MATHEMATICS 251: Number Theory
Block 3, 2005-2006
Marlow Anderson, TSC 206B, Ext 6543
Stefan Erickson, TSC 206A, Ext 6537
This course is designed to accomplish two goals.
First, it will provide you with an introduction to the
beautiful and useful mathematical theory behind the elementary arithmetic of
whole numbers (integers). Gauss
called mathematics the “queen of the sciences”, and in turn number
theory the “queen of mathematics”.
We will encounter prime numbers, cryptography, Pythagorean triples,
and Fermat’s Last Theorem!
Second, this course is an introduction to the more theoretical courses you will encounter in the junior and senior years in the mathematics major. There will be considerable emphasis on reading and writing formal proofs of mathematical statements. A proof is just a convincing argument from previously known facts. We will pay considerable attention to what constitutes an adequate proof, and what makes a well-written proof
Our
text is Elementary Number Theory, Fifth Edition, by David M.
Burton.
Here is our daily schedule for the block! The version we handed out is a pdf file.
Here are our grading and Honor Code Policies.
Here are the graded hand-in homework assignments for the block. In addition, there are homework problems you should work on collaboratively, and be prepared to discuss in class.
You will be doing an Independent Project in this course, on an additional topic in Number Theory. The pictures from lunch when we listened to the projects are here.
Websites you should check out:
Lots of information about prime numbers.
Interview with Andrew Wiles about Fermat's Last Theorem.
Some history on Fermat's Last Theorem.
Some information about the famous unproved Goldbach Conjecture.
How to get rich: solve one of the millennium problems, and the Clay Institute pays you $1,000,000.
The Six Degrees of Separation idea in mathematics: Erdos numbers.
A nice site for the history of mathematics.