# Revised syllabus for Linear Algebra II

New or substantially changed material is indicated in bold green.

Professor: Mark McClure

## Course purpose

With a prerequisite of Linear I, the expectation for this course is that you

• are familiar with linear systems of equations and can express those systems using the algebra of matrices,
• can use Gaussian elimination on matrices to solve linear systems of equations,
• understand the basics abstract vector spaces and linear transformations
• have heard that the finite dimensional vector spaces are exactly the Euclidean spaces $$\mathbb R^n$$ and that a linear transformation mapping $$R^n \to R^m$$ can be expressed as $$\vec{x} \to A\vec{x}$$ where $$A\in \mathbb R^{m\times n}$$,
• have heard that there are these things called eigenvalues and eigenvectors satisfying $$A\vec{x} = \lambda \vec{x}$$, and
• have some experience reading and writing proofs.

Not surprisingly, we will further develop all of these things in this second semester class. We will not, however, simply jump in at the end of Linear I. Rather, we will start over with a major focus on the applied perspective. Thus, in this class, we will:

• meet several interesting, real world problems,
• need to deal with large systems - potentially, thousands of variables,
• use the computer computer to solve problems, and
• study the algorithms that drive the computer.

Thus, we will not use the computer as a Black Box - rather, we will try to understand how the software works. When we do so, it turns out that the very foundations of linear algebra need to be reconsidered. We will need to re-examine Gaussian elimination, for example, to minimize the amount of numerical error that is introduced. The concepts of determinant and inverse, while still important conceptually, turn out to be essentially useless from the numerical perspective.

## Materials

• Text: We will use Applied Linear Algebra by Olver and Shakiban.
This is a reasonably priced text from Springer's outstanding Undergraduate Texts in Mathematics series that focus on exactly our subject matter.
Also, there is an online version available through our library. Simply search for "Olver Applied Linear Algebra" on the library's main page.
• Technology:
• Calculators: We won't be using calculators and they will not be permitted on quizzes or exams.
• Python: We'll write computer code in Python. I recommend you get Anaconda, a free Python distribution with loads of scientific libraries pre-installed.
• Our online forum : I've set up an online forum Linear Talk where we can discuss all kinds of aspects of linear algebra.
• Online office hours: I'll email you a Google Meet link where you can find me during the first half of our regularly scheduled class time. You are not generally required to attend office hours. This is simply an opportunity for you to ask questions. Of course, I can set up private links in situations where that's appropriate.

## Evaluation

The standard 90-80-70-60 scale will guarantee you an A, B, C, or D. However, it is quite likely that the final scale will be shifted down from this. You will be apprised of your standing as the term progresses.

• Exams: We already had the one exam we will have on Wednesday, February 26.
• Quizzes: We already had the one quiz we will have on Wednesday, February 5.
• Homework: There will be several types of homework:
• Daily textbook assignments: I'll typically post a couple of problems on our webpage for you to think about from each section that we cover. These provide important practice but will not be collected. Hopefully, some of these will be discussed on Linear Talk.
• Typed up HW: You will turn in a few written out problems as forum messages.
• Forum assignments: Occasionally, I'll post questions in the Assignments Category of our forum that will count for 10 to 20 points. Often, these questions will involve computational work on the computer.
• Computer labs: We'll have two more in depth computer labs. These will be turned in as forum messages.
• Final exam: Any final exam we have will be project based.
• Cheating: I don't deal with cheating. If I suspect cheating strongly enough, I simply refer you to the provost and fail you for that assessment.