Linear Algebra

Course Overview

This is a typical introductory course to Linear Algebra. It lays its foundations in the theory of Matrices and its relationship to Linear Transformations. The course will be divided mainly in three parts:

• Matrix Analysis, Determinants and Linear Systems of Equations: Become familiar with the operations that can be applied to matrices. Compute sums, products, determinants, inverses and transform matrices in order to study how to solve linear systems of equations.
• Vector Spaces, Linear Transformations and $\R^n$: Understand what a linear transformation is and why it is important. Comprehend how different operations'' ortransformations’’ such as rotations, translations, etc are particular examples of linear transformations. Study the particular example of the vector space $\R^n$.
• Inner product spaces and Spectral Theory: Arguably, the most difficult but useful part of the course for future courses in mathematics, engineering, computer science, etc. In this part we will analyze the basic tools used to study different types of vector spaces, how they decompose in basic ``building blocks’’ and, if time permits, apply these tools to real-life problems to see the potential of them.

By the end of the semester, students will:

• Understand what is a matrix, what are its basic operations and how to use them to solve systems of linear equations.
• Perform elementary operations to reduce a matrix, invert a matrix and solve systems of equations.
• Demonstrate how linear transformations are related to matrices and use the main properties of linear transformations.
• Describe the basic elements and properties of the vector space $\R^n$.

Prerequisites

• C- or better in MTH 141, MTH 131 or MTH 180.

Textbooks

• Open Source Textbook provided in Brightspace.

Grading

• Midterm Exam: 20%
• Quizzes: 20%
• Homework: 30%
• Cumulative Final Exam: 30%