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Department:
MATH
Course Number:
1564
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
2
Hours - Total Credit:
4
Typical Scheduling:
Every Fall
This is an intensive course on linear algebra, taught at a sophisticated and abstract level.
Prerequisites:
Course Text:
Linear Algebra by Jim Hefferon, available for free online.
Topic Outline:
Topic | Text Sections | Lectures |
---|---|---|
Solving Linear Systems and Gaussian Elimination | One.I.1-3 | 3 |
Reduced Echelon Form | One.III.1-2 | 2 |
Geometry of vectors | One.II.1-2 | 1 |
Abstract vector spaces | Two.I.1 | 1 |
Subspaces and spanning sets | Two.I.2 | 2 |
Linear independence | Two.II.1 | 1 |
Bases | Two.III.1 | 2 |
Dimension | Two.III.2 | 2 |
Vector spaces and linear systems | Two.III.3 | 1 |
Isomorphisms | Three.I.1-2 | 2 |
Linear transformations | Three.II.1-2 | 3 |
Computing linear maps | Three.III.1-2 | 2 |
Matrix operations | Three.IV.1-3 | 2 |
Inverses | Three.IV.4 | 1 |
Markov chains | Three.Topic | 1 |
Change of basis | Three.V.1-2 | 2 |
Orthogonal projection | Three.VI.1,3 | 1 |
Gram–Schmidt orthogonalization | Three.VI.2 | 1 |
Line of best fit | Three.Topic | 1 |
Determinants | Four.I.1-2 | 2 |
Laplace’s expansion | Four.III.1 | 1 |
Complex vector spaces | Five.I.1-2 | 1 |
Similarity | Five.II.1 | 1 |
Diagonalizability | Five.II.2 | 1 |
Eigenvalues and eigenvectors | Five.II.3 | 2 |
Method of Powers and Page Rank | Five.Topics | 2 |
Jordan canonical form | Notes | 1 |