# Spring 2021 - MATH 232 D200

## Overview

• #### Course Times + Location:

Mo, We, Fr 1:30 PM – 2:20 PM
REMOTE LEARNING, Burnaby

• #### Exam Times + Location:

Apr 20, 2021
3:30 PM – 6:30 PM
REMOTE LEARNING, Burnaby

• #### Instructor:

Seyyed Aliasghar Hosseini
sahossei@sfu.ca
• #### Prerequisites:

MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B.

## Description

#### CALENDAR DESCRIPTION:

Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations. Students with credit for MATH 240 make not take this course for further credit. Quantitative.

#### COURSE DETAILS:

This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

Topics Outline:
Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations.

Topic Details:

Vectors
• Vectors in Euclidean n-Space
• Dot Product and Orthogonality
• Lines and Planes
Systems of Linear Equations
• Row Reduction (Gaussian elimination) to Echelon form
• The Geometry of Linear Systems
• Applications in business, science and engineering
Matrices
• Matrix operations
• Matrix inverse; and properties of matrices
• Elementary matrices and calculating matrix inverses
• Matrices with special forms.
Linear Transformations
• Matrices as transformations
• Geometry of Linear Transformations
• Kernel and range
• Composition and Invertibility
• Application to Computer Graphics (optional)
Determinants
• Calculating determinants
• Properties of determinants
• Cramer's rule (optional)
Complex Numbers
• Arithmetic in Cartesian co-ordinates.
• The complex plane, complex conjugate, magnitude and argument (phase).
• Polar form, De Moivre's formula and Euler's formula.
Eigenvalues and Eigenvectors
• Properties and geometry
• Complex eigenvalues and complex eigenvectors
• Dynamical Systems and Markov Chains
• Application to Economics: the Leontief model (optional)
• The Power Method; Application to Internet Search Engines
• Matrix Similarity and Diagonalization
Subspaces of R^n
• Subspaces and Linear Independence
• Basis and Dimension
• The Fundamental Spaces of a Matrix
• Rank
• Change of basis
Orthogonality
• Projection
• Orthogonal bases and the Gram Schmidt process
• Orthogonal matrices (optional)
• Application to least squares approximation

#### Course Delivery

•  Lecture: synchronous- lectures will be held at fixed times, on-line
•  Midterm(s): synchronous; date: TBA
•  Final exam: synchronous; date: TBA

• Online Assignments 15%
• Quizzes 20%
• Midterm 1 25%
• Final Exam 40%

#### 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.

## Materials

#### MATERIALS + SUPPLIES:

Möbius Assessment account for online assignments (register through Canvas with SFU computing ID).

Required:

• Ability to scan documents (phone app acceptable)

Contemporary Linear Algebra
Howard Anton and Robert C. Busby
Wiley
ISBN: 9780471163626

OR

As an e-text available for purchase through Vitalsource (ISBN 9780471782834) here:
https://www.vitalsource.com/en-ca/products/contemporary-linear-algebra-howard-anton-robert-c-busby-v9780471782834

#### Registrar Notes:

SFU’s Academic Integrity web site 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

TEACHING AT SFU IN SPRING 2021

Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).