Spring 2022 - MATH 240 D100

Algebra I: Linear Algebra (3)

Class Number: 6545

Delivery Method: In Person

Overview

  • Course Times + Location:

    Mo, We, Fr 11:30 AM – 12:20 PM
    AQ 3149, Burnaby

  • Exam Times + Location:

    Apr 20, 2022
    7:00 PM – 10:00 PM
    WMC 3260, 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. Real and abstract vector spaces, subspaces and linear transformations; basis and change of basis. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. Applications. Subject is presented with an abstract emphasis and includes proofs of the basic theorems. Students with credit for MATH 232 cannot take this course for further credit. Quantitative.

COURSE DETAILS:

Linear Equations

  • Systems of Linear Equations, Row Reduction and Echelon Form
  • Vectors, Vector Equations, Matrices
  • The Matrix Equation Ax=b
  • Solution Sets of Linear Systems
  • Matrix Inverse
  • Linear Independence, Rank and Dimension
  • Introduction to Linear Transformations
  • The Matrix of a Linear Transformation
Vector Spaces
  • Vector Spaces and Subspaces
  • Null Spaces, Column Spaces, and Linear Transformations
  • Linearly Independent Sets; Bases for Subspaces
  • Coordinate Systems
  • The Dimension of a Vector Space
  • Change of Basis
Determinants
  • Determinants and their Properties
  • Cramer's Rule
Complex Numbers
  • Arithmetic in Cartesian Co-ordinates
  • The Complex Plane,Complex Conjugate, and Magnitude
  • Polar Form, De Moivre's Formula and Euler's Formula
  • Roots of Quadratic Polynomials
Eigenvalues and Eigenvectors
  • Complex Eigenvalues
  • The Characteristic Equation
  • Diagonalization
  • Eigenvectors and Linear Transformations
  • Application: The Leslie Age Distribution model
Orthogonality and Least Squares
  • Inner Product, Length and Orthogonality
  • Orthogonal Sets
  • Orthogonal Projections
  • The Gram-Schmidt Process
  • Application: Least Squares Problems

Grading

  • Quizzes 10%
  • Hand-In Proofs 10%
  • Midterm 1 15%
  • Midterm 2 15%
  • Final Exam 50%

Materials

REQUIRED READING:

Linear Algebra and Its Applications
5/E
Lay, Steven R.; Lay, David C.; McDonald, Judith; McDonald, Judi J.
Pearson Education
ISBN: 9780321982384

RECOMMENDED READING:

Linear Algebra
Jim Hefferon
Orthogonal Publishing L3c; 3rd ed. edition (Jan. 1 2017)
https://hefferon.net/linearalgebra/
ISBN: 978-1944325039

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.