Simon Fraser University
Engaging the World

Course Outlines

Fall 2022 - APMA 920 G100

Numerical Linear Algebra (4)

Class Number: 4095

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 7 – Dec 6, 2022: Tue, Thu, 2:30–4:20 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Conditioning and stability of numerical methods for the solution of linear systems, direct factorization and iterative methods, least squares, and eigenvalue problems. Applications and mathematical software.

COURSE DETAILS:





This is a foundational course in which you'll be introduced to core ideas in numerical linear algebra: how to factor matrices to reveal important structure, computing solutions of least squares problems, and uncovering spectral properties.  Linear algebra - and numerical algorithms for linear algebra - are very important in data science. We'll perhaps see why. 

Syllabus:
Review of matrix analysis concepts: range, nullspace, unitary and Hermitian matrices, norms
SVD and the 4 fundamental subspaces, lower-rank approximation
QR and the Gram Schmidt process, 
Triangularization: Householder reflections,  Givens rotations
Conditioning, accuracy and stability
LU factorization, least squares
Krylov subspaces
Eigenvalue iterative methods


Prerequisites:

Undergraduate courses in Linear Algebra and Numerical Analysis. Programming experience. Working knowledge of MATLAB or SciPy/NumPy (MATLAB may prove easiest.

Grading

  • Homework 45%
  • Project & Presentation 25%
  • Final Exam 30%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient). 

Materials

MATERIALS + SUPPLIES:

There is no required textbook, but there are strongly recommended books:
 
   - Numerical Linear Algebra, Trefethen & Bau, SIAM 1997 [or 2022, take your pick!]
    - Linear Algebra and Learning from Data, Gil Strang, Wellesley-Cambridge 2019
 
Please be prepared to take notes in class! Modulo pandemic-related issues, this course meets in person. 

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html