Algebraic Structures


Welcome to the course wiki for the Spring 2010 manifestation of MA4140: Algebraic Structures at Plymouth State University. This wiki is viewable by anyone, but content can only be added and edited by authorized users, which basically means students registered in the class.

In the Web2.0 world, more and more of reading, writing, and communicating mathematics occurs online. A major component of the course will be the course wiki at, which will provide an opportunity for you (as students) to collaborate together, and for me (the instructor) to provide feedback visible to all.

What is a wiki, you ask? According to Wikipedia, the world's largest wiki site:

A Wiki ([ˈwiː.kiː] <wee-kee> or [ˈwɪ.kiː] <wick-ey>) is a type of website that allows users to add, remove, or otherwise edit and change most content very quickly and easily.[1]

As a part of the network, this site is a customizable piece of the internet where users can edit content, upload files, communicate and collaborate.

During the semester, you will use the wiki to:

  1. Ask questions of your Professor and fellow students and post responses to these questions.
  2. Collaboratively post content to chapter summaries consisting of definitions, theorems, and standard examples for use on the in-class portion of exams.
  3. Post group projects.

Part of your grade will be based on your participation in the online wiki. I will be able to see what contributions you have made to the site, and grade you accordingly. For more information, see the course syllabus.

getting started

During the first week of classes, I will send you an invite to join the wiki. To join, you will need to sign up for a free Wikidot account. Please use your real name when signing up. (As a Wikidot member, you can create your own free wiki or web page.) Once you are signed up, your first task is to create a user profile. For more information, go here.

what is this course all about?

This course is an introduction to abstract algebra. Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras [2]. For more information, see the Wikipedia article located here. We will spend most of our time studying groups, but we will have an opportunity to explore additional topics in your group projects. We will take an axiomatic approach (definition, theorem, and proof) to the subject, but along the way, you will develop intuition about the objects of abstract algebra, pick up more proof-writing skills, and skills that enable you to better read, understand, and communicate mathematics. We will also discuss how the field of abstract algebra fits into the broader "picture" of mathematics and take a look at some applications. The emphasis of this course is on your ability to read, understand, and communicate mathematics in the context of abstract algebra.

getting help

There are many resources available to get help. First, I recommend that you work on homework in groups as much as possible, and to come see me whenever necessary. Also, you are strongly encouraged to ask questions in the course forums, as I will post answers there for all to benefit from.

Notice that there is a help menu located at the top of the page and in the sidebar on the left. Of particular interest will be the useful tips page, which you are welcome to add to (anyone can edit this page).

To effectively post to the forum or add entries to the chapter summaries, you will need to learn the basics of LaTeX, the standard language for typesetting in the mathematics community. See the quick LaTeX guide for help with $\LaTeX$ or click on the how do I typeset mathematics? link in the help menu. If you need additional help with $\LaTeX$ or editing/posting content in the wiki, post a question in the forum.

There are substantial resources available online to help you learn the Wikidot markup, which is quite simple. I regularly consult Wikidot's Wiki Syntax page and Wikidot's Quick Reference Guide.

Lastly, you can always contact me.

credit & license

Many of the ideas and some of the content for this wiki was inspired by Elisha Peterson's wiki and his Real Analysis course wiki, as well as Andy Schultz's Number Theory course wiki.

All of the work contained in this site is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License