Linear Algebra
Linear algebra is a foundational area of mathematics, finding widespread application in statistics, machine learning, economics, physics, and across the sciences. The starting point for this course is to consider basic properties of matrices and techniques for solving systems of linear equations. Abstracting and formalizing the process of solving linear equations leads us to the notion of a vector space and related ideas, such as linear independence, dimension, and basis. The course then turns to further properties of matrices and vector spaces, including determinants, eigenvalues and eigenvectors, and linear transformations. As time permits, we will study various applications of linear algebra, such as image compression, dynamical systems (with a focus on ecological applications), Markov chains, and Google's PageRank algorithm. Students who successfully complete this course will gain a solid introduction to the calculational techniques and key constructions and ideas of linear algebra that will prepare them for further work in the sciences and mathematics. Additionally, students will gain experience working at a level of generality and abstraction above that encountered in a typical introductory calculus sequence. Evaluation will be based on weekly problem sets. Students who enroll in this course should have successfully completed a high-school-level algebra class and be motivated to explore a powerful and broadly-used branch of mathematics that for most has a very different feel than the functions-precalculus-calculus sequence. Calculus is not a prerequisite for this class.