Welcome to the course web page for the Fall 2011 manifestation of MA4140: Abstract Algebra at Plymouth State University.
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. We will spend most of our time studying groups. Group theory is the study of symmetry, and is one of the most beautiful areas in all of mathematics. It arises in puzzles, visual arts, music, nature, the physical and life sciences, computer science, cryptography, and of course, throughout mathematics. This course will cover the basic concepts of group theory, and a special effort will be made to emphasize the intuition behind the concepts and motivate the subject matter.
In order to promote a more active participation in your learning, we will incorporate ideas from an educational philosophy called the Moore method (after R.L. Moore). Modifications of the Moore method are also referred to as inquiry-based learning (IBL) or discovery-based learning.
Here is a great video about inquiry-based learning in mathematics. The video is part one of three and the other two parts are worth watching.
Much of the course will be devoted to students proving theorems on the board and a significant portion of your grade will be determined by how much mathematics you produce. I use the work "produce" because I believe that the best way to learn mathematics is by doing mathematics. Someone cannot master a musical instrument or a martial art by simply watching, and in a similar fashion, you cannot master mathematics by simply watching; you must do mathematics!
Furthermore, it is important to understand that proving theorems is difficult and takes time. You shouldn't expect to complete a single proof in 10 minutes. Sometimes, you might have to stare at the statement for an hour before even understanding how to get started. In fact, proving theorems can be a lot like the clip from the Big Bang Theory located here.
In this course, everyone will be required to
- read and interact with course notes on your own;
- write up quality proofs to assigned problems;
- present proofs on the board to the rest of the class;
- participate in discussions centered around a student's presented proof;
- call upon your own prodigious mental faculties to respond in flexible, thoughtful, and creative ways to problems that may seem unfamiliar on first glance.
As the semester progresses, it should become clear to you what the expectations are. This may be new to many of you and there may be some growing pains associated with it.
For more details, see the syllabus.
We will not be using a textbook this semester, but rather a theorem-sequence adopted for inquiry-based learning (IBL) and the Moore method for teaching mathematics. The theorem-sequence that we will be using is written by David M. Clark (SUNY New Paltz) and are titled Theory of Groups. The notes are available for free from Journal of Inquiry-Based Learning in Mathematics. You can obtain the 39 page PDF of the notes by going here. Note: The previous link takes you to the "instructor version" of the notes. The only difference is the "To the instructor" section, which you can safely ignore. Also, we will not cover Chapter 8, so please don't print those pages.
In addition to working the problems in the notes, I expect you to be reading them. We will not be discussing every detail of the notes and the only way to achieve a sufficient understanding of the material is to be digesting the reading in a meaningful way. You should be seeking clarification about the content of the notes whenever necessary by asking questions in class or posting questions to the course forum.
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 forum on our Moodle page, as I will post comments there for all to benefit from.
To effectively post to the course forum, 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 $\LaTeX$. If you need additional help with $\LaTeX$, post a question in the course forum.
You can also visit the Math Activity Center, which is located in Hyde 351. This student-run organization provides peer tutoring services for most 1000 and 2000 level math courses and some 3000 level courses. Tutors are typically math majors interested in teaching math and practicing their instructional skills. You can drop in anytime during open hours.
Lastly, you can always.