Applied Linear Algebra

Course Description

The concepts of linear algebra are extremely useful in physics, economics, natural sciences, and engineering. Many difficult problems can be handled easily once the relevant information is organized in a way that can be studied using mathematical structures. One way to organize data is to use matrices and linear transformations. This course will provide students with knowledge of these concepts and their applications in areas such as graph theory and networking.

This course covers systems of linear equations and matrix algebra with emphasis on applications. Topics include systems of linear equations and their solutions, matrices and matrix algebra, determinants and inverse matrices, linear independence and bases, linear transformations, eigenvalues and eigenvectors. Areas of applications include graph theory, and cryptography. More specifically, the course will examine how complex networking problems from graph theory can be formulated and solved using tools from linear algebra.

Upon successful completion of the course students will be able to:
1. Understand and apply standard matrix operations
2. Solve linear systems using matrix theory
3. Develop the ability to solve problems using matrices
4. Evaluate determinants and inverses
5. Understand linear independence and bases for vector spaces
6. Apply concepts to solve networking problems
7. Write rigorous mathematical proofs

Prerequisites: Students need a solid background in algebra. Calculus experience is not required.