CMPUT 340 Winter 2022: Introduction to Numerical Methods

course webpage for previous years

Schedule

Syllabus

Class Date and Time:

Tue-Thu 12:30-1:50pm (CSC B-10)

Zoom link

Labs:

Tue 5-7:50pm (CSC 1-59)
Thu 2:00-4:50pm (BUS 2-09)

Instructor

Rupam Mahmood

Teaching Assistants

Junaid Ahmad
Javier Carlos Sales-Ortiz
Jeramy Luo
Esraa Elelimy

Course Description

There are many mathematical problems in linear equations, non-linear equations, optimization, interpolation, approximation, and integration that are useful in the study of different computational fields such as machine learning, computer graphics, vision, and robotics. In this course, we cover the problem formulations involving these topics and computational solutions to these problems, often known as numerical methods. En route, we cover the basics of computer arithmetic and errors.

Objectives

To obtain a working knowledge of how to apply numerical methods to real-world problems and a thorough understanding of the mathematics and properties of these methods.

Prerequisites

• CMPUT 204 (Algorithms 1) or 275 (Introduction to Tangible Computing II);
• MATH 125 (Linear Algebra 1), 214 (Intermediate Calculus I);
• one of STAT 141 (Introduction to Statistics), 151 (Introduction to Applied Statistics I), 235 (Introductory Statistics for Engineering) or 265 (Statistics I), or SCI 151 (Introduction to Applied Statistics I).

It is important to prepare yourself for this course through a review of the prerequisite material. Students who do not have the required prerequisites at the time of taking this course should not expect supplementary professorial tutoring from the instructor.

Course Topics

• Numerical Computing basics: Numerical representations, Computational accuracy and stability, forward and backward error analysis, software and hardware for numerical computing.
• Linear Equations: Some real-world applications and motivations, Systems of linear equations and LU factorization, Sensitivity and Conditioning, Overdetermined systems, Linear Least Squares, methods for QR factorization, Linear Regression, Data Fitting and Interpolation, Eigenvalue Problems, methods for Eigen and SVD factorizations.
• Nonlinear Equations and Optimization: Basic 1D search methods with and without derivatives. Convergence rates and stopping criteria, Multidimensional root finding, Newton and Gauss-Newtons methods. Conditions for extrema, local and global min and max. Unconstrained optimization.
• Numerical Quadrature (Integration) and Differentiation: Numerical Quadrature, Numerical Differentiation, Richardson Extrapolation.
• Numerical solution of Differential Equations: Initial value problems, boundary value problems, partial differential equations.

Course Evaluation

• Midterm exam 16%
• Final exam 20%
• Assignments (4) 8% each
• Labs (4) 8% each
• Participation bonus: 5% (class and slack discussion)
• Project (replaces an assignment or a lab)

Course Materials

Michael T. Heath: Scientific Computing. An Introductory Survey, 2nd Edition.

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 Behavior (online at www.governance.ualberta.ca) and avoid any behavior which could potentially result in suspicions of cheating, plagiarism, misrepresentation of facts, and/or participation in an offense. Academic dishonesty is a serious offense and can result in suspension or expulsion from the University.”

All forms of academic dishonesty are unacceptable at the University. Any suspected offense will be reported to the Faculty of Science. Anyone who is found in violation of the Code of Student Behavior may receive a sanction. Typical sanctions include conduct probation, a mark reduction or a mark of 0 on an assessment, a grade reduction or a grade of F in a course, a remark on the transcript, and a recommendation for suspension or expulsion.