Jul 13, 2024
2018-2019 Course Catalog
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# CSCI 2033 - Elementary Computational Linear Algebra

Credits: 4
Hours/Week: Lecture 4 Lab None
Course Description: This course is an introduction to the numerical methods of Linear Algebra and their application to solving computational problems. Topics covered will include matrices, linear transformations, linear vector spaces, inner product spaces, systems of linear equations, Eigenvalues, and singular values. Algorithms and computational matrix methods will be presented using MATLAB. Matrix methods will be used to solve a variety of computer science problems.
MnTC Goals
None

Prerequisite(s): MATH 1081 , CSCI 1081  or college-level course in programming
Corequisite(s): None
Recommendation: None

Major Content
1. Vectors; linear combinations; matrices; matrix operations
2. Elementary linear mappings; applications in graphics and statistics
3. Systems of linear equations; applications
4. Theory of linear equations: complexity, operation counts; applications
5. Vector spaces; abstract linear spaces; subspaces; linear dependence; basis and dimensions; row reduced form; null space; range; Applications
6. Determinants Theory; Proofs; Applications
7. Inner Products.; Orthogonality; Least Squares; Norms, Condition Numbers, and Numerical Stability; Applications
8. Abstract linear transformations; Applications
9. Eigenvalues. Spectra of Symmetric matrices; Diagonalization of symmetric matrices; Applications
10. Singular Value Decomposition; Applications

Learning Outcomes
At the end of this course students will be able to:

1. demonstrate an understanding of the basic theorems and techniques of linear algebra
2. develop the numerical methods which approximate linear algebraic equations
3. create and apply appropriate algorithms and numerical methods to solve a variety of problems
4. use Matlab (or similar tool) to implement algorithms and computational methods
5. use symbolic methods to identify and solve linear algebraic problem

Competency 1 (1-6)
None
Competency 2 (7-10)
None

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