Revised syllabus for Linear Algebra II

New or substantially changed material is indicated in bold green.

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.

Advice

Learning Mathematics: I believe that mathematics is a wondrous but challenging field. I assume that most people in this class have interest in mathematics and appreciate its unique challenges. There will be times of frustration ahead. Buckle down and work hard.
Help: You are not in this endeavor alone. You have four major sources of help:
- Me: I like to talk to people about mathematics. That's why I chose this profession. My full schedule with office hours is shown below. You will almost always find me in my office during my office hours but please feel free to approach me any time you have questions.
- Your classmates: Most people learn mathematics best by talking through it with others. You will find that you can both learn from and help your fellow classmates. You should get to know one another very well.
- Linear Talk Too: A kinda combination of the previous two that never sleeps!
- The text: It is very important that you read the text and reread the text and raise questions about the text with me and others until you understand it. We are aiming for a deeper level of understanding than in a lower level course and we are trying to learn to communicate that understanding. You should emulate the text in your mathematical writing.
- The Math Lab: We all know the Math Lab rocks! It's open long hours and is located right across the hall from my office. You will be welcome there and will definitely find people to talk to about mathematics. The Math Lab is also available now through a Moodle forum. Just log onto Moodle and look for the course titled "Math Lab Forum for all Math and Stat Students" to meet with your favorite Math Lab tutors!

Your rights and responsibilities

It's worth understanding your rights and responsibilities as a student at UNCA. One of my responsibilities is to make sure you have the information that you need to do that. Since this is common to all classes, I've got that information on this legalese document.