Frequency:
Fall
Student Body:
Math majors and graduate students in related areas
Background and Goals:
This course is an undergraduate introduction to number theory.
Alternatives:
N/A
Subsequent Courses:
N/A
Course Content:
- Divisibility, the Euclidean algorithm and the GCD, linear Diophantine equations, prime numbers and uniqueness of factorization.
- Congruences, Chinese remainder theorem, Fermat's "little" theorem, Wilson's theorem, Euler's theorem and totient function, the RSA cryptosystem.
- Number-theoretic functions, multiplicative functions, Mobius inversion.
- Primitive roots and indices.
- Quadratic reciprocity and the Legendre symbol.
- Perfect numbers, Mersenne primes, Fermat primes.
- Pythagorean triples, Fermat's "last" theorem with proofs of special cases.
- Fibonacci numbers.
- Continued fractions.
- Distribution of primes, discussion of prime number theorem.
- Primality testing and factoring algorithms.
credits:
3 (N-A)
semester:
Fall
prereqs:
MATH 320, 340, 341 or 375 or graduate or professional standing or member of the Pre-Masters Mathematics (Visiting International) Program