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, Fifth Edition, Otto Bretscher, Pearson 2019.
Schedule
| Class | Topics | Section |
|---|---|---|
| 1 | Linear Systems; Gaussian Elimination | 1.1 |
| 2 | Guassian Elimination | 1.2 |
| 3 | On the Solutions of Linear Systems | 1.3 |
| 4 | Introduction to Linear Transformations and Their Inverses | 2.1 |
| 5 | Linear Transformations in Geometry | 2.2 |
| 6 | Matrix Products | 2.3 |
| 7 | The Inverse of a Linear Transformation | 2.4 |
| 8 | Image and Kernel | 3.1 |
| 9 | Subspaces; Bases; Linear Independence | 3.2 |
| 10 | Dimension | 3.3 |
| 11 | Exam 1 | |
| 12 | Coordinates | 3.4 |
| 13 | Linear Spaces, Linear Transformations (omit spaces of matrices and sequences) | 4.1, 4.2 |
| 14 | Matrix of a Linear Transformation | 4.3 |
| 15 | Orthogonal Projections and Bases | 5.1 |
| 16 | Gram-Schmidt, Orthogonal Matrices | 5.2, 5.3 |
| 17 | Least Squares, Data Fitting | 5.4 |
| 18 | Intro Determinants | 6.1 |
| 19 | Properties of the Determinant | 6.2 |
| 20 | Geometric Interpretation of Determinant; Cramer's Rule | 6.3 |
| 21 | Diagonalization | 7.1 |
| 22 | Exam 2 | |
| 23 | Finding Eigenvalues | 7.2 |
| 24 | Finding Eigenvectors | 7.3 |
| 25 | Symmetric Matrices | 8.1 |
| 26 | Quadratic Forms; Singular Values | 8.2, 8.3 |
| 27 | Continuous Dynamical Systems | 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
Course Assessment Tools
- Term average, based mostly on hw (no more than 5% of course grade), in-class quizzes, and two (or three) in-class examinations: 60% of grade.
- Comprehensive written final exam: 40% of grade.
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.
