The course covers several applications of linear algebra in natural sciences, engineering and computer science. Students taking this course need to be introduced to computer-based tools for performing linear algebra computation (row reduction, matrix multiplication, singular value decomposition etc.). Preferred tools for teaching this content are Python with its computing libraries (SymPy, NumPy) and Jupyter Notebook (or JupyterLab) as the programming environment. The Anaconda Distribution of Python (www.anaconda.com/products/individual)includes all these tools.
What is it good for. Linear algebra is a major area of mathematics with a lot of applications to computer science, engineering, data analysis, business etc. I will explain several of such applications during this course. Here are some interesting discussions of uses of linear algebra from the perspective of computer programmers, statisticians, engineers.
What should be easy. One reason behind usefulness of linear algebra is that computations involved in many of its problems are fairly easy to perform. In effect, computations in this course should be easier than the ones you saw e.g. in calculus classes.
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 computing 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 you will need to learn and understand how they relate to one another. Both computational and theoretical problems will appear in homework assignments and exams.
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 applications the amount of data is far too large to compute anything by hand. Typically one uses conceptual knowledge of linear algebra to set up a problem and to interpret its solution, but computations are handled by a computer. Computer-based components of this course are intended to reflect this. Computing tools we will use (Python, Jupyter notebook) are free 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.
