The University of Alberta policies inlcude, but are not limited to, the following:
