### Applied Linear Algebra – MATH 510

CG • Section 8WK • 11/08/2019 to 04/16/2020 • Modified 07/28/2020

### Course Description

This course focuses on developing an understanding of vector spaces and their transformations as is revealed by the theory of linear algebra and matrices through both examples and proofs.

Prerequisites

MATH 132 and MATH 250

### Rationale

This course is an introduction to finite dimensional linear algebra at the graduate level. After successful completion of this course the student should be able to calculate and explain all the major theorems and results of standard undergraduate linear algebra.

The topics covered include matrices, linear transformations, change of basis, eigenvalues, canonical forms, quadratic forms and applications. This should prepare both teachers and students for further study or instruction in linear algebra.

### Measurable Learning Outcomes

Upon successful completion of this course, the student will be able to:

1. Student will be able to calculate row reductions and explain how the Gauss-Jordan algorithm is used to solve linear systems,
2. Student will be able to calculate and explain basic matrix algebra including multiplication and determinants,
3. Student will be able to calculate and explain linear independence of subsets in a vector spaces,
4. Student will be able to calculate and explain spanning sets in linear algebra,
5. Student will be able to explain when a transformation is linear and how to find its matrix with respect to a basis,
6. Student will be able to calculate and explain coordinate systems and change for vectors and linear transformations,
7. Student will be able to calculate and explain lengths and angles in a vector space given a norm or inner product,
8. Student will be able to calculate and explain orthogonal projections and the application to least squares,
9. Student will be able to compute eigenvalues and eigenvectors and appropriate canonical forms,
10. Student will be able to communicate with the language of linear algebra and apply theorems of linear algebra to solve real world applications.

### Course Assignment

Four video demonstrations of proofs or calculations

Videos must be concise, precise, and well-practiced before taping.  Each video should be less than eight minutes in length and points will be deducted for videos over ten minutes long.

Student Video Introduction

Homework assignments

Quizzes over the course videos

Handwritten midterm exam

A handwritten, comprehensive final examination