Linear Algebra

"Every body is genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid." ~ Albert Einstein

What is Linear Algebra?

Many of you might ask: what is matrix algebra and why do we care about this branch of mathematics? Here are some thoughts.

Finding the solution to a system of linear equations is the main core for which linear algebra embraces. In this course, we will learn some crucial tools and techniques that help us analyze or solve a system algebraically and geometrically.

Since the solution to a system can be represented by a line, a plan or a hyper-plane, and the unique solution to a system can be represented as a point formed by the intersection of those lines, planes, or hyper-planes, the study of the solution to a system naturally leads us to a geometric demonstration. This is the world in which we will spend lots of time with.

Furthermore. we will see that matrices and vector spaces provide a more convenient form when thinking about systems of linear algebra. In particular, we will learn about linear transformations, a concept for mapping between two vector-spaces but still preserves the vector-space structure. In another words, every matrix can be thought of a linear transformation, and every linear transformation can be represented by a matrix. This special topic is very exciting to me, and I hope, in time, you all will be all enthusiastic about the relationship between matrices and linear transformation.

Matrix/Linear Algebra, matrices and vector spaces have an outstanding number of applications throughout the physical science, and we will explore some of these as we progress through the course.

I am looking forward to seeing how much we will learn, and to your project presentations at the end of the course.

This course is designed as a FLIPPED MATRIX ALGEBRA course.

In a traditional class, students come to class to listen to lectures, and do practices outside of classroom on their own schedule. A flipped class flips that model by letting students watch video lectures on their own schedule and do practices in class with the instructor and their peers.
Visit this website if you’d like to learn more about the effectiveness of flipped classrooms.