Patrick (patrickwonders) wrote in math_class,

  • Mood:

NumberTheory101 (#0): Introduction

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.

Links to all of the classes

  1. (#1): Modular Arithmetic and answers
  2. Euclidean Algorithm and answers
  • Post a new comment


    default userpic

    Your IP address will be recorded 

    When you submit the form an invisible reCAPTCHA check will be performed.
    You must follow the Privacy Policy and Google Terms of use.