MATH 34600: Elements of Linear Algebra
Career: Undergraduate
Category: Regular
Term Offered: Fall, Spring, Summer
Pre-requisites: C or better in Math 21200
Hours/Credits: 3 HR/WK; 3 CR
Date Effective: Fall 2024
Course Supervisor: Matt Auth
Catalog Description
Vector spaces, basis and dimension, matrices, linear transformations, determinants, solution of systems of linear equations, eigenvalues, and eigenvectors.
Text
Linear Algebra with Applications, W. Keith Nicholson, Lyryx 2021 (Revision A).
Suggested Schedule
| Class | Topics | Section |
|---|---|---|
| 1 | Solutions and Elementary Operations | 1.1 |
| 2 | Gaussian Elimination | 1.2 |
| 3 | Homogeneous Equations | 1.3 |
| 4 | Matrix Operations | 2.1, 2.2 |
| 5 | Matrix Multiplication | 2.3 |
| 6 | Matrix Inverses, Elementary Matrices | 2.4 |
| 7 | Elementary Matrices | 2.5 |
| 8 | The Cofactor Expansion | 3.1 |
| 9 | The Determinant of Matrix Inverses | 3.2 |
| 10 | Exam 1 | |
| 11 | Diagonalization and Eigenvalues | 3.3 |
| 12 | An Application to Systems of Differential Equations | 3.5 |
| 13 | Subspaces and Spanning, Linear Independence | 5.1 |
| 14 | Linear Independence | 5.2 |
| 15 | Best Approximation and Least Squares | 5.6 |
| 16 | Examples and Basic Properties | 6.1 |
| 17 | Subspaces and Spanning Sets | 6.2 |
| 18 | Linear Independence and Dimension | 6.3 |
| 19 | Finite Dimensional Spaces | 6.4 |
| 20 | Examples and Elementary Properties | 7.1 |
| 21 | Kernel and Image of Linear Transformation | 7.2 |
| 22 | Exam 2 | |
| 23 | Kernel and Image of Linear Transformation (continued) | 7.2 |
| 24 | Orthogonal Complements and Projections | 8.1 |
| 25 | Orthogonal Diagonalization, The SVD | 8.2, 8.6.1 |
| 26 | The Matrix of a Linear Transformation | 9.1 |
| 27 | The Matrix of a Linear Transformation (continued) | 9.1 |
| 28 | Review | |
Course Learning Outcomes
After taking this course, the student should be able to:
- Solve systems of linear equations. a, c, e2
- Evaluate the determinant. a, e2
- Compute inverses of square matrices. a, e2
- Understand basic properties of vector spaces, subspaces, and their bases. c, e1, f, g
- Understand linear dependence and independence. e1, f, g
- Compute eigenvalues and eigenvectors. a, e2
- Understand basic properties of linear transformations. c, e1, f, g
Departmental Learning Outcomes
The mathematics department, in its varied courses, aims to teach students to:
a. Perform numeric and symbolic
computations.
b. Construct and apply symbolic and graphical
representations of functions.
c. Model real-life problems mathematically.
d. Use technology appropriately to analyze mathematical
problems.
e. State (e1) and apply (e2) mathematical definitions and
theorems.
f. Prove fundamental theorems.
g. Construct and present (generally in writing, but
occasionally orally) a rigorous mathematical argument.
