# Spring 2022 - MATH 232 D100

## Overview

• #### Course Times + Location:

Mo, We, Fr 11:30 AM – 12:20 PM
SSCC 9001, Burnaby

• #### Exam Times + Location:

Apr 20, 2022
7:00 PM – 10:00 PM
GYM CENTRAL, Burnaby

• #### Prerequisites:

MATH 150 or 151 or MACM 101, with a minimum grade of C-; 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 may not take this course for further credit. Quantitative.

#### COURSE DETAILS:

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.
• Roots of quadratic polynomials.
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

•  Midterm(s): synchronous; date: TBA
•  Final exam: synchronous; date: TBA

## Grading

• Quizzes (5, every other week, 15 min in length, not during midterm weeks) 15%
• Computing Assignments (5, every other week, not during midterm weeks) 15%
• Midterms (2, 15% each) 30%
• 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

#### REQUIRED READING:

An Introduction to Linear Algebra
Daniel Norman and Dan Wolczuk
3rd Edition
Pearson
ISBN: 987-0-13-468263-1

#### RECOMMENDED READING:

Supplemental book (downloaded as a free .pdf):

Introduction to Applied Linear Algebra Vectors, Matrices, and Least Squares
Stephen Boyd and Lieven Vandenberghe

ISBN: 978-1-316-51896-0

#### Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

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 2022

Teaching at SFU in spring 2022 will involve primarily in-person instruction, with safety plans in place.  Some courses will still be offered through remote methods, and if so, this will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware 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.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the spring 2022 term.