## Bulletin Listing

Prerequisites: MATH 225 or MATH 325; and MATH 209 or MATH 309 or CSC 210 or CSC 215; all with grades of C or better.

Explore techniques for solving huge linear systems, covering both the theory behind the techniques and the computation. Review and further develop earlier concepts and use them to efficiently solve problems across the natural and social sciences. Problems are drawn from numerical analysis, mathematical biology, data analysis and machine learning, imaging and signal processing, chemistry, physics, economics, computer science, engineering, and other disciplines.

## Course Outline

The course will be project based involving several programming assignments on applications in Linear Algebra.

Potential Topics

• Basis, subspaces, orthogonal projections, and matrix decompositions

• Optimization - gradient descent method, conjugate gradient

• Applications of Least squares approximation

• Image processing using singular value decomposition

• Data analysis with principal component analysis

• Vibrations, damping, and resonance

• Fast Fourier transform, signal processing

• Applications in quantum mechanics

• Linear systems of ordinary differential equations

• Solutions for linear and nonlinear equations

## Student Learning Outcomes

When a student completes this course they will be able to…

SLO #1 Students understand and are able to apply ideas such as basis, subspaces, and orthogonal projections to solve computational and theoretical problems.

SLO #2 Students should be able to identify a good technique for solving a particular problem and be able to efficiently implement the technique using available software.

SLO #3 Students should be proficient in navigating the wealth of linear algebra software available and be able to adapt them for their applications.

*Submitted by Eric Hsu, May 16 2024*