About This Course

This course provides an introduction to linear algebra, a major area of mathematics with a lot of applications to computer science, engineering, data analysis, business etc. Several such applications will be demonstrated during the course.

What should be easy about this course

One reason behind usefulness of linear algebra is that computations involved in many of its problems are fairly easy to perform. For example, during the first week of classes you will learn a procedure for row reduction of a matrix. As you will see row reduction is straightforward, but majority of computational problems we will deal with later on will boil down to performing row reduction of some matrix. Overall, computations in this course should be easier than the ones you can encounter e.g. in calculus courses.

What may be harder

This course will mix computational parts with some theory. Understanding of linear algebra concepts is necessary for any serious applications (e.g. you won’t have any use of eigenvectors unless you understand what an eigenvector is). This is usually a more difficult facet of linear algebra courses: there are a lot of new notions that one needs to learn and understand how they relate to one another.

Why we will use computers in this course

Manual calculations are useful when one is learning linear algebra, since they show how linear algebra works. However, in almost all modern applications the amount of data is far too large to compute with it by hand. Typically one needs conceptual knowledge of linear algebra to set up a problem and to understand its solution, but computations are handled by a computer. Computer-based components of this course are intended to reflect this reality. Computing tools we will use (Python, Jupter notebook) are freely available and used in many industries, so there is a good chance that you will find them of use in other courses and in your professional career.