Lecture 1: The Integers, Modular Arithmetic, and the Euclidean Algorithm

Date:  Jan. 5

Background Material and Further Resources

Reading

Topics

  1. Integers Z
  2. Modular arithmetic Z_n
  3. Rings and Fields (division and units)
  4. Integral domains and zero divisors (A finite integral domain is a field)
  5. Ideals and quotient rings
  6. Factorization and Unique Factorization Domains
  7. Greatest Common Divisors and the Euclidean algorithm
  8. Extended Euclidean algorithm
  9. Computing inverses in Z_n using the extended Euclidean algorithm
  10. Computing time analysis

Assignment

The assignment description contains a summary of the material introduced in this lecture.
Created: Jan. 5, 2000 (revised Jan. 12) by jjohnson@mcs.drexel.edu