Linear Algebra
165 lessons across 27 topics
1. Essential Questions
1How Can The Same Mathematical Object Be Viewed As A Vector, A Matrix, A Function, Or A Transformation?2How Does Orthogonality Simplify Geometry, Computation, And Approximation?3In What Ways Does Linear Algebra Power Modern Applications In Science, Economics, And Machine Learning?4What Do Span, Basis, And Dimension Reveal About Structure?5What Makes A System Of Equations “linear,” And Why Does Linearity Matter?6Why Do Eigenvalues And Eigenvectors Capture Long-term Behavior So Effectively?
2. Introduction to Linear Systems
3. Matrix Methods for Systems
4. Matrix Algebra
5. Inverses and Determinants
6. Vectors in Euclidean Space
7. Span, Linear Independence, Basis, and Dimension
8. Abstract Vector Spaces and Subspaces
9. Linear Transformations
10. Midterm Review and Midterm Assessment
11. Eigenvalues and Eigenvectors
12. Diagonalization and Dynamical Systems
13. Inner Products and Orthogonality
14. Least Squares and Applications
15. Symmetric Matrices, Spectral Ideas, and Applications
105Applications In Machine Learning, Graphics, And Economics106Applying The Spectral Theorem In Simple Settings107Explaining Why Symmetry Matters108Interpreting Data Through Linear Structure109Intro To Singular Values (optional Extension)110Orthogonal Diagonalization111Principal Component Intuition112Symmetric Matrices
16. Projects, Review, and Final Preparation
17. Final Assessment
18. Suggested Texts and Resources
19. Teaching and Learning Methods
122Computational Labs Using Matrix Software123Direct Instruction On Core Definitions, Theorems, And Procedures124Frequent Retrieval Practice And Cumulative Review125Geometric Visualizations And Conceptual Discussion126Guided Practice With Increasing Complexity127Proof-lite Reasoning Early, With Optional Proof Extension Tasks128Real-world Application Problems