Dive into the fundamental concepts of linear algebra with MATH251, a foundational course designed to introduce students to the theory and applications of vectors, matrices, and linear transformations. From systems of linear equations to eigenvalues and eigenvectors, this course covers essential topics in linear algebra, empowering students to develop a deep understanding of mathematical structures and their real-world implications.

Course Highlights:Vectors and Vector Spaces: Explore the geometric and algebraic properties of vectors in Euclidean space, including vector addition, scalar multiplication, dot products, and cross products.

Matrix Algebra: Learn about matrix operations such as addition, subtraction, multiplication, and inversion, and understand their applications in solving systems of linear equations and representing linear transformations.

Linear Transformations: Gain insights into linear transformations, including properties such as linearity, invertibility, and kernel space, and learn how to represent them using matrices.

Eigenvalues and Eigenvectors: Understand the concepts of eigenvalues and eigenvectors, and learn how to compute them for square matrices and their applications in diagonalization and solving differential equations.

Orthogonality and Orthogonalization: Explore the concept of orthogonality, including orthogonal vectors, orthogonal projections, and Gram-Schmidt orthogonalization, and understand their applications in geometry and optimization.

Determinants and Cramer's Rule: Learn about determinants of matrices and their properties, and understand how to use determinants to compute matrix inverses and solve systems of linear equations using Cramer's Rule.

Vector Spaces and Subspaces: Understand the properties of vector spaces and subspaces, including basis vectors, dimensionality, and spanning sets, and learn how to apply these concepts in linear algebra problems.

Applications in Computer Graphics and Data Analysis: Explore real-world applications of linear algebra in computer graphics, data analysis, cryptography, and engineering, and understand how linear algebra concepts are used to solve practical problems.

Who Should Enroll:MATH251 is ideal for students pursuing degrees in mathematics, computer science, engineering, physics, or related fields, as well as anyone interested in developing a strong mathematical foundation. This course is suitable for beginners with a solid understanding of algebra and calculus, as well as those seeking to deepen their knowledge of linear algebra concepts and their applications in diverse fields.

# MATH251 - Linear Algebra

- Ayman Saber