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MATH 671 Number Theory

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

Special information

Note: Graduate status required.
18 Credit Credentialing Pathways
3 Graduate credits

Effective May 2, 2018 to present

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.
  • Analyze and create proofs of fundamental results in number theory at the graduate level.