The goals of the course are to become proficient explorers of number theory, including understanding and recreating its principal:

  • definitions
  • theorems
  • algorithms
  • paradigms
  • methods
  • proofs

as applied to the following topics:

  • the Euclidean algorithm
  • the factorization of integers and the distribution of primes
  • modular arithmetic and the tool of looking at a problem from the perspective of just one prime at a time
  • generalizations of the ring of integers: other number rings
  • the study of integral solutions to equations, particularly quadratic forms

The goals of this course, as all my undergraduate courses, include, to become proficient in the culture and practice of theoretical mathematical thinking, specifically to:

  • understand written mathematics
  • communicate mathematics
  • study mathematics effectively in an independent way
  • distinguish logical correctness and error
  • cultivate mathematical creativity
  • synthesize and use novel definitions
  • create novel proofs

and, I hope, to have fun in the process.