AcademicsLinear Algebra Workshop

Instructor: Matt Ollis, Sci 218, matt@marlboro.edu

Timetable: TuF 1:30 - 2:50

Course Outline: In this course we take the study of linear algebra in two directions. First, we we take the theoretical study of eigenvalues and eigenvectors further, culminating in the result that every square matrix is similar to a matrix in Jordan Canonical Form. Second, we look at some of the many applications of linear algebra---possibilities include Fourier series, error-correcting codes and numerical techniques. A significant proportion of the course will be guided individual or small-group study, allowing you to control to some extent the ratio between applied and theoretical work. We'll also learn to use Mathematica to handle some of the repetitive calculutions.

During the first three weeks, whilst we work towards the Jordan Canonical Form, we will also plan the rest of the semester. Much will depend on your interests. All that is fixed at the moment is that at least one major applied topic will be covered as a class. Other than that, we will talk about possible directions and how they fit with your needs and interests. We will then work either as a class or in smaller groups (or some combination) as appropriate.

Credits and Grades: The flexibility of the course is reflected in the range of credit you can choose to earn. There are a couple of caveats though. You should think of the default choice as being 4 credits. Even if you choose to take just 2 or 3, you must be prepared to work at 4-credit pace for parts of the semester (the first three weeks in particular). Of course, this will be balanced by working at a lesser pace at other times. On the other hand you may choose 5 or 6 credits. Bear in mind that a 6-credit course is a lot of work.

Exact criteria for grading will be decided with each student individually. However, you can expect a final take-home exam which covers at least the initial theoretical work, the major applied topic which we cover in class and any other work which we do as a whole class. There will also be regular homework assignments and in-class quizzes. If it turns out that we split into several small groups to pursue different topics, then you will be asked to give a short presentation on your topic to the rest of the class.

Prompt submission of homework and class attendance and participation are expected. Your overall grade may be affected by upto one letter grade by these factors.

Texts: The initial text will be Jim Hefferon's free online book Linear Algebra. Which texts are used after this will depend on our choice of topics.