All engineers need a solid foundation in mathematics. My name is Jeff Chasnov and I'm a professor of mathematics at the Hong Kong University of Science and Technology. I teach math to engineering students and this is a course on matrix algebra. [SOUND] You take the blue pill, the story ends. You take the red pill, and you stay in wonderland, and learn all about matrix algebra. What does matrix algebra have to do with engineering? [SOUND] >> Matrix algebra is needed by computer engineers. The hottest area right now is AI, and the basic algorithms depend on matrix algebra. For example, self-driving cars, Google Homes, Siri, and Amazon Echo all use AI and some form of matrix algebra. >> Matrix algebra has many applications in electrical engineering. For example, we use it to analyze complicated electrical circuits using Kirchhoff's laws. Construct the transfer matrix and control systems theory, and solve complex electromagnetic problems using the finite element method. >> Civil engineers need to have a solid background in matrix algebra to conduct design anaylsis, such as structural analysis for buildings and bridges, to compute the stress and strains in construction materials. >> So this is the first course on matrix algebra. And matrix algebra is all about matrices. If you don't yet know what a matrix is, don't worry. I'll tell you. The course will start slowly but it will quickly accelerate. Let me give you a brief overview of the course. In the first module, I'll define what a matrix is and how to manipulate matrices. This is basic knowledge that all engineers need to know. In the second module, we'll build on this basic knowledge and learn how a computer solves very large systems of linear equations. Engineers need to solve linear equations when analyzing circuits, performing structural analysis, and when analyzing big data. In the third module, we'll become more abstract and learn about vector spaces, and the vocabulary of linear algebra. These abstract concepts are widely used and will make it easier to understand more advanced engineering mathematics. Such as analysis and orthogonal polynomials. Finally in the fourth module, we'll learn all about determinants. And a very important matrix equation called the eigenvalue problem. Engineers may encounter eigenvalues and eigenvectors when studying mechanics, vibrations, and big data. You should know that when I lecture, I don't like to use PowerPoint or other types of slides. I like to physically write mathematics. I like to show students how I think when I solve math problems. So I am going to use a light-board in this course to give them my lectures. A light-board is very special because it allows me to talk directly to you as I explain the mathematics. After each video I'll give you a few problems to solve so you can practice. And after each topic I'll give you a practice quiz with some more problems to solve. At the end of each module I'll give you an assess quiz on the topics covered. There will be four assess quizཟes and you'll need to pass each of them to pass the course. I'm a math professor, not an engineer, and the goal of this course is to teach you the fundamental mathematics of matrices. For those of you who want to become an engineer your engineering professors will show you how to apply what you learn in this course. [SOUND] Unfortunately no one can be told what the matrix is. You have to see it for yourself. Do you want to enter the matrix? The matrix algebra course. [SOUND] [SOUND]