Welcome to the course web page for the Spring 2011 manifestation of MA4220: Number Theory at Plymouth State University.
What is this course all about?
Number theory is the study of integers under the operations of multiplication and addition. Though this seems a humble beginning, it is surprising how quickly one can ask mathematical questions about integers which are exceedingly difficult to resolve. Indeed, there are numerous problems which are thousands of years old that have yet to be resolved, as well as many other ancient problems which have only been resolved due to very sophisticated mathematics. It is this contrast between simplicity and complexity which forms the aesthetic of many number theoretic problems. In this class we’ll develop some basic tools which allow us to begin analyzing the structures which govern the integers.
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 1 of 3.
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 will be new to many of you and there may be some growing pains associated with it.
For more details, see the syllabus.
This semester we will be using the book Number Theory Through Inquiry by Marshall, Odell, and Starbird (ISBN: 978-0-88385-751-9). I expect you to be reading the textbook. I will not be covering every detail of the textbook 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 material in the textbook 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 on our Moodle page.
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 .