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Linear Algebra

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Prerequisites: Qualifying math score and completion of Calculus BC or equivalent

Course Format: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: One full year of high school credit equal to or greater than an AP class or one semester of college credit

Course Code: LIN

Course Description

Description

Linear Algebra is an online and individually-paced course equivalent to a first-year college linear algebra course. This course covers the entire syllabus from the Johns Hopkins semester-based, in-person Linear Algebra course, plus several additional topics. Computer based interactives, homeworks and quizzes help to reinforce concepts taught in the class. Projects covering advanced applications will introduce students to mathematical typesetting with LaTeX. Online course materials supplement the required textbook.

Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructor via email with any questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well to prepare for the graded assessments, which include quizzes, homework, midterm exams, and a cumulative final. Instructors use virtual classroom software allowing video, voice, text, screen sharing and whiteboard interaction.

Topics include:

  • Linear Equations
  • Matrix Algebra
  • Determinants
  • Vector Spaces
  • Eigenvalues
  • Orthogonality
  • Least Squares
  • Symmetric Matrices
  • Quadratic Forms

For a detailed list of topics, click the "List of Topics" tab.

Image of Linear Algebra banner.

 

Materials Needed

A textbook purchase is required for this course.

Linear Algebra and its Applications, 4th edition, by David C. Lay.

ISBN 13: 978-0-321-38517-8

Linear Algebra textbook

List of Topics

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

Linear Equations in Linear Algebra

  • Systems of Linear Equations
  • Row Reduction and Echelon Form
  • Vector Equations
  • The Matrix Equation Ax->=b->
  • Solution Sets of Linear Systems
  • Applications of Linear Systems
  • Linear Independence
  • Introduction to Linear Transformations
  • The Matrix of a Linear Transformation

Matrix Algebra

  • Matrix Operations
  • The Inverse of a Matrix
  • Characterizations of Invertible Matrices
  • Subspaces of Rn
  • Dimension and Rank

Determinants

  • Introduction to Determinants
  • Properties of Determinants
  • Cramer's Rule, Volume, and Linear Transformations

Eigenvalues and Eigenvectors

  • Eigenvalues and Eigenvectors
  • The Characteristic Equation    
  • Diagonalization    
  • Eigenvalues and Linear Transformations    
  • Complex Eigenvalues    
  • Discrete Dynamical Systems

Vector Spaces

  • Vector Spaces and Subspaces
  • Null Spaces, Column Spaces, and Linear Transformations
  • Linearly Independent Sets; Bases
  • Coordinate Systems
  • The Dimension of a Vector Space
  • Rank
  • Change of Basis
  • Applications to Difference Equations
  • Applications to Markov Chains

Orthogonality and Least Squares

  • Inner Products Length, and Orthogonality
  • Orthogonal Sets
  • Orthogonal Projections
  • The Gram-Schmidt Process
  • Least-Squares Problem
  • Inner Product Spaces

Symmetric Matrices and Quadratic Forms

  • Diagonalization of Symmetric Matrices
  • Quadratic Forms
  • The Singular Value Decomposition

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Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

 

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile app.