Collections of Lectures
Number Theory 101
#1 (Modular Arithmetic)
#2 (Euclidean Algorithm)
#3 (Chinese Remainder Theorem)
#4 (Fundamental Theorem of Arithmetic)

math_class: Number Theory 101 (Introduction)

link to LiveJournal thread

How is this going to go?

My name is Patrick (patrickwonders on LiveJournal). I've tutored many folks one-on-one and I've written a few articles on PlanetMath. This, however, is my first foray into lecturing (on math) to a group of people that I don't already know pretty well. So, make it to bring to my attention anything that I pass over too lightly or beat into the ground.

I'm going to shoot for a new lecture every Thursday evening (GMT). Some of the lectures will be longer than others depending upon the depth of the material being discussed. I will give problems for people to practice with when appropriate. I'll post the solutions to the problems on Monday evening (GMT). On LiveJournal, I will keep the body of the lessons and all problem solutions behind <lj-cut> tags.

What are we going to learn?

I'm going to work mostly out of two books called Elementary Number Theory---one by Burton, the other by Jones and Jones. I will probably follow along through the topics of Burton spritzing in other stuff in appropriate places. I will keep a running bibliography here:

  • Burton, David M. Elementary Number Theory: Fifth Edition. McGraw-Hill Higher Education, Boston, 2002. ISBN 0-072-32569-0.
  • Jones, Gareth A. and J. Mary Jones. Elementary Number Theory. Springer-Verlag, London, 1998. ISBN 3-540-76197-7.
  • Singh, Simon. Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. Walker and Company, New York, 1997. ISBN 0-802-71331-9.

You will not need any particular textbook for this class.

I'm more than willing to take requests. But, at the very least, I hope to cover divisibility in the integers, the Fundamental Theorem of Arithmetic, Fermat's Little Theorem, RSA Encryption, a survey of Prime Factorization methods, an intro to the Discrete Logarithm problem, continued fractions, partitions, the Riemann Zeta Function, and some information about Fermat's Last Theorem. I plan on liberally sprinkling the lectures with mentions of unsolved problems in Number Theory.