MATH A235: Applied Linear Algebra
| Item | Value |
|---|---|
| Curriculum Committee Approval Date | 05/03/2023 |
| Top Code | 170100 - Mathematics, General |
| Units | 3 Total Units |
| Hours | 54 Total Hours (Lecture Hours 54) |
| Total Outside of Class Hours | 0 |
| Course Credit Status | Credit: Degree Applicable (D) |
| Material Fee | No |
| Basic Skills | Not Basic Skills (N) |
| Repeatable | No |
| Grading Policy | Standard Letter (S),
|
| Associate Arts Local General Education (GE) |
|
| Associate Science Local General Education (GE) |
|
| California General Education Transfer Curriculum (Cal-GETC) |
|
| Intersegmental General Education Transfer Curriculum (IGETC) |
|
| California State University General Education Breadth (CSU GE-Breadth) |
|
Course Description
Introduction to linear algebra, classical linear algebra problems, and applications to computer science and related technologies including matrices, determinants, linear spaces, linear transformations, and eigenvalues. PREREQUISITE: MATH A185 or MATH A185H or MATH A182H or Appropriate OCC Math placement. Transfer Credit: CSU; UC.
Course Level Student Learning Outcome(s)
- Apply the theory and techniques of linear algebra in applications from physics, operations research and other scientific disciplines.
- Solve linear systems, including under- and over-determined systems.
- Relate linear transformations to their matrices with respect to given bases.
- Describe linear transformations as functions mapping an n-dimensional space to an m-dimensional space.
Course Objectives
- 1. Apply matrix methods to systems of linear equations
- 2. Use bases and orthonormal bases to solve problems in linear algebra
- 3. Find the dimension of spaces such as those associated with matrices and linear transformations
- 4. Apply determinant methods to matrices and systems of equations
- 5. Describe the properties of Rn
- 6. Find eigenvalues and eigenvectors and use them in applications
- 7. Prove basic results in linear algebra about independence of vectors, properties of subspaces, linearity, injectivity and surjectivity of functions, and properties of eigenvectors and eigenvalues
- 8. Use linear algebra techniques and theory to solve selected applications
Lecture Content
Basic Matrix Theory matrix operations and their properties matrix transpose special matrices diagonal triangular symmetric trace of a matrix Solve Systems of Linear Equations Using Matrix Methods Gaussian and Gauss-Jordan elimination row reduction using elementary matrices calculating inverse matrices and usign them to solve systems of equations Determinants elementary properties cofactor expansion determinants and row operations detAB=(detaA)(detB) Cramers Rule Rn and other Real Vector Spaces definition of a vector space subspaces linear combinations linear independence and dependence spanning set basis dimension Matrix Generated Spaces row space column space null space rank nullity Linear Transformations definition of a linear transformation nullspace (kernel) and range nullity and rank rank-nullity theorem injectivity and surjectivity inverse linear transformation matrix representations of linear transformations change of basis matrix Inner Product dot product definition of an inner product space norm orthogonal and orthonormal vectors angle between vectors orthogonal and orthonormal sets and bases Graham-Schmidt Process Eigenvalues and Eigenvectors definition of eigenvalues and eigenvectors characteristic polynomial algebraic multiplicity of eigenvalues eigenspaces, geometrix multiplicity diagnoalization includin g orthogonal diagonalization of symmetric matrices Applications such as least squares regression analysis, stochastic matrices, and the use of technology as it relates to linear algebra
Method(s) of Instruction
- Lecture (02)
Instructional Techniques
Lecture, discussion, written homework.
Reading Assignments
As assigned from text. 1 hour
Writing Assignments
Writing is encouraged throughout the course but is not necessarily a part of the grading or exams. 1 hour
Out-of-class Assignments
As assigned by instructor. 4 hour
Demonstration of Critical Thinking
Several written tests and a comprehensive final.
Required Writing, Problem Solving, Skills Demonstration
Several written tests and a comprehensive final.
Eligible Disciplines
Mathematics: Masters degree in mathematics or applied mathematics OR bachelors degree in either of the above AND masters degree in statistics, physics, or mathematics education OR the equivalent. Masters degree required.
Textbooks Resources
1. Required Larson, Ron. . Elementary Linear Algebra. , 8th ed. Boston: Cengage Learning, 2017 Rationale: -
Other Resources
1. Other appropriate textbook as chosen by faculty.