Advanced Topics in Number Theory
Prerequisites: MATH 201 or the equivalent or permission of the instructor.
Topics chosen from: Pythagorean triples, Fermat's Last Theorem, Pell's equation, Fermat descent, primes in arithmetic progressions, Mersenne primes, perfect numbers, primitive roots, primality testing, Carmichael numbers, RSA encryption, quadratic residues, quadratic reciprocity, integers as the sum of squares, Gaussian integers, continued fractions, the distribution of primes, Diophantine approximation, elliptic curves; others.
Outcomes: Understand the importance of historically significant concepts and problems in number theory; Understand the proofs of related theorems; Solve problems and prove theorems from topics covered in class.
Topics chosen from: Pythagorean triples, Fermat's Last Theorem, Pell's equation, Fermat descent, primes in arithmetic progressions, Mersenne primes, perfect numbers, primitive roots, primality testing, Carmichael numbers, RSA encryption, quadratic residues, quadratic reciprocity, integers as the sum of squares, Gaussian integers, continued fractions, the distribution of primes, Diophantine approximation, elliptic curves; others.
Outcomes: Understand the importance of historically significant concepts and problems in number theory; Understand the proofs of related theorems; Solve problems and prove theorems from topics covered in class.