I believe that linear algebra is the most important area of math that most people have never heard of. While it has long been important in engineering and the sciences, it is also widely used in the currently popular fields of machine learning and data science.
To give you an idea of how widely it is used, check out the titles of these books:
An Introduction to Wavelets Through Linear Algebra
Fundamentals and Linear Algebra for the Chemical Engineer
Graph Algorithms in the Language of Linear Algebra
Intermediate Dynamics: A Linear Algebraic Approach
Introduction to Linear Algebra: A Primer for Social Scientists
Introduction to Linear Algebra in Geology
Introduction to Matrix Methods in Optics
Linear Algebra and Optimization for Machine Learning
Linear Algebra for Economists
Linear Algebra for Signal Processing
Matrix Algebra From a Statistician's Perspective
Theory of Matrix Structural Analysis
My goal in this course is to introduce you to linear algebra in such a way that you not only understand the purpose of the various topics, but that you also see how you can apply the material. I hope that if you begin the course thinking "what is linear algebra used for?" that you end the course thinking "what can't you use linear algebra for?"
We will cover standard topics of linear algebra that you can find in any linear algebra textbook, but I also spend a lot of time on topics that are less common in an undergraduate linear algebra course: least squares, singular value decomposition, and numerical linear algebra.
I am a big believer that in order to learn to do something, you have to actually practice doing it. Therefore, I do the following:
work problems by hand, explaining the steps used and promoting understanding of why we are doing it
in a few cases the problems are too large or complex to do by hand, so I wrote a computer program in the Python programming language to do the work or plot the values
provide practice problems with solutions, showing my work for obtaining the answers
It is also easy to claim that linear algebra is useful but then not back it up. Therefore, for each major topic I include practical applications.
Finally, let me leave you with a quote from Linear Algebra: A Happy Chance to Apply Mathematics by Gilbert Strang, who teaches linear algebra at MIT: "I believe that linear algebra is the most important subject in college mathematics. Isaac Newton would not agree! But he isn't teaching mathematics in the 21st century (and maybe he wasn't a great teacher, we will give him the benefit of the doubt). Certainly Newton demonstrated that the laws of physics are best expressed by differential equations. He needed calculus: quite right. But the scope of science and engineering and management (and life) is now so much wider, and linear algebra has moved into a central place."
