Linear Algebra II

Created by: University of Waterloo Mathematics, powered by Möbius

Description

The Linear Algebra II Content Pack is a Möbius course developed by the University of Waterloo that you can use as a customizable starting point to a complete linear algebra course in Möbius. This Content Pack complements the Linear Algebra I Content Pack also authored by the University of Waterloo. This Content Pack explores: vector spaces, linear mappings, inner product spaces, and orthogonal diagonalization. This customizable resource contains 7 units of sectioned lessons and assignments enhanced with Möbius capabilities including algorithmic questions, in-lesson questions with unlimited practice, adaptive questions, interactive narratives, Geogebra resources, Math Apps, hints and immediate feedback, and end-of-section assignments.

How does Möbius take the University of Waterloo’s content to the next level?

  • Lessons contain interactive elements like Interactive Narratives, HTML objects, Math Apps, or Geogebra applications to help solidify difficult STEM concepts.

  • Learn how Möbius’ unique STEM question types throughout this content provide the best STEM learning experience.

  • Work with over 50 configurable assessment properties when modifying existing or building your own assessments.

Course Structure

  • All content is organized into 7 units for easy navigation
  • Course materials provide a solid foundation for creating your course offering which include 26 lessons that promote Active Learning by including illustrative visualizations, interactive elements, and example problems with immediate feedback
  • Different forms of assessment materials are distributed across 9 assignments to evaluate student comprehension through a variety of different question types
  • Pull from a vast selection of over 360 questions that you can use to create your own lessons and assignments or supplement existing ones
7 units
26 lessons
9 assignments
360+ questions

Unit 0: Getting Started

Unit 1: Abstract Vector Spaces

  • 1a Vector Space Axioms

  • 1b Subspaces

  • 1c Basis and Dimension

  • 1d Coordinates

  • 1e Putting It All together

Unit 2: Linear Mappings

  • 2a Definition and Examples

  • 2b Range and Nullspace

  • 2c Vector Space Isomorphisms

  • 2d Matrix of a Linear Mapping

  • 2e Matrix of a Linear Mapping and Diagonalization

  • 2f Putting It All together

Unit 3: Inner Product Spaces I: Rn

  • 3a Inner Products on Rn

  • 3b Orthogonality

  • 3c Method of Least Squares

  • 3d Putting It All together

Unit 4: Inner Product Spaces II: General Inner Product Spaces

  • 4a Introduction to Inner Product Spaces

  • 4b Orthogonality

  • 4c Orthogonal Complement

  • 4d Putting It All together

Unit 5: Orthogonal Diagonalization and Applications

  • 5a Diagonalization of Symmetric Matrices

  • 5b Quadratic Forms

  • 5c Singular Value Decomposition

  • 5d Optimization (Linear Programming)

  • 5e Infinite dimensional Inner Product Spaces

  • 5f Putting It All together

Assignments

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