Number Theory

This course introduces basic number theory - a topic that epitomizes the beauty and elegance of pure mathematics. Modern applications of number theory are also introduced. Review of modular arithmetic. Chinese remainder theorem. Fermat's little theorem, Wilson's theorem. Number-theoretic functions: T,O, Euler's -function, Mobius inversion formula. Applications to cryptography. Primitive roots, indices.

Legendre's symbols, quadratic reciprocity law. Continued fractions, Pell's equations.

Primality tests and factorization of integers, RSA cryptosystem.