MATH 671

Number Theory

3 Graduate credits
Effective May 2, 2018 – December 18, 2018

Graduation requirements this course fulfills

This course covers divisibility; congruences and residues, including the Chinese Remainder Theorem; primes and their distribution; the Euler-phi function; quadratic reciprocity; public-key cryptography, particularly the RSA cryptosystem; elliptic curves and their group structure.

Prerequisites

Learning outcomes

General

  • Understand the importance of prime numbers.
  • Analyze the algebraic and arithmetical structure of a group of finite residues of a given prime number.
  • Solve some diophantine equations.
  • Generate a public-key cryptosystem.
  • Find rational points in an elliptic curve.