Instructor: Dr. Bartosz Protas
Office: HH 326, Ext. 24116
Office hours: 13:30-14:30 on Tuesdays and Thursdays
Teaching Assistant: Masahiro Oishi
Email: oishim_AT_mcmaster_DOT_ca
Office: ITB 115
Office hours: 12:30-13:30 on Tuesdays
Announcements:
Outline of the Course:
The main focus of this course will be on the use of numerical computation to solve problems in linear algebra. Following an introduction to MATLAB, we will discuss relevant properties of the finite-precision arithmetic. Then we will introduce various techniques, both direct and iterative, for efficient solution of systems of linear equation. We will also study numerical computation of eigenvalues and eigenvectors, as well as some other useful decompositions and factorizations. In addition to discussing theoretical aspects such as conditioning, computational complexity and convergence, for every problem we will also present an implementation of the actual solution method using MATLAB. As a motivation, we will be using examples taken from various areas of numerical mathematics complemented with some ideas from abstract algebra.Topics:
Dates |
Topics |
Chapters from the textbook |
Jan 7 - Jan 24 |
introduction, MATLAB, finite-precision arithmetic |
1 |
Jan 28 - Feb 28 |
review of linear algebra, linear systems, direct and iterative solution methods |
2 |
Mar 3 - Mar 20 |
orthogonal projections, QR factorizations |
3 |
Mar 24 - Apr 8 |
eigenvalues and eigenvectors, singular value decomposition |
4 |
Course Objectives:
By the end of the course students should be able to develop MATLAB codes for the numerical solution of some standard problems in linear algebra.Primary Reference:
Supplemental Reference:
Software:
All of the computational examples will be presented using MATLAB. This software is available on the computers in the computer lab. Lab hours (see above) are reserved for unsupervised work with computer-based assignments. Unless they are reserved for large-class tutorials, students should be able to work in the computer labs in BSB also outside the allocated time-slots. Students are as well encouraged to purchase The Student Edition of MATLAB to be able to work with MATLAB at home.Prerequisites:
Linear Algebra II (MATH2R03)Assignments:
Five homework assignments will be posted on the course website on the dates indicated in the table below. The assignments will be due by midnight on Tuesday the following week. Solutions of the assignments should be submitted by e-mail to math2t03_AT_math_DOT_mcmaster_DOT_ca using the template provided. Late submissions will not be accepted. Only four best assignments are counted towards the final mark. The assignments and solutions will be posted on the course webpage.Homework Post & Due Dates:
# |
Post Date |
Due Date |
HW 1 |
January 22 |
January 29 |
HW 2 |
February 5 |
February 12 |
HW 3 |
February 26 |
March 4 |
HW 4 |
March 18 |
March 25 |
HW 5 |
April 1 |
April 8 |
Class Quizzes:
There will be two in-class quizzes on February 5 and March 18 in T29-101. They will last 50 minutes and will cover analytical issues only (no programming). Only the McMaster standard calculator Casio fx-991 will be allowed during the quizzes.Final Exam:
The course will be completed by a three-hour final examination. The date and location of the final exam will be announced by the Registrar's office in mid-term.Marking Scheme:
Excused Absences:
Exemptions from the assignments or tests for valid reasons are possible, but must be requested through the office of the Associate Dean of the Faculty that you are registered with. In the event of an exemption, no make up test or assignment will be administered, but your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or assignment.Academic Integrity:
You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.Important Notice:
The instructor reserves the right to modify elements of the course and will notify students accordingly (in class and post any changes to the course website).