Theory of Numbers

(1-5 Credit Hours) · Undergraduate

Number theory is one of the oldest parts of mathematics. The aim of this course is to introduce students to some classical and important basic ideas of the subject including the following: The ring of integers; congruences; rings of integers modulo ; the Chinese Remainder Theorem; Wilson's Theorem; Fermat's Little Theorem for prime modulus; Euler's generalization of Fermat's Little Theorem to arbitrary modulus; primitiveroots; quadratic residues modulo primes; quadratic reciprocity; factorisation of large integers; basic version of the RSA encryption method. AS - St Andrews, Scotland: This course introduces topics in number theory, including prime numbers, modular arithmetic, continued fractions, Pell's equation, Gaussian integers, and applications to cryptography. It also covers areas of more advanced math, such as quadratic residues and primitive roots, applying these ideas to the analysis of well-known equations and theorems. The course also explores how number theory connects to other areas of math, such as abstract algebra and cryptography.