Advanced Number Theory
Prerequisites: MATH 201.
This course will cover Pythagorean triples, problems related to Fermat's Last Theorem, Pell's equation, Fermat's method of descent, primes in arithmetic progressions, Mersenne primes, perfect numbers, primitive roots, primality testing, Carmichael numbers, RSA public key encryption, quadratic residues, and quadratic reciprocity. Additional topics will be covered as time permits.
Outcomes: Students will be able to solve important practical and theoretical number theory problems; Students will be exposed to both significant recently solved number theory problems and currently unsolved conjectures.
This course will cover Pythagorean triples, problems related to Fermat's Last Theorem, Pell's equation, Fermat's method of descent, primes in arithmetic progressions, Mersenne primes, perfect numbers, primitive roots, primality testing, Carmichael numbers, RSA public key encryption, quadratic residues, and quadratic reciprocity. Additional topics will be covered as time permits.
Outcomes: Students will be able to solve important practical and theoretical number theory problems; Students will be exposed to both significant recently solved number theory problems and currently unsolved conjectures.