Linear algebra is at the core of all of modern mathematics, and is used everywhere from statistics and data science, to economics, physics and electrical engineering. However, learning the subject is not principally about acquiring computational ability, but is more a matter of fluency in its language and theory.
In this course, we will start with systems of linear equations, and connect them to vectors and vector spaces, matrices, and linear transformations. We will be emphasizing the vocabulary throughout, so that students become comfortable working with the different aspects.
We will then introduce matrix and vector operations such as matrix multiplication and inverses, paying particular attention to their underlying purposes. Students will learn not just how to calculate them, but also why they work the way that they do.
Next, we define the key concepts of basis and dimension, which form the foundation for many of the more advanced concepts of linear algebra. The last chapter concerns inner products, which allow us to use linear algebra for approximating solutions; we will see how this allows for applications ranging from statistics and linear regression to digital audio.
Week 1 Systems of Linear Equations, Introduction to Vectors and Matrices
Week 2 Linear Combinations, Span, Matrix-Vector Multiplication
Week 3 Linear Independence and Linear Transformations, Homework 1
Week 4 Matrix Multiplication and Inverses, Homework 2
Week 5 Bases and Coordinates
Week 6 Dimension and Rank/Nullity, Homework 3
Week 7 Inner Products and Projections, Homework 4
Week 8 Final Exam
This course is Part One of a two-part course. Part Two will cover topics such as determinants and eigenvectors.