Math 4C Course Topics

 

Linear Algebra • A Modern Approach

by David Poole, Brooks/Cole Publishing

 

Categories:  1.  Must be covered in detail

                  2.  Must be covered at least briefly

                  3.  Do not cover unless you have extra time after adequately

                       doing 1 and 2.

 

There are a number of EXPLORATIONS throughout the text.  Dependent on the ability level of the class, use your professional judgement to include or exclude particular explorations.  A suggestion would be to assign them as extra credit for students who may want to pursue the topics.

 

Category    Section                                  Section Topics

 

 

 

 

1

1.0

Introduction:  The Racetrack Game

1

1.1

The Geometry of Vectors

1

1.2

Length and Angle:  The Dot Product

1

1.3

Lines and Planes

2

1.4

Code Vectors and Modular Arithmetic

 

 

 

 

 

 

1

2.0

Introduction:  Triviality

1

2.1

Introduction to Systems of Linear Equations

1

2.2

Direct Methods for Solving Linear Systems

1

2.3

Spanning Sets and Linear Independence

2

2.4

Applications

3

2.5

Iterative Methods for Solving Linear Systems

 

 

 

 

 

 

1

3.0

Introduction:  Matrices in Action

1

3.1

Matrix Operations

1

3.2

Matrix Algebra

1

3.3

The Inverse of a Matrix

1

3.4

Subspaces, Basis, Dimension, and Rank

1

3.5

Introduction to Linear Transformations

2

3

3.6

 

Applications :  Markov Chains and Leslie Matrices

Applications :  Representing Graphs

 

 

 

 

 

 

3

4.0

Introduction:  A Dynamical System of Graphs

1

4.1

Introduction to Eigenvalues and Eigenvectors

1

4.2

Determinants

1

4.3

Eigenvalues and Eigenvectors of n x n Matrices

1

4.4

Similarity and Diagonalization

2

4.5

Iterative Methods of Computing Eigenvalues

3

4.6

Applications and the Perron-Frobenius Theorem

 

 

 

 

 

 

1

5.0

Introduction:  Shadows on a Wall

1

5.1

Orthogonality in Rn

1

5.2

Orthogonal Complements and Orthogonal Projections

1

5.3

The Gram-Schmidt Process and QR Factorization

1

5.4

Orthogonal Diagonalization of Symmetric Matrices

3

5.5

Applications

 

 

 

 

 

 

1

6.0

Introduction:  Magic Squares

1

6.1

Vector Spaces and Subspaces

1

6.2

Linear Independence, Basis, and Dimension

1

6.3

Change of Basis

1

6.4

Linear Transformations

1

6.5

The Kernel and Range of a Linear Transformation

2

6.6

The Matrix of a Linear Transformation

3

6.7

Applications

 

 

 

 

 

 

1

7.0

Introduction:  Taxicab Geometry

1

7.1

Inner Product Spaces

1

7.2

Norms and Distance Functions

1

7.3

Least Squares Approximation

3

7.4

The Singular Value Decomposition

2

7.5

Applications