We will cover the basic ideas required for understanding elementary linear algebra. This includes preliminaries like what a vector and matrix are, how to use Gauss-Jordan elimination to solve systems of equations, determinants, inverse matrices, and more. The goal of this short course is to give a solid foundational understanding of the concepts that motivate these mathematical objects, going beyond a strictly formula-based introduction to the concepts you may receive in a pre-calculus or calculus class. I hope students will come away with a great understanding of what ideas like vectors or matrices are about, what motivated them, how they are useful, and what problems they solve. The motivation for this course is that many first introductions to the topics of matrices and vectors do a poor job of motivating why they're interesting and useful, or why they follow the rules that they do, leaving students confused or feeling like they're just following a set of rules. The concepts covered will be perfect as a first introduction to the material for anyone planning to take Multivariable Calculus (aka Calculus III), Differential Equations, Linear Algebra, or any course that requires an understanding of vectors and matrices.

We'll discuss differential equations: solutions, analysis, categorization, etc. Designed to be a companion to a differential equations class or for people interested in getting ahead in their mathematics education. We'll cover topics typically covered for solving and analyzing basic differential equations: separation of variables, integrating factors, solving higher order linear equations, techniques for estimation, etc. Pre-requisites include a basic understanding of what derivatives and integrals are and a basic understanding of what a differential equation is. Sessions will be added surreptitiously as the course develops and interests are specified.