Linear Algebra is a foundational course that explores the theory and applications of systems of linear equations—an essential mathematical framework underlying numerous fields in science, engineering, and technology. From modeling physical systems to powering technologies like machine learning, robotics, computer vision, and data science, linear algebra provides powerful tools for understanding and solving real-world problems. This course begins by introducing vectors in two to *n* dimensions and progresses to systems of linear equations and matrices, which serve as bridges between equations and geometric representations. Students will study fundamental concepts such as vector spaces, subspaces, bases, determinants, and linear transformations. Emphasis will be placed on understanding how matrices encode transformations in vector spaces and how matrix operations can reveal geometric and algebraic properties of these transformations. Students will learn to predict the existence and nature of solutions to linear systems, analyze and construct vector spaces, derive orthogonal bases, and apply the theory of eigenvalues and eigenvectors to solve ordinary differential equations. The course encourages abstract thinking and a thorough introduction to proof-writing, offering a strong theoretical base for advanced studies in mathematics and a wide range of applications in computational and natural sciences. By the end of the course, students will not only develop a deep appreciation for the structure and beauty of linear algebra but also gain the ability to apply its methods to model and solve problems across diverse domains. This course is particularly valuable for students in computer science, engineering, physics, and other quantitative disciplines.
