MATH 2307: Linear Algebra

Course description

This course covers the fundamental ideas of linear algebra and its applications. Topics covered include linear equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors, and orthogonality. The emphasis is on comprehending theoretical principles, computational techniques, and real-world applications such as computer graphics, machine learning, and differential equations.

Course Objectives

By the end of this course, students will be able to:

1. Solve linear equations with row reduction and matrix techniques.
2. Demonstrate proficiency in matrix operations, inverse computation, and property understanding.
3. Determine linear independence, span, basis, and dimension for vector spaces.
4. Analyze determinants and evaluate their relevance in linear transformations.
5. Identify eigenvalues, eigenvectors, and use diagonalization techniques.
6. Use orthogonality and least-squares approaches in practical applications like data fitting and machine learning.

Required Materials

1. David C. Lay, Steven R. Lay & Judi J. McDonald – Linear Algebra and Its Applications, 6th Edition, Pearson, 2020.
2. Howard Anton & Chris Rorres – Elementary Linear Algebra, 12th Edition, Wiley, 2019.
3. Gilbert Strang – Introduction to Linear Algebra, 5th Edition, Wellesley-Cambridge Press, 2016.