Week 1 task 2: Review a few linear and abstract algebra techniques to prepare for work in class.

The goal of these tasks is to review some things that we are going to use next week.  I have provided links to some resources I've found by looking online.  Please let me know when you find something that doesn't make sense--I can create alternate resources if these aren't making sense. 

For most of these review topics, I have found both a video and a text-based web site that you could use as a resource.  Many of these topics are also explained on Khan Academy, and that's a find source if you prefer it.  Almost all of these topics are also discussed in either the Abstract Algebra or the Linear Algebra book you have as a reference. You do not have to look at all of these references: if you find one source that makes sense to you, there's no need to look at the others too.

For most of these review topics, I have provided a practice problem for you.  If you understand the part of the video or textbook that explains how to solve that practice problem, then you have understood the thing I wanted you to review.

While I want you to do some reviewing so we can jump into things a little more quickly next week, I want this week to be a lighter work-load than the on-campus weeks.  Let me know if the review is taking you more than 4 hours, and if you get stuck on anything (the resources here aren't helping) also let me know so I can either provide better resources or adjust the assignment.

Review topic
 Video
 Web page
 Relevant textbook
 Other notes
Definition of a group
 Defn of group (Socratica)
Abstract Algebra
 We'll review this in class too, so just watch the video or spend a few minutes reading in the textbook.
Dihedral group
 Dihedral group (Socratica)
Abstract Algebra
 Also something I don't expect you to know all the details of before we discuss it in class
Solve a system equations by Gauss-Jordan Elimination
 Gaussian Elimination ...
Linear Algebra
 Do practice problem 1 and bring to class next Monday
Find the determinant of a 2x2, 3x3, 4x4 (and 5x5) matrix, using expansion for the 4x4 (and 5x5) cases 3x3 case
4x4 case
 A short review
Another option
 Linear Algebra
 Do practice problem 2 and bring to class next Monday
Write complex numbers in exponential form. Multiply complex numbers in exponential form
 exponential form
(includes where this form comes from)
 Exponential form
Just the formulas
 Abstract Algebra
 This is really similar to polar form for complex numbers. It would be great if you could get to the point where the exponential form makes sense to you.
Add, subtract, multiply and divide complex numbers
 add, subtract, multiply, and divide add, subtract, multiply, and divide. ??
 I'm hoping you mostly know this already--I would look for this in a college algebra or pre-calculus book.

Practice problems: Word document, .pdf document