Applied Linear Algebra. (3-0) 3 Credit Hours

Catalog description

Prerequisite: MAT 1213 or equivalent. This course provides a rigorous introduction to linear algebra with a focus on applications in optimization, data analysis, and neural networks. Students develop a foundational understanding of linear systems of equations, vectors, matrices, and methods for solving systems such as Gaussian elimination. The course introduces key algebraic structures including vector spaces, norms, inner products, linear independence, bases, rank, and linear mappings. Determinants, traces, eigenvalues, eigenvectors, and matrix factorizations are covered with emphasis on their computational aspects. Advanced topics in vector calculus include gradients, partial derivatives, Taylor series, matrix calculus, and higher-order derivatives. The course integrates optimization methods such as gradient descent, constrained optimization using Lagrange multipliers, and convex optimization. Applications to machine learning are explored through the mathematical foundations of principal component analysis, the theory and implementation of feed-forward artificial neural networks, backpropagation algorithms, activation functions, and performance measures. Students apply theoretical knowledge through projects involving linear optimization and neural network construction. Course Fee: LRS1 $46.20; STSI $21.60.