Understanding concepts from linear algebra is essential to the serious study of many disciplines, ranging from physics and chemistry to economics and computer and data science, not to mention the further study of higher mathematics. In this course, we'll be looking at both computational and theoretical aspects of linear algebra, as well as at a number of applications. The "basic stuff" of linear algebra comprises vector spaces and the linear mappings between them. These mappings are represented by matrices, and a lot of linear algebra is concerned with reducing the enormous amount of data contained in a matrix to a few salient numbers and properties.
There aren't many prerequisites for the course other than basic high-school algebra and a willingness to stretch your mind around some awesome abstract concepts—higher (than 3)-dimensional spaces, deducing things abstractly from basic principles, and learning how to interpret and exploit the deductions. It will be an exciting and fast-paced journey through topics such as Gaussian elimination, linear systems, linear transformations and their matrix representations, eigenvalues and eigenvectors, the singular-value decomposition, and principal component analysis.
*Academic credit is defined by the University of Pennsylvania as a course unit (c.u.). A course unit (c.u.) is a general measure of academic work over a period of time, typically a term (semester or summer). A c.u. (or a fraction of a c.u.) represents different types of academic work across different types of academic programs and is the basic unit of progress toward a degree. One c.u. is usually converted to a four-semester-hour course.
Instructors
Dennis DeTurck
- Professor of Mathematics
- Robert A. Fox Leadership Professor
- Undergraduate Chair of the Mathematics Department
