MAT 448E - Number Theory

Course Objectives

1. To provide an introduction to the study of properties of integers.
2. To prepare students to graduate-level courses in number theory and
algebra.
3. To demonstrate applications of number theory (such as public-key
cryptography).

Course Description

Divisibility, Euclidean algorithm, prime numbers, congruances, Chinese remainder theorem, Fermat’s
little theorem, Euler’s theorem primitive roots, congruances with prime-power moduli, Binomial theorem,
algebraic integers, quadratic residues, quadratic reciprocity, Jakobi and Legendre symbols, Euler’s
function, Möbius inversion formula, multiplicative functions, Continued fractions, rational approximation,
Diophantine equations, Pell’s equation.