Syllabus for Linear Algebra
Professor: Mark McClure
Course purpose
From the perspective of calculus, the linear functions are about the simplest imaginable; they are literally the functions of the form \(f(x)=mx\), where \(f:\mathbb R \to \mathbb R\). In the more advanced study of linear algebra, however, we focus on functions mapping \(\mathbb R^n \to \mathbb R^m\) or, more generally from one vector space to another. While the motivation for moving to higher dimensions like this is mostly application, the subject also provides a nice opportunity to carefully study the power of abstraction.
In this class we will:
- Begin with applied systems of equations,
- express those systems using the algebra of matrices,
- generalize that work to encompass abstract vector spaces, and
- bring that all back to the concrete geometrical realm.
NSF Grant #1821509
I personally have long been an advocate for the use of open education resources. Thus, I have volunteered to take part in a research study that seeks to investigate how teachers and students use open textbooks and software. I decided to participate in this particular study because developers need information from users to improve the use of open educatial resources in the teaching and learning of mathematics. As students in my class, you can volunteer to participate as well by:
- Completing an online student survey (textbook use, perceptions of learning, attitudes towards technology, demographics and background information)—about 45 minutes
- Taking a math test at the beginning and at the end of the term — about 30 minutes each.
- Completing a bi-weekly log recounting how you use course textbook both inside and outside of the classroom—about 20 minutes per log—for the duration of the course, for a total of 100 minutes
Most of these activities will be required as part of the class anyway. Of course, it's very useful to have student participants so we can learn what works and what does not with the textbook. I will distribute forms that have more details on the project, your rights as research participants, and contact information of the investigators if you have more questions. You can also read more about the grant on its NSF webpage.
Materials
- Text: We will use A First Course in Linear Algebra by Rob Beezer. This is an open text made freely available through a specialized license. You may download a PDF for free or purchase a hard copy online for about $35.
- Technology:
- Calculators: We won't be using calculators and they will not be permitted on quizzes or exams.
- Sage: We'll make occasional use of Sage to perform computations with large systems. The easiest way to access Sage is via the online Sage Cell Server.
- LaTeX: I'll expect you to type up a few HW assignments using LaTeX. I recommend:
- Our online forum : I've set up an online forum Linear Talk where we can discuss all kinds of aspects of linear algebra.
- Online HW: We'll be using the freely available MyOpenMath system for online HW.
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: There will be two exams during
the semester worth about 100 points apiece. Likely dates for the exams are:
- Wednesday, October 2 or Thursday, October 3
- Wednesday, November 13 or Thursday, November 14
- Quizzes: There will be two quizzes -
each, three weeks ahead of an exam:
- Wednesday, September 11 or Thursday, September 12
- Wednesday, October 23 or Thursday, October 24
-
Knowledge Assessments:
All students will take knowledge assessments motivated by the grant. They will be required of everyone in the course but will be essentially stress-free. You will earn 20 points for doing each of these. The dates of these are:
- Tuesday, September 3 or Wednesday, September 4 and
- Tuesday, November 20 or November, 21
- Final exam: There will be a comprehensive, final exam worth around 180 points at 11:30 AM on Monday, December 10.
- Homework: There will be several
types of homework:
- Daily textbook assignments: I'll typically assign problems 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.
- Online HW: We'll use the freely available MyOpenMath system for online HW, when the problems are purely computational.
- Typed up HW: Several times during the term (perhaps 3 to 5 times), I'll ask you to type up your solution to a textbook problem for 10 to 20 points.
- 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.
- Late work: In general, I don't accept late work.
- Cheating: I don't deal with cheating. If I suspect cheating strongly enough, I simply refer you to the provost and fail you for the class.
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: 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.
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.