Every problem is on first approximation a linear problem. This makes linear algebra--the art and science of solving linear equations--the single most useful mathematical subject. In this course we will introduce the fundamental concepts of vector spaces and linear transformations and study them through the lenses of geometry and algebra. We will learn how to analyze matrices by hand and by machine. Along the way we will encounter applications from a variety of fields.
- Instructor: Trevor Hyde
What is symmetry? How do we quantify and analyze it? What does it mean to say that two objects have the same symmetry? Mathematicians developed the concept of a group to answer these questions. In this course we will learn the ropes of group theory. These investigations will lead us to study other fundamental structures of modern algebra, including rings and fields. Along the way we'll pick up some valuable experience computing with Sage and typesetting in LaTeX.
- Instructor: Trevor Hyde